BEER FOAM PHYSICS
CENTRALE LANDBOUWCATALOGUS
0000 0359 1142
Promotor: Prof. Dr. A. Prins
hoogleraar indefysicaendefysischechemievanlevensmiddelen,
met bijzondere aandacht voor dezuivel.
,ON>0?2O\
\3tt-
A.D. Ronteltap
BEER FOAM PHYSICS
Proefschrift
ter verkrijging van de graad van
doctor in de landbouwwetenschappen,
op gezag van de rector magnificus,
dr. H.C. van der Plas,
in het openbaar te verdedigen
op vrijdag 1 december 1989
des namiddags te vier uur in de aula
BIHLIÜTHEEK
van de Landbouwuniversiteit te Wageningen
LANDBOUWUNIVERSITEIT,
WAOUNINCEN
&ti fk> ^1
pv3o??JD« j \t>VLt
1. Stikstofgaskaninbierschuimdekwaliteitzowelverbeteren
alsverslechteren.
Dit proefschrift
2. De door Hartong uitgevoerde proef met éénwel en één niet
afgedekt bierglas is een goede proef om te laten zien
waardoor bierschuim inzakt. Zijn verklaring, dat in een
afgedektbierglasverdamping endaarmeecoalescentie wordt
voorkomen,zoueengoedeverklaringkunnenzijn,maarhetis
nietdejuiste.
Vancraenenbroeck, R., Cerevisia 4:191 (1982).
3. Hetisonjuistaantenemendatdebellengrootteverdelingin
debovenstebellenlaagvanbierschuimrepresentatiefisvoor
debellengrootteverdeling inhetgeheleschuim.
Clenister, P.R., Segel, E., Koeppl, D.C., ASBC Proc. pp. 150 (1966).
4. Een hoge oppervlakte dilatatie of shear viscositeit werkt
nietperdefinitiestabiliserendopschuim.
Barbeau, W.E., Kinsella, J.E., Colloids and Surfaces. 17:169 (1986).
5. "Bubbleghosts"zijndissipatievestructuren.
Prigogine, I., Stengers, I., "Orde uit Chaos." Ed: Uitgeverij Bert Bakker, Amsterdam. (1988).
6. Menverwachtdatdeproduktiv!teitpermanuuralsgevolgvan
automatiseringtoeneemt,terwijlmenvergeetdateenmanuur
tijdenshetautomatiserenvaakweinigproduktiefis.
7. Deindepraktijkvaakgehanteerdemethodeomdegevoeligheid
voor oproming van emulsies te voorspellen door middel van
centrifugerenkanmakkelijktotverkeerdeconclusiesleiden.
Pearce,K.N.,Kinsella,J.E.,J.Agric.Food Chem.26(3):716(1978).
8. De stelling, dat natuurkundigen zich niet zouden mogen
bezighoudenmetde"FundamenteleVragen",isreductionistisch
vanaard.
Lagendijk, A., "De arrogantie van de fysicus." Intermediair 38:17 (1989).
Stellingen bij het proefschrift "Beer Foam Physics" door A.D. Ronteltap, 1 december 1989 te Wageningen.
9. Het terugdringen van de CO,-ultstoot in Nederland met
jaarlijks2%zaleeninvloedophetbroeikaseffecthebbendie
in omvang ongeveer gelijk is aan de invloed op de
inzaksnelheid vanbierschuim.
/10.Het is onjuist te veronderstellen dat aan alcoholgebruik
slechts negatieve aspecten zijn verbonden voor de
volksgezondheid.
Stampfer, M.J., Colditz, CA., Willett, W.C., Speizer, F.E., Hennekens, C.H., N. Engl. J. Med.
319:267 (1988).
11.Het feit dat vandalisme als noodzakelijk kwaad wordt
geaccepteerd brengt de oplossing van dit probleem niet
naderbij.
12. "Vergrijzen"iseenongelukkigetermomhetouderwordenvan
mensenaantegeven.
13.Bijmooiweerishetschuimgedragvanbiervanminderbelang.
Stellingen bij het proefschrift"Beer FoamPhysics"doorA.D. Ronteltap,1december 1989teWageningen.
VoorMariëlle
ABSTRACT
Ronteltap,A.D.,(1989).Beerfoamphysics.Ph.D.thesis.
AgriculturalUniversity,Wageningen,(pp.133,Englishand
Dutchsummaries).
Keywords:
beer foam, bubble formation, drainage, coalescence,
disproportionation, bubble-size distribution, surface
rheology.
Abstract:
Thephysicalaspectsofbeerfoambehaviorwerestudied
intermsofthefourphysicalprocesses,mainlyinvolved
inthe formation and breakdown of foam. These processes
are, bubble formation, drainage, disproportionation and
coalescence.Indetail,theprocesses disproportionation
andcoalescencewerestudied.Themechanismofcoalescence
was determined using, amongst others, a falling film
apparatus.Thespreadingofsurfaceactivematerialonthe
film surface proved to initiate coalescence.Disproportionation ina foam ismainly influenced bypartial gas
pressuredifferences.Surfacerheologicalaspectsdominate
the rate of disproportionation when thegas composition
throughout a foam is uniform. The effect of the four
physical processes on various foam phenomena can be
explained.Thedisappearanceofbeerfoamisaresultof
thecombinedactionofdrainageandgasdiffusionfromthe
foam to the surrounding atmosphere.When spreading substances areadded tobeer foam from anexternalsource,
coalescence is initiated and foam collapse occurs. The
four physical processeshave adifferent effect on foam
behavior.Therefore,adistinctionbetweentheseprocesses
was made using an optical glass-fibre probe technique.
Withthistechniquethebubble-sizedistribution,thegas
fractioninthefoam,theheightofthefoamandthelevel
ofthefoam-liquidinterfacecanbemeasuredasafunction
oftime.
PREFACE
Thisthesisisnottheworkofasingleperson.Itcould
neverhavebeenwrittenifIwouldnothavebeenhelpedby
somanypeople.Itisnotpossibletomentionallofthem
here, and to thank each of them in person. However, I
would like to express my gratitude to several contributors.
The research work on beer foam, described in this
thesis,would notevenhavestarted ifGert JanMutsof
HeinekenTechnischBeheerB.V.hadnotinitiated itwith
suchenthusiasm.ThecollaborationbetweenhimandprofessorA.Prinshasbeenagreatinspiration.AfterGertJan
Mutswas transferred toanother jobwithin thecompany,
Mar
jaHollemansreplacedhim,guidingtheresearchonbeer
foam into the right direction. Time after time, she
succeeded tobridgethedistancebetweenthefundamental
view,prevailingattheuniversityofWageningen,andthe
general,practicalapproachatthebreweryinZoeterwoude.
Hercontributionhasbeenofimmensevalue.
ThefatherlycoachingofprofessorA.Prinsduringthe
entireperiodofthisresearchworkhasbeenatremendous
learning experience. Thepatient way heteaches hisPhD
studentsmakesitadaytodayjoytoworkwithhim.His
original research approach, his vivid flexibility and
reassuring attitude hasnever failed tobe acontinuing
encouragement.
Inthisthesisresultsarepresented acquired byJacco
Wijkmans, Ellen de Jong, Adriaan Garritsen and Bart
Schultewho,asstudents,helpedmetocarryoutsomeof
theexperiments.IthankeachofthemfortheircontributionandhopethattheyhavelearnedasmuchfrommeasI
learnedfromthem.Inaddition,ChrisBisperinkcontributedtotheexperimentalworkpresentedhere.Hissupport
inthelaboratoryhasbeenagreathelpandIhopethathe
willsucceedtounravelmoreofthephysicalmysteriesof
beerfoamwithinthenearfuture.
I would also liketoexpressmythankstoBartDamsté
andMaarten deGeeof theMathematics department of the
AgriculturalUniversity,Wageningen,whowith dedication
spentmanyhourstohelpmetodevelopanumericalmodel
thatdescribesthetransportofgas.
Thedevelopmentofanewmethodtodeterminebubble-size
distributionsinfoamwouldnothavebeenpossiblewithout
thespontaneoushelpofJacobJanFrijlinkandPetervan
Halderenwhomadeavailabletheirtimeandtheirknowledge
of the optical glass-fibre technique. I would like to
thank Jan Daniël Houthuijsen and Ton Erenst for their
contributiontothecomplexautomationoftheapparatus.
ThescientificdiscussionsIhadwithmycolleaguesHans
Westerbeek, Karin Boode and Coen Akkerman have been an
inspiringchallengetomeeachtime.Theymadeasignificantcontributiontothecompletionofthisthesis.
I thank B.W. Drost of Heineken for his confidence in
thisbeer foam study and forhiswillingness tosupport
theHeinekenfinancialcontributionwholeheartedly.
The support of the LEB fonds,hasmade itpossibleto
distributethisthesisinanappropriateedition.
CONTENTS
page
1.OUTLINE OF THIS STUDY
1
2. BUBBLE FORMATION
2.1. Introduction
References
4
4
7
3.CREAMING AND DRAINAGE
3.1. Introduction
References
8
8
12
4. COALESCENCE
4.1. Introduction
4.2.Aim and Approach
4.3. Experimental
4.4.Results
4.5. Discussion
References
14
14
20
23
27
40
43
5.DISPROPORTIONATION
5.1. Introduction
5.2.Aim and Approach
5.3. Theory
5.4. Experimental
5.5.Results
5.6. Discussion
References
45
45
52
53
57
58
73
77
6. BEER FOAM PHENOMENA
6.1. Thecreaminess of the foam
6.2. The riseof the foam-liquid interface
6.3. The influence of temperature
6.4. Thecoarsening of the foam
6.5. Thecollapse of the foam
6.6. Cling
6.7. The influence of airentrapment
6.8. The influence ofchemical composition
References
7.BEER FOAM STABILITY
81
81
82
82
84
84
90
90
91
92
93
8 . MEASUREMENT OF FOAM BEHAVIOR
8.1. Introduction
8.2. Aim and Approach
8.3. Experimental
8.4. Results
8.5. Discussion
References
95
95
105
106
110
116
119
9 . CONCLUSIONS
122
LIST OF SYMBOLS
SUMMARY
SAMENVATTING
CURRICULUM VITAE
124
126
129
133
OUTLINEOFTHISSTUDY
The appearance is one of the most important quality
characteristicsofbeertotheconsumer.Itisbelievedto
beevenmore important thantaste,although thismaybe
disputed.Theappearanceofthebeerdependsmainlyonthe
behavior of the foam. It has become evident that the
qualityofthefoaminfluencestheoverallperceptionof
theconsumertoagreatextent.Therefore,thecontrolof
foambehaviorisessential.Forthatreason,anextensive
researchonthebehaviorofbeerfoamhasbeencarriedout
inthelastdecades,allovertheworld.
The approach has mostly been to analyze the chemical
components of beer, like proteins, metal ions and hop
constituents,andtotrytofindacorrelationwithafoam
number. These efforts have given an enormous amount of
experimental results, that are partly useful, but are
sometimesalsovery inconclusiveandconfusing.Thereis
a lot of contradiction in beer foam literature. The
researchworksofarhasnotsatisfactoryledtoabetter
controlofbeerfoambehavior.
Oneofthemainreasonsforthelackofinsightisthat
research has predominantly been concentrated on the
chemical aspectsof foam.Thebehavior of beer foamcan
not be explained with the knowledge of the chemical
composition alone. For example, the contribution of
surfaceactivecomponentstothebehaviorofthefoammay
be either negative or positive or both, depending on,
amongst others, their concentration, their interaction
withothercomponentsandtheirlocationinthefoam.Two
chemicalcomponents,eachhavingapositiveeffectonfoam
behavior,mayhaveanegativeeffectwhentheyaremixed
andviceversa.Inaddition,twofoams,thathaveexactly
thesamechemicalcomposition,maybehaveverydifferent.
Severalexamples of thelatterwill begiven inchapter
6.8.
At the beginning of this research work, the need was
expressed foranadditionalapproachinordertobeable
to fully understand beer foam behavior. The ultimate
objective was toacquire more fundamental,physical and
phenomenologicalknowledgeofbeerfoambehavior.Itwas
anticipatedthat,iffundamentalknowledgeaboutbeerfoam
could beobtained, theeffectof thecomposition onthe
behaviorofthefoamcouldbeexplained.Inotherwords,
theopiniondominated thatthegapbetween thechemical
compositionandthebehaviorofthefoamwastoolargeto
explain various phenomena. It was expected that more
fundamental and physical research could relate foam
behaviortothechemicalcompositionofbeerinabetter
way.
Thescopeofthisstudyhasbeentoexplainbeerfoam
behaviorintermsoffourphysicalprocessesthatmainly
determine foam formation and breakdown. They are (i)
bubbleformationandgrowth,(ii)creaminganddrainage,
(iii)coalescenceand (iv)disproportionation.Aneffort
hasbeenmadetodistinguishbetweentheseprocesses,to
discover the main physical process, and to find the
predominant parameters, that are involved in beer foam
behavior. Unfortunately, the behavior of foam does not
mainly depend on one single physical process.All four
processes,mentionedabove,areinvolved.Inaddition,the
processesareinterrelatedandtheirprogressdependsvery
muchontheprogressoftheotherprocesses.
Thefourphysicalprocessesarediscussed inchapter2
trough5andtheimportantparametersfortheprogressof
these processes are reviewed. Chapter 2 and 3, where
respectivelybubbleformationanddrainagearediscussed,
arereviewsofavailableliterature.Researchworkwasnot
carried out on these subjects. In chapter 4 and 5,the
resultsofresearchworkarealsoincluded.Inchapter4,
coalescenceisdiscussedindetail.Inparticular,coalescence, initiated by the spreading of surface active
material isconsidered. Inchapter 5,theeffect ofthe
gascompositioninthefoamandofthesurfacedilational
viscosityontherateofdisproportionationiselucidated.
Experimentalresultsofbubbledissolutionarecomparedto
model calculations. Inchapter 6, theappearance ofthe
foam and the occurrence of several phenomena, like the
creaminess of the foam, foam collapse and cling, are
explained in terms of the four physical processes. In
chapter7,adefinitionofthestabilityoffoampropertiesisgiven.Themeasurement of beer foam behavior is
discussedinchapter8,whereareviewisgivenofseveral
methodstomeasurefoamcharacteristics.Anewlydeveloped
apparatus todetermine foam characteristics bymeansof
themeasurement of thebubble-size distribution is also
presentedinthatchapter.Inchapter9,finalconclusions
on foam behavior are given. The influence of the four
physicalprocessesonbeerfoambehaviorisexplained.
2.BUBBLEFORMATION
2.1.Introduction
Althoughthebubbleformationprocessdoesnotseemto
influencefoambehavioratfirstsight,thisinfluenceis
quite pronounced. Very important factors for beer foam
behavior, like thegas composition,bubble size,bubble
surface composition and the structure of the foam, are
determinedduringthebubbleformationprocess.
Ingeneral,bubblescanbeproduced inaliquidby (i)
agitating orwhipping, (ii)byspargingordiffusinggas
through a porous material, and (iii)by decreasing the
pressure of a with gas saturated liquid. In the latter
case,theliquidbecomessupersaturatedasaresultofthe
pressurerelease.Consequently,bubblescannucleateand
grow.
Inbeer,bubblesmaybeformedbyairentrapmentduring
dispense.However,themostimportantmechanismforbubble
formation inbeer isnucleation,becausebeer issupersaturatedwithcarbondioxideafterpressurerelease.
A review on bubble nucleation was given by Blander
(1979).Heexplained thattwokindsofbubblenucleation
can be distinguished, viz. homogeneous nucleation and
heterogeneousnucleation.Asaresultofthecreationof
a new surface during bubble formation an energy barrier
hastobeovercome.Forhomogeneousnucleation,i.e.the
spontaneous formation of a bubble nucleus, the energy
barrierishighandthereforehomogeneousnucleationwill
onlyoccuratveryhighsupersaturationvalues.Thevalue
ofthesupersaturationpressurecanbeestimated,assuming
thattheLaplacepressureofaverysmallbubblemustbe
overcomeinthecourseofbubbleformation.Walstra(1989)
simply calculates that homogeneous nucleation does not
takeplaceunlessthesupersaturation isintheorderof
108Nm"2(supposingthattheminimumradiusforabubbleis
1 nm and the surface tension is 50mNm"1). For beer,a
pressureof thatvalue isquiteunrealistic. Thismeans
thatbubblesdonotoriginatespontaneously inbeer,but
thatheterogeneousnucleationoccurs.Bubblesgrowfroma
catalyticsiteinordertoovercometheenergybarrierfor
bubbleformation.Thissitemaybeforexampleacrackin
the wall of a container, or a gas pocket in dispersed
material.
Wardetal (1970)developed atheory forheterogeneous
bubble formation using ageneralized Kelvin equation to
describe the relation between the pressure at which
nucleationoccursandthegasconcentrationintheliquid.
Theyputforward theconceptofthecriticalradius.The
conceptisbasedonthefactthattheradiusofanucleus
must have at least a minimal, critical size to allow
bubble growth. If the radius of the nucleus is smaller
thanthatcriticalradiusthenucleusisunstableandwill
rapidly dissolve. The critical radius therefore is an
unstable equilibrium, threshold value. The concept was
extendedbyWardetal(1982)andconditionsforasecond
stablecriticalradiuswereformulated.Theothercritical
radius is largerthanthefirst,and isaresultofthe
factthattheconceptwasdevelopedforaconfinedvolume
of liquid. Ward et al (1983)described the growth of a
bubblefromaconicalpit.Inaddition,theemergenceof
abubbleisdiscussed inrelationtothewettingpropertiesof the liquid and theconicalpit.Ward and Levart
(1984)stated that a number of bubble nuclei may be in
stable equilibrium with the liquid if the value of the
supersaturation is low and the contact angle issmall.
Wardetal(1985)described theevolutionofabubbleto
afinalstableequilibriumsize.
More quantitative work on bubble nucleation was put
forward by Wilt (1986), who reported a model for the
homogeneousandheterogeneousnucleationratesofbubbles
in carbonated beverages. Confirmation is given that a
supersaturation ratio of carbonated beverages should at
least be a thousand fold in order to allow homogeneous
nucleation.Heestimatedthatthesupersaturationratioof
an opened carbonated beverage is about 5 and therefore
homogeneousnucleationisquiteimpossible.Heterogeneous
nucleation however is likely to occur indepressurized
carbonated beverages, depending on the contact angle
between the liquid and the nucleation site and on the
shapeofthissite.Hereported thatespeciallycavities
are good nucleation spots. The effect of the surface
tension on the nucleation growth rate is discussed.
Ciholas and Wilt (1988) extended this model for the
sphericalcavitycase.
The experimental measurement of the bubble nucleation
rateandoftheamountofbubblesformedperunitoftime
hasbeendifficult.Therefore,experimental confirmation
of nucleation theories has not been put forward until
recently. Lubetkin and Blackwell (1988) described an
acousticmethod,thatallowsthemeasurementofthebubble
nucleationrate.
Theinitialbubble-sizedistribution inafoamdepends
ontheconditionsduringbubbleformation.Heterogeneous
bubbleformationisschematizedinfigure1.1.
LIQ UID
LIQUID
LIQUID
(BUBBLE)
r T_ J lit
Figure 1.1: Heterogeneous bubble nucleation, growth and detachment The nucleation
site is wetted by the liquid.
Themomentofbubbledetachmentfromthenucleationsite
is if buoyancy (ApgV)becomes bigger than the adhesive
force (the vertical component of a*0), whereAp is the
density difference betweenthegasand the liquid,gis
gravity,Visthevolumeofthebubble,Oistheperimeter
ofthebubblewhereitisattachedtothenucleationsite
andaisthesurfacetension.Therefore,thebubblesize
ismainlydeterminedbythesurfacetensionatthemoment
of bubble detachment. The nucleation and growth of a
bubble goes very swift. The bubble surface is expanded
rapidly during thegrowthof thebubble.Therefore,the
increased surface tension under expansion conditions is
significant. The history of the bubble surface and the
surface dilational viscosity at given expansion rate
determine the surface tension. The expansion rate is,
amongstothers,determinedbythesupersaturationvalue.
Ifsmallbubblesaredesiredinafoamthedynamicsurface
tensionunderexpansionconditionsshouldbelow.
Anotherimportantfactorthatmayinfluencetheinitial
bubblesizeistangentialconvectionduringthedispense
of the beer. As a result of convection, the moment of
bubble detachment will be advanced. Consequently, the
bubbleswillremainsmaller.
References
Blander, M., Adv. in Colloid and Interface Sei. 10:1
(1979).
Ciholas,P.A., Wilt,P.M., J.ColloidandInterfaceSei.
123(1):296 (1988).
Lubetkin,S.,Blackwell,M.,J.ColloidandInterfaceSei.
26(2):610 (1988).
Walstra,P.,"PrinciplesofFoamFormationandStability."
In: Focus on Foams. Ed: A.J. Wilson, Wiley and sons.
(1989).Tobepublished.
Ward,C.A.,Balakrishnan,A.,Hooper,F.C.,J.BasicEng.
92:695 (1970).
Ward, C.A., Tikuisis, P., Venter, R.D., J. Appl. Phys.
53(9):6076 (1982).
Ward,C.A., Johnson,W.R.,Venter,R.D.,Ho,S.,Forest,
T.W.,Fraser,W.D.,J.Appl.Phys.54(4):1833 (1983).
Ward,C.A., Levart,E.,J.Appl.Phys.56(2):491(1984).
Ward, C.A., Yee, D., Tikuisis, P., J. Appl. Phys.
58(1):273 (1985).
Wilt, P.M., J. Colloid and Interface Sei. 112(2):530
(1986).
3.CREAMINGANDDRAINAGE
3.1.Introduction
Thecreaming ofbubbles istheriseof thebubblesto
thetopofthesystem.Drainageistheliquidflowfroma
foam to the liquid underneath. It is not well defined
where creaming stops and drainage begins. In fact,one
could argue that it is the same process because both
processes have many things in common. E.g. the main
driving force for both processes is gravity. One could
alsoarguethatcreamingbecomesdrainageassoonasthe
bubblesstarttointerfereandtoinfluenceeachotherin
theirmotion.
ThecreamingprocessmaybedescribedwithStokeslaw.
However, this law can only be applied if the bubble
surfaceisimmobileandtheReynoldsnumberislow.
Theeffectofthemobilityofthesurfacewasdiscussed
byVan 'tRietetal(1984).Asaresultofthetangential
shearonthesurfaceoftherisingbubble,thesurfaceis
expandedatthetoppolarendofthebubbleandcompressed
at the bottom of the bubble. Consequently, the surface
tensiongradient,thatisaresultofthesurfacedeformation, counteracts the shear. The surface reaches a
stationary-state and the surface becomes lessmobileor
even motionless. In the latter case, bubbles can be
regarded as solid particles, as far as the rise of the
bubbles is concerned. For beer this condition is most
likely met because sufficient surface active components
arepresent.
Theothercondition forStokeslaw,i.e.thecondition
oflowReynoldsnumbers,isprobablynotmetforbeer.The
densitydifferencebetweentheliquidandthegasishigh,
bubblesarecomparativelylarge,theviscosityofbeeris
low and therefore creaming will advance rapidly. In
addition,thebubblesmayhydrodynamicallyinteract.For
thesereasons,theriseof larger bubbleswill notobey
Stokeslaw.
Deviations from Stokes law may also be explained by
variations in size during the rise of the bubble. The
pressure in the liquid decreases as a function of the
height in the glass. Therefore, the bubble will expand
during the rise of the bubble.However, this effect is
very small.A variation inbubble sizeasaconsequence
of gas uptake or dissolution can be more important as
discussedinchapter5.1.
Drainage occurs if the bubbles become more densely
packed. The foam becomes dryer and the bubbles become
deformed. This leads to a series of events, that is
describedbyIvanovandJain(1979)andWasanandMalhotra
(1986)and Ivanov and Dimitrov (1989). Duringdrainage,
the foam evolves gradually from a foam with spherical
bubblestoafoamwithpolyhedralbubbles.Inapolyhedral
foamthePlateaubordersuctioncontributesasadriving
forcefordrainage (e.g. Scheludko(1957)),inadditionto
gravity.As aconsequence of thecurvature of aPlateau
border, thepressure inside the Plateau border islower
thaninsidethebubbleandintheplanefilm.Therefore,
liquid will flow from the film to the Plateau border.
Through thePlateau borders this liquid will drain from
thefoamasaresultofgravity.
Thedrivingforcesfordrainage.Plateaubordersuction
and gravity, arecounteracted by acomplex interplay of
surfaceandbulkrheologicalproperties.Drainagedepends
very much on the viscosity of the film liquid. Slow
drainage istheresult ofhighbulkviscosity ascanbe
seen from Eg. [3.1]. Another balancing parameter for
drainagemaybeasurfacetensiongradient,thatisdriven
byliquidmotion(DjabbarahandWasan(1985)).Asaresult
ofthissurfacetensiongradient,thebubblesurfacemay
come toatotal stand still (Raoet al (1982)). Inthat
case, drainagecanbedescribed as theliquid flow from
between two rigid surfaces. Consequently, the drainage
ratedeceleratesbecauseshearforcesslowdowntheliquid
flow. For the same reasons, the surfaces of Plateau
bordersmay be immobile too (Kann (1984)). However,the
volume-surfaceratioofPlateaubordersishigherthanthe
volume-surface ratio of films and therefore no sound
conclusion can be drawn about the mobility of Plateau
bordersurfaces.Drainagefromfilmswith(partly)mobile
surfacehasbeendescribedbyIvanov(1985).Filmdrainage
foruneven film thinning hasbeendescribed by Liemand
Woods (1974).
Therateofdrainagefromfilmscanbeapproximatedwith
theclassicalReynolds(1886)lawforliquiddrainage,if
thesurfacesofthefilmcanbedescribedastwocircular,
planeparallelplates (Eg. [3.1]):
de
28 3 AP
dt
3Tjr2
[3.1]
where6isthefilmthickness,iPisthedrivingpressure,
tistime, TJistheviscosityofthefilmliquidandris
theradiusof acircular planeparallel film. From this
equationanorderofmagnitudecalculationcanbemadeto
determinetherateoffilmdrainage.Thedrainagetimefor
aplaneparallelfilmtoreachthecriticalfilmthickness
of rupture can be described with Eg. [3.2] (see e.g.
Malysaetal(1980)):
3i]A
4neiUp
wheretcisthecriticaldrainagetime,i.e.thetimeto
reachthecritical filmthickness,Aisthesurfacearea
of the plane parallel film and 9Cis the critical film
thickness. The interpretation of iP isnot alwayseasy.
The driving force for drainage from between two liquid
planeparallel,horizontal filmsinapolyhedral foamis
Plateaubordersuction.Inthatcase, AP isequaltothe
capillary pressure (Pc). Assuming that &P is equal to
(2o/r),thecriticaldrainagetimebecomes:
10
[3.2]
3Tjr3
[3.3]
4elo
Eg. [3.3]clearlyindicatesthatthecriticaltimefor
filmruptureverymuchdependsonboththeradiusandthe
criticalfilmthickness.
ForthinnerfilmstheassumptionthatAPisequaltothe
Laplacepressureisnotvalid.Asthesurfacesofthefilm
approach,theVanderWaalsattractiveforcemaystartto
contributeasadriving forcefordrainage.Inaddition,
acounteractingpressurecanbepresent,thatbecomesmore
important ifthefilmthicknessdecreases.Thiscounteracting pressure was called disjoining pressure (TT)by
Derjaguin (1941). Taking into account this disjoining
pressure the driving pressure for drainage can then be
writtenas:
AP =Pc-TT
[3.4]
AP is not a constant during drainage because, as the
film becomes thinner,the disjoining pressure increases
andiPdecreases.Theliquiddrainagefromfilmsmaycome
toacompletestopifthedisjoiningpressurebetweenthe
twosurfacelayerscanbalancethecapillarypressure.In
thatcaseafilmcanbestabilized,thatmayexistovera
verylongperiodoftimeifevaporationcanbeexcluded.
Scheludko(1962)formulatedtheconditionsfortheequilibriumfilmwiththefollowingequation:
dPc
de
dïï
=
de
[3.5]
Thedisjoining pressuremay beeither based onelectrostatic repulsion or steric effects, mostly of polymer
11
molecules likeproteins.For lowmolecular weight surface
activematerial,verythinequilibrium filmsmaybeformed
typically intherangesmallerthan1urn.Filmsmay become
sothinthatgreyorblackspotsappearinthefilm.These
spots, called Newton Black spots, were, amongst others,
described byScheludko (1967). Thelocalthicknessof the
film at these spots determines whether the film will
rupture or not (Radoev et al (1983). The critical film
thickness of films of high molecular weight material is
mostlythickerthantheequilibriumthickness,whichmeans
that these films will rupture before the equilibrium
thickness is reached. For these films, a correlation
betweenthedrainagetimeand filmrupturecanbefoundas
described by Djabbarah and Wasan (1985).
References
Derjaguin, B.V., Landau, L.D., Acta Physicochimica USSR
14:633 (1941).
Djabbarah,N.F.,Wasan,D.T.,AIChEJ. 31(6):1041 (1985).
Ivanov, I.B., Dimitrov, D.S., Somasundaran, P., Jain,
R.K.,Chem. Eng. Sei. 40(1):137 (1985).
Ivanov, I.B., Jain, R.K., "Dynamics and Instability of
Fluid Interfaces."In:LectureNotesinPhysics.Ed:T.S.
Sorensen. Springer-Verlag. NewYork.pp. 121. (1979).
Ivanov, I.B., Dimitrov, D.S., "Thin Film Drainage" In:
Thin Liquid Films.Ed: I.B. Ivanov. pp.379 (1989).
Liem, A.J.S., Woods, D.R., Can. J. Chem. Eng. 52:222
(1974).
Kann, K.B.,Colloid J. 46(3):508 (1984).
Malysa, K., Cohen, R., Exerowa, D., Romianowski, A., J.
Colloid and Interface Sei. 80(1):1 (1980).
Radoev,P.B., Scheludko,A.D.,Manev,E.D.,J.Colloid and
Interface Sei. 95(1):254 (1983).
Rao, A.A., Wasan, D.T., Manev, E.D., Chem. Eng. Commun.
15:63 (1982).
Reynolds, O., Phil. Trans. Roy. Soc. London A177:157
(1886).
12
Scheludko,A.,KolloidZ.155:39 (1957).
Scheludko, A., Proc. Kon. Neder1. Akad. Wetensch. Ser.
B65:87 (1962).
Scheludko, A., Adv. Colloid and Interface Sei. 1:391
(1967).
Van 't Riet, K., Prins,A., Nieuwenhuijse, J.A., "Some
EffectsofFoamControlbyDispersed NaturalOilonMass
TransferinaBubbleColumn."Eur.Congr.Biotechnol.3rd,
Volume3,VerlagChemie:Weinheim,WestGermany,pp.521.
(1984).
Wasan,D.T.,Malhotra,A.K.,AIChESymp.Ser.82(252,Thin
LiquidFilmPhenomena):5(1986).
13
4.COALESCENCE
4.1.Introduction
Coalescenceinfoamsisthemergeoftwobubblescaused
by the rupture of the film between the bubbles. Two
smallerbubblesbecomeonelargerbubble.Manymechanisms
forcoalescencehavebeenproposed.Allmechanismshavein
common,thatcoalescenceoccurspreferentiallyifthefilm
thicknessislow.
Inliterature,coalescenceisoftenrelatedtodrainage.
Filmscandraintoacertainequilibrium thickness.When
this equilibrium thickness is reached, the film may
persistoveraverylongperiodoftime.Equilibriumfilms
only rupture when the film liquid evaporates, or when
disturbancesoccur.Theruptureoffilmsmayalsooccurat
acertaincriticalfilmthickness(8a),thatishigherthan
theequilibrium filmthickness.Apossiblemechanism for
thisrupture atthecritical film thickness isgivenby
VrijandOverbeek (1967). Theystatedthatcomparatively
thickfilmsmayruptureasaresultofspontaneousfluctuationsinfilmthickness.
The rupture of films,at a higher thickness than the
equilibrium thickness, may occur as a consequence of
external influences. Two possible mechanisms, that have
beendescribed,arethe "hydrophobicparticlemechanism"
andthesocalled "spreadingmechanism".
The hydrophobic particle mechanism was described by
Garrett (1979), Dippenaar (1982) and Aronson (1986). A
smallhydrophobicparticle,positioned inaliquid film,
caninitiatecoalescence.Thesurfaceofthefilmnextto
the particle is curved as a consequence of the poor
wettingproperties.Therefore,theLaplacepressureinthe
film islocally higher thaninthegasphaseand inthe
partofthefilmwithplanesurfaces.Consequently,there
willbeapressuregradientinthefilm,whichcausesthe
liquidtoflowawayfromtheparticle.Ruptureofthefilm
occursasschematicallydisplayedinfigure4.1.
14
HYDROPHOBIC PARTICLE
FILM LIQUID
3'
Figure 4.1:Film rupture, initiated by the hydrophobic particle mechanism.
About thismechanism several remarkscanbemade, (i)
Theparticlehastopiercethrough both surfaces ofthe
film and therefore, the diameter of the hydrophobic
particles must be at least equal to or larger than the
film thickness. If the particle has a diameter smaller
thanthefilmthicknessthemechanismdoesnotwork,(ii)
The contact angle of the liquid onto the hydrophobic
surfacemustbecloseto180°.(iii)TheLaplacepressure
dependson tworadiiofcurvature.Thedriving forceis
notonlybased onthecurvatureofthefilm nexttothe
particle.Thiscurvaturecanbecompensatedbyacurvature
perpendicular totheplaneofthedisplay infigure4.1.
In that case, the pressure throughout the film is in
equilibrium and coalescence will not occur. For that
reason,holeformationinafilmisalsodeterminedbythe
shapeofthehydrophobicparticle.Ingeneral,spherical
particleswillnotinitiatecoalescencebecausetheradius
of a spherical particle can be equal to both radii of
curvature of the film on theparticle surface.However,
anisometric hydrophobic particles can very successfully
initiate film rupture, (iv) The influence of surface
viscosity onthisprocessisambiguous.Ononehand,the
liquid motion in the film will cause a surface tension
gradient in the film that opposes the liquid motion
(Gibbs-Marangonieffect).Therefore,thesurfaceviscosity
willslowdowntheliquidmotion,buttheruptureofthe
15
filmcannotbestoppedbyasurfacetensiongradient.On
theother hand however,thesurface tensionnext tothe
particle increases as a result of surface expansionand
thereforetheLaplacepressureincreases.Thismayenhance
coalescence since the Laplace pressure is the driving
forceforfilmrupture.
Thesecond possiblemechanism forcoalescence,induced
by particles or droplets,is the "spreading mechanism".
ThismechanismwasfirstdescribedbyRoss(1950)andRoss
et al (1953). Recently, the mechanism was discussed by
Kruglyakov (1989).Infigure4.2,thespreadingmechanism
isdisplayedschematically.
\
\
ÎK/ V
»M
:
\
Figure 4.2: Film rupture, initiated by the spreading mechanism. For the sake of clarity the
dimensions of the film were exaggerated.
Ifsmalldropletscomeintothesurfaceofabeerfilm
(2), surfaceactivematerialmay spread onto thebubble
surface (3).Byviscousforcestheliquidofthefilmis
dragged alongradially inthedirectionofthespreading
material (4).A thin spot in the film results (5).The
thinspotmayeventuallybecomeunstableandcoalescence
mayoccur (6).
Filmruptureisonlycausedbythespreadingmechanism
if the droplets come to the surface of the film, the
spreading of surface active material occurs,and enough
material spreads.Therefore,thereareseveral important
parameters,whichinfluencecoalescencebythespreading
mechanism: (i)Within the relevant time scale the film
layerbetweenthedropletandtheatmospheresurrounding
thefilmmustdrain.Thecriticaldrainagetimeforthis
16
processmaybeestimatedwithEg.[3.3]asdescribed,(ii)
The spreading mechanism only works ifmaterialspreads.
Infigure 4.3 anillustration isgivenof the spreading
conditions. To spread, the surface tension of the film
liquid (CJW) must be higher than the sumvector of the
surface tension of thedroplet (a0)and the interfacial
tensionofthefilmliquidandthedroplet (aow).Forthis
reason,thecompositionoftheparticleisimportant.
GAS
FILM
Figure 4.3: The spreading condition; if o w > o o w + o o surface active material will spread.
Forthesamereason,thesurfacerheologicalaspectsof
beerfoamareveryimportant.Thesurfacetensionofbeer
inafoamcanvaryapproximatelybetween9-55mNm"1under
dynamic conditions (see also chapter 5.5).The dynamic
surface tension depends strongly on thedeformation and
thedeformationrateofthebubblesurface.Thespreading
of surface activematerial on a film will predominantly
occurifthesurfacetensionishigh.Thismeansthatfilm
ruptureismostlikelytooccurifafoamfilmsurfaceis
expanded,(iii)Thedroplethastohaveaminimumsizein
ordertocontainenoughspreadingmaterialtocausefilm
rupture.Ifthedropletistoosmall,itmayhappenthat
spreadingoccursbutthatthespreadingdoesnotproceed
farenough to formahole inthe film. Inthatcasethe
film can be restored. This is only valid for a given
dropletcomposition, (iv)Thecompositionofthedroplet
isalso important foryet another reason thanmentioned
above. Ifthedroplet doesnot contain enough spreading
material, spreading may occur, but the film does not
rupture, (v)Thin films will rupture easier than thick
films,becauselessliquidhastobedraggedalongbythe
17
spreading layer, (vi) The bulk viscosity of the film
liquidcontributestothemechanism.Athigherviscosity
ofthefilmliquid,thepenetrationdepthofthespreading
motion inthe film increases and coalescencewill occur
moreeasily (Eg. [4.1]).
Morequantitativeworkonthissubjectwasreportedby
Prins (1986,1988). Assuming that the droplet completely
spreads on the film surface and that film rupture will
takeplaceifthepenetrationdepth (p)ofthespreading
motionislargerthanthefilmthickness,thepenetration
depthcanbedeterminedwithEg. [4.1]:
p=R(i)7asdp)1/3
[4.1]
where R is the initial radius of thedroplet, T\isthe
bulkviscosityofthefilmliquid,os(=a„-(aow+a0))isthe
spreadingtension,disthethicknessofthespreadlayer
and j)isthedensity of the film liquid. Thisequation
showsthat,withincreasingviscosityofthefilmliquid,
thepenetrationdepthincreasesandtherewiththechance
thatfilmruptureoccurs.
Coalescenceincomparativelythickfilmscanbestudied
bymeansofafallingfilmapparatusasdescribedbyLin
(1981 ab ). With the falling film apparatus a thin liquid
sheetisproducedfromacontainerwithaslit.Thesheet
fallscontinuouslybetweentwoguidewires,untilitfalls
intoavessel.Fromthisvesseltheliquidispumpedback
to the container (figure 4.5).The falling rate of the
film is determined by the flow rate of the liquid and
gravity.VanHavenberghandJoos(1983,1984)describedthe
behaviorofthefalling filmquantitatively.Theinitial
velocityoftheliquid(v0)canbecalculatedifthewidth
oftheslit(60),theflowrate(Q)andtheslitlength(1)
are known. Assuming that the flow rate is constant and
that the film falls obeying the gravity law, the film
thickness(8)andtheliquidvelocity(v)ateverydistancefromtheslit(x)canbecalculated (Brown (1961)):
18
Q = v0e0i = v e i
[4.2]
and:
v2=v2+2gx
[4.3]
Theeffectofthebulkviscosityofthefilmliquidon
thevelocityofthefilmwasneglectedinEg. [4.3].This
isallowedbecausetheviscosityhasminoreffectonthe
velocityofthefilmforlowviscosity aqueoussolutions
asshownbyVanHavenberghandJoos (1983).
Ifthe free falling film isdisturbed by somesortof
obstruction,aV-shapededgecanappearinthefilm.The
V-shaped edge appears if the falling velocity ishigher
than the bursting velocity (u)of the disturbance. The
angle of the edge isdetermined by thevelocity of the
filmandtheburstingvelocityofthedisturbance.After
a negligible short period of time thebursting velocity
reaches a maximum, that can be described by the Culick
equation (Culick (I960)):
u =(2a/p9)'i
[4.4]
TheV-shapededgeisaMachwave.Theburstingvelocityis
relatedtothefallingvelocitybyEg. [4.5]:
u=vsin(a)
[4.5]
whereaistheMachangleoftheedge.Thesurfacetension
of the film at the location of the disturbance can be
calculatedifEg.[4.4]andEg.[4.5]arecombinedtogive
Brown'srelation:
a =%p8v2sin2(a)
[4.6]
UsingEg. [4.6], thedynamicsurfacetensioninthefilm
canbeobtainediftheMachangleismeasuredandthefilm
thicknessisknown.
19
Inthefreefallingfilmcoalescencecanbeinitiatedby
adding emulsion droplets of the right composition and
size.Theformationofholescanbestudied.Withstroboscopelight,apatternasdisplayedinfigure4.4canbe
obtained.Withevery flashofthestroboscopic lightthe
sameholeisobserved.Howevereachtimetheholeisseen
larger, because it expands, and lower because it moves
alongwiththefreefallingfilm.Becausetheeyecannot
distinguishbetweenseparate flashesandholdsapicture
foracertainamountoftime,thepatternasdisplayedin
figure4.4isperceived.
Figure 4.4: The picture obtained with stroboscopic light when film rupture occurs in the
free falling film.
The envelope drawn as a dotted line along the holes in
figure4.4 hasthe sameMach angleastheV-shaped edge
thatwasintroducedinthefilmbyadisturbance.Thefilm
velocityandtheburstingvelocityhavethesamevaluein
bothcases.Therefore,theactualsurfacetensionatfilm
ruptureconditionscanbecalculatedfromEg. [4.6],ifa
picturelikefigure4.4isobtained.
4.2.AimandApproach
Itisawellknownfactthatthebehaviorofbeerfoam
ishighlysusceptibletotheinfluenceoflipidcomponents
20
(Jacksonetal(1980)).Asmallamountoflipidcancause
rapidfoamcollapse.Beercontainsasmallamountoflipid
components, like fatty acids and phospholipids. These
componentshaveanegativeeffectonbeerfoambehavior.
However,theeffect,thatthesedissolvedlipidcomponents
haveonthebehavior ofbeer foam, ismuch smallerthan
theeffectoflipidcomponentscoming fromothersources
thanthebeeritself.Forexample,dirtybeerglassesor
lipid material from theconsumer lipsmay increase foam
collapseenormously.Therefore,itcanbearguedthatnot
onlythepresenceoflipidmaterial,butalsotheactual
condition of the lipid material is important. If lipid
materialismolecularlydissolved relatively littleharm
isdoneto foambehavior,but ifitispresent assmall
lipidparticlesordropletsitcanruinaniceheadinno
time.
In the foam literature two possible explanations for
thisexceptionalbehavioraregiven.Inbothcaseslipid
particles or droplets initiate coalescence. Coalescence
caneitherbecausedbytheinteractionbetweenahydrophobicparticle and the film liquid orby themotionof
spreading material on the film surface. A distinction
betweenthehydrophobicparticlemechanismandthespreadingmechanismcanbemadebecausetheeffectofseveral
parametersonbothmechanismsisdifferent.
The particle size can be used to distinguish between
thesemechanisms.Forthehydrophobicparticlemechanism
thediameteroftheparticlemustbeatleastequaltothe
thickness of the film. For the spreading mechanism the
diameter of the droplet may be smaller than the film
thickness.Inaddition,asaconsequenceofthespreading
ofmaterial,thedroplet-sizedistributionwillshiftto
smallerdropletsifthespreadingmechanism prevails.It
isexpected that theparticle sizewill remain thesame
ifthehydrophobicparticlemechanismoccurs.Thesurface
tensionthatprevailsunderdynamicconditionswillhave
aparamounteffectonfilmrupture.Ifitisthespreading
mechanismthatinitiatesfilmrupture,thedynamicsurface
tension of the falling film must be so high that the
21
spreading tension is greater than zero. Therefore, the
surface tension in expansion must be low in order to
prevent coalescence. In the case of the hydrophobic
particlemechanism,theeffectofthesurfacerheological
aspectsarenotwell known.Inaddition,athigherbulk
viscosity,theprocesswillbeacceleratedinthecaseof
thespreadingmechanismanddeceleratedinthecaseofthe
hydrophobic particle mechanism. In order to determine
which of the mechanisms of film rupture occurs and to
studytheeffectoftheabovementionedparametersonfilm
rupture,varioustechniqueswereused.
The stability of a liquid film as affected by the
presence of small dropletsof different composition and
size was measured with a falling film apparatus. The
effectofthedynamicsurfacetensiononthestabilityof
the falling film was investigated by performing surface
rheological and spreading experiments. The spreading
experimentswerecarriedouttodeterminewhethersurface
activematerialspreadsfromemulsiondropletsontoabeer
surface.Thelowestsurfacetensionatwhichthespreading
of surface active material occurs was determined for
emulsiondropletsofdifferentcomposition.
In order to be able to compare the outcome of the
spreadingexperimentswiththeresultsobtainedwiththe
falling film apparatus the dynamic surface tension in
expansion of several beers was measured with various
surface rheological methods.The falling film apparatus
wasusedasdescribed inchapter4.1.Additional surface
rheologicalexperimentswerecarriedoutwithaLangmuir
troughandwithanoverflowingcylindertechnique.
The Langmuir trough could be used in two different
configurations. In one configuration, the apparatus is
equippedwithasinglebarrier.Thetroughwithasingle
barrierwasusedtosimulatethetransientphenomenathat
occurinthefoam,likebubbleformationandfilmrearrangements.Intheotherconfiguration,theLangmuirtrough
isequippedwithacaterpillarbelt.Theapparatusequipped with the caterpillar belt was used to measure the
surfacetensionatsteady-stateconditions.Therelative
22
deformation rate of the surface (dlnA/dt) is constant
duringthisexperiment (Prins(1976)).
The maximum surface expansion rate in the Langmuir
trough is lower than the expansion rate in the falling
film apparatus. In addition, in practical situations,
surfacescanbeexpandedmorerapidlythancanbeachieved
with the Langmuir trough. Therefore, an overflowing
cylinder technique asdescribed by Piccardi and Ferroni
(1951,1953),Padday (1957)andJoosandDeKeyser(1980)
wasusedtomeasurethesurfacetensionathighersteadystateexpansion rates.Theexperiments were carried out
withbeersofdifferentbulkviscositytostudytheeffect
ofbulkviscosityonfilmstability.
4.3.Experimental
The falling film apparatus consists of a temperature
controlledvesselcontaining 2literofbeer,fromwhich
liquid canbepumped uptoacontainerwithathinslit
(9o=750pm,1=13cm). Fromtheslittheliquidfallsasa
film,between two sidewires,back intothevessel.The
apparatus isdisplayed in figure4.5. Thelength of the
filmisapproximately 40cm.Theliquid flowrates,that
couldbeused,werefromlxlO"5m3s_1to2.9xl0"5m3s_1.
Emulsionsofknowndroplet-sizedistributionanddroplet
composition were added to the beer in the falling film
apparatustostudyholeformation.Theemulsionsweremade
ofbeer and 2%commercial soyaoil (Reddy)withvarying
amountsofemulsifier (eitherglycerol-mono-oleate(GMO)
or Tween 80). A Rannie homogenizer was used at various
pressures (0.5 to 8 Bar)in order to produce emulsions
with different droplet-size distributions. The dropletsize distributions were measured either with a light
scatteringtechniqueasdescribedbyWalstra (1968),with
amicroscopetechniqueorwithaCoulterCounter,dependingonthedroplet-sizedistributionoftheemulsion.
The number of holes that could be produced in the
falling film apparatus were measured. This was, unless
23
indicated otherwise,donewitha2%soya-oil,containing
1% GMO, emulsion homogenized at 0.5 Bar. The amount of
emulsionaddedtothebeerwas0.1%(v/v).Thetemperature
duringthesemeasurementswas20"C.Thenumberofholesis
expressed as number per unit of volume to make a fair
comparisonatdifferentflowratespossible.
.--CONTAINER
WITH SLIT
.LIQUID
FILM
FLOWMETER
-GUIDEWIRE
v
VESSEL
PUMP-
Figure 4.5: The falling film apparatus.
Inordertodeterminewhetheracertainmaterialspreads
ontoasurface,simplespreadingexperimentswerecarried
out. Intoa small container thesurface tensionofbeer
wasmeasured using aWilhelmy plate technique.When the
equilibrium surfacetensionwasreached,smalloildroplets, containing different amounts of emulsifier, were
addedtothesurfaceofthebeer.Asuddendecreaseofthe
measured surface tension was taken as evidence of the
spreadingofsurfaceactivematerial.Inordertosimulate
the increased surface tension in the falling film, the
beer was diluted with water. The equilibrium surface
tensionofthebeerwasthusincreased.
Additionalsurfacerheologicalexperimentswerecarried
outwithaLangmuirtroughequippedwithasinglebarrier.
At the beginning of each experiment the surface had a
totalareaof90cm2.Thesurfacewasthenexpanded toa
24
total areaof 450cm2,an increaseof 400%.Therateof
expansion could be chosen between 2.3xl0"5 and 2.3xl0"2
ms"1.TheLangmuirtroughisdisplayedinfigure4.6.
WILHELMYPLATE
Figure 4.6: The langmuir trough equipped with a single barrier.
The Langmuir trough, equipped with acaterpillar belt
with several barriers,was used to measure the surface
rheological behaviour at steady-state conditions. The
measurementswerecarriedoutwithexpansionratesvarying
from 2xl0"4 to 2xl0_1 s"1.Theexperimental setup isdisplayedinfigure4.7.
CATERPILLARBELT WILHELMYPLATE
BARRIER
Figure 4.7: The Langmuir trough equipped with the caterpillar belt
An overflowing cylinder technique was used tomeasure
the dynamic surface tension of beer under expansion
conditions. The overflowing cylinder technique is displayed in figure4.8. The liquid under investigation is
pumpedfrombelowintoaverticalcylinder,andisallowed
to overflow radially at the top of the cylinder. The
diameter of the inner cylinder at thetop is 8cm. The
liquidoverflowsintoanoutercylinder,fromwhichitis
pumped againintotheinnercylinder.Atthetopofthe
innercylinder the liquid isradially expanded. Aftera
25
certainshortperiodoftimeasteady-stateequilibriumis
achieved, in which surface expansion and diffusion of
surfaceactivematerialtothesurfaceareinequilibrium.
The surface tension under expansion conditions can be
easilymeasuredwithaWilhelmyplatetechnique.Forthe
Wilhelmyplatearoughenedglassplatewasused.
Figure 4.8: The overflowing cylinder.
Themeasurement of the relative surface expansion rate
is more elaborate. (Bergink-Martens et al (1989)). The
relative expansion rate that can be reached with the
apparatushasamaximum ofabout 5s"1,depending onthe
kindofliquidunderinvestigation,theflowrateandthe
distance from the center of the cylinder. The relative
surface expansion rate (dlnA/dt), that is essential to
determine the surface dilational viscosity defined in
equation [5.9], can only be acquired by measuring the
surfacevelocity.Thiscanbecarriedoutbyaddingsmall
floating particles to the surface and measure their
velocity.
The bulk viscosity of the beer was measured using a
Ubbelohde capillary viscometer (capillary constant ca.
5xl0'9 m2s"2). The experiments were carried out using 7
differentaliquotsofbeer(beerAtoG ) .
26
4.4.Results
Inordertoestablishwhethercoalescence isinitiated
accordingtothehydrophobicparticlemechanismoraccordingtothespreadingmechanism,theeffectofthesizeof
the particles was determined in relation to the film
thickness.Thethicknessofthefilmasafunctionofthe
distance from the slit is displayed in figure 4.9 for
differentliquidflows.Thefilmthicknesswascalculated
with Eq. [4.2]andEg. [4.3].
Figure 4.9: The calculated half film thickness of the free falling film as a function of the
distance from the slit The flow rates were resp. 3, 2 and 1x1CT5 n v V 7 .
As can be seen from figure 4.9 the film thickness is
initiallythesameasthethicknessoftheslit(750um).
Thereafter,thefilmthicknessrapidlydecreasestoabout
100um.Thethickness of the filmat acertaindistance
fromtheslitisproportionaltotheflowrate.Itcanbe
concluded that the thickness of the film can only be
manipulated byafactorofthree.Higher flowratesthan
2.9xl0"5m3s"1couldnotbeestablished withtheavailable
pump. At a flow rate lower than lxlO"5 m3s_1 the film
becomesunstable.
27
Asdescribed aboveholescanbe formed inthe filmby
adding emulsions. The emulsions used were prepared at
different homogenization pressures and with various
emulsifierconcentrations.
25
20
:xlOJm_1)
10
0.5 Bar
10
20
30
droplet radius<urn)
50
Figure 4.10: The droplet size distribution of different emulsions. The 8 and 4 Bar
emulsions contain 2% soya-oil. The 0.5 Bar emulsion contains 2% soya-oil with 1 %
CMO.
In figure 4.10 the droplet-size distributions of the
emulsionspreparedwithbeerEand2%soya-oilathomogenization pressures of 8 and 4 Bar are given. Also,the
droplet-size distribution of an emulsion prepared with
beerand2%soya-oil,containing1%GM0,ispresented.The
latteremulsionwaspreparedatahomogenizationpressure
of0.5Bar.Ingeneral,thedroplet-sizedistributionsof
emulsions prepared with beer and 2%soya-oil containing
GM0, omnibus paribus, were somewhat more narrow than
emulsionspreparedwithoutGM0,butthemeandropletsize
wasapproximatelythesame.
When 2mlof theemulsions,prepared with 1%GM0at8
and 4 Bar homogenization pressure, were added to the
fallingbeerfilm (2literofBeer E), thefilmremained
stable at all normal flow rates.No hole formation did
occur.However,inthelightofastroboscopeaflickering
28
ortwinklingofsmalllightspotsinthefilmwasvisible.
The twinkling can be described as "stars in sky". This
twinkling may beexplained by the spreading of material
on the film surface. In that case, the spreading layer
reflectslightinadifferentwaythanthefilmwithouta
spreading layer. Hole formation does not take place
becausetheamountofspreadingmaterialmaybetoolowto
accomplishtherequiredpenetrationdepth.
When2mlofemulsion,preparedat0.5 BarwithbeerE
and2%soya-oil,containing 1%GMO,wasaddedto2liter
ofbeerE,holeformationoccurredinthefilm.Thenumber
of holes,measured at standard conditions, is given in
table4.1.
Table 4.1:The number of holes formed in afree falling beer film. The beer under investigation
was beer E.
flow rate
(mV7)
2.94x10" 5
2.54x10~s
2.21x10" s
1.72x10"5
number of holes
(m" 3 )
2x10 3
4x10 3
9x10 3
13X103
number of holes
(s"7)
5.9x10~2
10.2x10~2
19.9x10" 2
22.4x10" 2
Oneof thereasons thatthenumberofholes formed in
the film is very low compared to the concentration of
droplets (ca. 108inthefilm)mustundoubtedlybethatnot
allthedropletspresent inthefilmcometothesurface
ofthefilm.Anotherreasonmaybethatonthebasisof
thenumberofdropletsinthesystemandtheflowratethe
conclusion canbemadethatonly thelargerdroplets in
thesystem initiateholeformation.Thisissupportedby
the fact that the film remained undisturbed when the
emulsionswithsmalleremulsiondropletswereadded.For
thesamereasonthenumberofholesdependsverymuchon
thefilmthickness.
Evenlargerdroplets(radiusof ca. 1mm)wereaddedto
thefilmbyinjectingsoya-oilcontaining1%GMOintothe
containerwiththeslit.Incontradictionwiththeexpec-
29
tationsthesedropletsdidnotcauseholeformation.The
explanation for this phenomenon can be that droplets
largerthanacertainsizedonotcomeincontactwiththe
surfaceofthefilm.Thethinliquidbeerfilmbetweenthe
dropletandtheatmospheresurroundingthefilmdoesnot
draincompletelywithintheshorttimespaninthefalling
film. The film falls in approximately 0.3 s. With Eg.
[3.3]thecriticaldrainagetime(tc)forthefilmbetween
the oil droplet and the surrounding atmosphere can be
estimated.Ifthecriticalthickness(0C)ofbeerfilmsis
assumed to be 300 nm (Ivanov and Dimitrov (1989)), the
critical drainage time as given in table 4.2 can be
calculated for different droplet radii. Also given in
table4.2 isanoverviewoftheobservationsmadeinthe
falling film when droplets of different composition and
size areadded tothe film. Themost likely explanation
forthebehaviorofthefilmisadded.
Table 4.2: The observations made in the falling film when droplets of various size and
composition are added.
droplet radius
(pm)
tc
(s)
observation
<T f )
explanation
1
10" 7
no holes
no twinkling
droplets come to the surface but do not spread
10
10" 4
no holes
no twinkling
droplets come to the surface but do not spread
100
10-'
no holes
no twinkling
droplets come to the surface but do not spread
1000
100
no holes
no twinkling
droplets do not come to the surface
without emulsifier:
with emulsifier:
30
1
10 ,-7
no holes
twinkling
droplets come to the surface and spread but
the droplets are to small to initiate holes
10
10 -4
no holes
twinkling
droplets come to the surface and spread but
the droplets are to small to initiate holes
100
10~1
holes
no twinkling
droplets come to the surface, spread and initiate
holes
1000
100
no holes
no twinkling
droplets do not come to the surface
Summarizing theabove,thedropletswithadiameterof
approximately thesamesizeasthefilmthicknesscaused
film rupture. Material from droplets of smaller size
appearedtospread,butdidnotcausethefilmtorupture.
Dropletswithadiametermuchlargerthanthefilmthicknessdonotinitiateholeformation,probablybecausethey
donotcomethroughthebeerfilmbetweenthedropletand
thesurroundingatmosphere.
From theseexperiments no definite conclusions can be
drawnaboutthemechanism forhole formation.Eitherthe
hydrophobicparticlemechanismorthespreadingmechanism
canoccur.
l.Sr<xl0 3 m -1 >
V
o
1
u
m i
e
f
r
\ after
•
1.5
Y-s.before
9
n
c
a
0
10
2b
36
4Ö
droplet radius (um>
" 5b
Figure 4.11 a : Thedroplet-size distribution of
the 0.5 Bar 2% soya oil/1% CMO emulsion
before and after the experiment determined
with a microscope.
Figure 4.1tb:The droplet-size distribution
of the 0.5 Bar 2% soya oil/1% GMO emulsion before and after the experiment determined with a Coulter Counter for droplets
>50 ^ m .
Infigure4.11ab thedroplet-sizedistributionisgiven
ofthe0.5Baremulsioncontaining1%GMObeforeandafter
theexperiment asdeterminedwithamicroscopetechnique
andaCoulterCounter.Withbothmethodsitcanbeclearly
seenthatthedroplet-sizedistributionshiftstosmaller
dropletsduringthefallingfilmexperiment,meaningthat
thelargerdropletsbecomesmaller.Thisobservationwas
alsomadebyRoberts(1977)whodescribesthespontaneous
emulsificationofdefoamerduringthebreakdownofafoam.
Thismaybearesultofthespreadingofmaterialonthe
surfaceofthefilm.Thespreadlayerbreaksupandforms
smaller droplets.Thisobservation is in agreement with
theobservation thatafter acertain period of timethe
31
formationofholesstops.Theseresultsindicatethatthe
formation of holes iscaused according tothe spreading
mechanism.Bydecreasingtheflowrateandthusthefilm
thicknesstheformationofholescanbeinitiatedagain.
Emulsions, homogenized at 8, 4 and 0.5 Bar were also
prepared without GMO.Whentheywere added tothefilm,
omnibusparibus,noholeswere formed. In addition,the
"starsinthe sky"werenotobserved. Theadditionofa
certain amount of GMO to the emulsion appears to be
necessary forhole formation. Theessential additionof
emulsifiercanbeexplained infavorofbothcoalescence
mechanisms. The addition may change the contact angle
betweenthebeerfilmandtheemulsiondropletinsucha
way that the hydrophobic particlemechanism works.This
isnotvery likely,because itcanbeexpected thatthe
additionofanemulsifierwouldalterthewettingproperties to make the droplet more hydrophilic. However, no
definiteconclusionscanbedrawn.Ontheotherhand,the
addition of GMO to the emulsion droplet may alter the
spreadingpressurefromnegativetopositive.Thismeans
thatnosurfaceactivematerialspreadsfromanemulsion
droplet without GMO and that material spreads if it
containsacertainminimumamountofGMO.
In order to establish which of the above mentioned
mechanismsoffilmruptureoccursspreadingexperimentsof
soya-oildropletsontoabeersurfacewerecarriedoutas
a functionoftheGMOconcentration (table4.3).
Table 4.3: Spreading experiments of soya-oil onto the surface of beer E carried out as a
function the GMO concentration. The initial surface tension was 41 mNm"'.
32
droplet composition
spreading
soya-oil
soya-oil as emulsion
soya-oil 1 %GMO
soya-oil 2% GMO
soya-oil 3% GMO
soya-oil 4% GMO
no
no
no
yes
yes
yes
final surface tension
(mNm" 7 )
41
41
41
39
37
37
Itbecomesclearthatinordertospreadsurfaceactive
materialontoabeersurfaceacertainminimum amountof
GMOmustbeaddedtothesoya-oil.Thepuresoya-oildoes
notspreadonthesurfaceofthebeer.Ifthespreadingof
surface activematerial initiates hole formation inthe
fallingfilmtheminimumamountofGMO,addedtotheoil,
mustbelargerthan1%,becausethesoya-oilcontaining1%
GMOdoesnotspreadonthebeersurface.Thisassumption
isnot inagreement with theobservation thatholesare
formedinthefallingfilmwhenthe2%soya-oilcontaining
1%ofGMOisaddedtothefilm.Thedisagreementmaybea
consequenceof the factthatthe surface tensionof the
falling film is higher than the equilibrium surface
tension.Thisisaresultofthecreationofanewsurface
attheslitandthesurfaceexpansionthattakesplacein
thefilm.
60
CmNm
±
>
21x10 V s
10
IS
20
distance from the s l i t (cm)
25
Figure 4.12: The dynamic surface tension of a free falling beer film as a function of the
distance from the slit for various flow rates. Determined according to Van Havenbergh.
Infigure4.12thedynamicsurfacetensionisgivenfor
beer E as a function of thedistance from the slit for
variousflowrates.Theobservationsarenotcompletelyin
agreement with the results of Van Havenbergh and Joos
(1983),madewithSDSsolutions.Theseauthorsfoundthat
33
the surface tension in the film continuously decreases
fromabout72mNm"1closetotheslittolowervaluesat
thelowerpartof the falling filmdepending ontheSDS
concentration.Thedeviationbetweenresultspresentedin
figure 4.12 and the results of Van Havenbergh and Joos
(1983) may be explained by the fact that the dynamic
surfacetensionofbeerinsteadofSDSwasmeasured.The
surfacetensionofthebeerfilmisbetween50mNm"1and65
mNm"1.Thisisrelevant,becausesurfaceactivematerial,
thatdoesnotspreadonabeersurfaceinequilibrium,may
spreadontheexpandedsurfaceofthefallingbeerfilm.
Toinvestigatethissuppositioninmoredetail,thebeer
wasdilutedwithwatertosimulatetheprevailingsurface
conditionsinthefreefalling film.Asaconsequenceof
thismanipulation the surface tensioncanbemadeequal
forbothsituations,althoughthesurfacecompositionmay
bedifferent.Forthisreason,thecomparisonhaslimited
value.Theresultsofthespreadingexperimentsondiluted
beersurfacesaregivenintable4.4.Thesurfacetension
atwhich spreading occurs forvarious concentrations of
GMOislowerthanthesurfacetensionmeasuredinthefree
fallingbeerfilm.Evenfromsoya-oildropletscontaining
lowconcentrationsofGMO(0.25%),surfaceactivematerial
1
spreadsonthesurfaceofdilutedbeer(a>50mNm')
and
initiateshole formation in the free falling beer film.
Thisisastrong argument in favoroftheoccurrenceof
thespreadingmechanism.
Table 4.4: Spreading experiments of soya-oil onto diluted beer surfaces carried out as a
function the GMO concentration.
droplet composition
spreading surface tension
(mNm -7 )
soya-oil 2% GMO
soya-oil 1%GMO
soya-oil 0.75% GMO
soya-oil 0.5% GMO
soya-oil 0.25% GMO
soya-oil 0% GMO
41
44
46
48
50
>72*
no spreading on water.
34
The dynamic surface tension of the beer in expansion
appears to be important for coalescence, initiated by
soya-oildroplets,becauseitdetermineswhetheragiven
droplet spreads or not. Therefore, the dynamic surface
tensionofbeerwasmeasuredinvariousways.Experiments
werecarriedoutinaLangmuirtrougheitherequippedwith
asinglebarrierorequippedwithacaterpillarbelt.The
results obtained with the experiment using a single
barrieraredisplayedinfigure4.13.
52
s
u
r
—
A
i *>
B
c
e
t 48
n
s
i
o 46
n
F
„,h
r~—;.<-^
^sTS'
<mN/m>
44
^
D
"•'~~—:
c
, ..
T
^~**^
G
42
40
0
100
200
expansion <% oforiginal
300
surface)
400
Figure 4.13: The surface tension as a function of the expansion for various beers.
Thelinearexpansionrateofthebarrierswas2.3xl0"2ms"1.
As can beclearly seen thesurface rheological behavior
of the beers is remarkably different. The equilibrium
surfacetensionvariesfrom38mNm"1to47.4mNm"1.Whenthe
surfaceisexpanded400%thesurfacetensionofallbeers
rises. The final surface tensionof beers underdynamic
conditionsliesbetween45.1mNm"1and51.9mNm"1.Itseems
that thecurves are shifted over approximately thesame
distanceasthedifferenceinequilibriumsurfacetension.
The surface rheological behaviour of beer, under the
steady-state conditions in the Langmuir trough equipped
withthecaterpillarbelt,isdisplayedinfigure4.14.As
canbeseenthesurfacetensionofthebeersdependsvery
35
muchonthedeformationrate.Athighdeformationratethe
surface tension does not increase as much as at lower
deformationrateshowingthatbeerisshearthinningwith
respecttothesurfacedilationalviscosity.Thesequence
forthebeersisverymuchthesameasinfigure4.13.
54
s
u
a
o
e
tn
s
i
^— ~
52
50
f
+8 • ls<+>'
' ft
——
B
C
"_JL_—
—————'
o
n
46
<mN/m>
44
i
G
42
40
38
C
0.04
0.08
0.12
dlnA/dt < s - l )
0.16
0.2
Figure 4.14: The dynamic surfacetension asafunction of the steady state expansion rate
as measured with the Langmuir trough equipped with the caterpillar belt
Theoverflowingcylinderwasusedtomeasurethedynamic
surface tension at higher steady-state expansion rates
thanwiththecaterpillar beltmethod (max.0.2 s"1). In
figure 4.15 the value of the surface expansion rateof
beer D isgiven as a function of the distance from the
centeroftheinnercylinder.Ascanbeseentherelative
expansionrateisnotuniformoverthecylinder.Instead
thedlnA/dt increases fromabout 2to8s"1.Thesurface
tensionismeasured atthecenterofthecylinder,where
dlnA/dtisapproximately constant.Theplatehasawidth
of2.6cm.
However, since the dlnA/dt at that place can not be
determined exactly the surface viscosity can not be
calculated.Inaddition,thesurfaceviscosityisunknown
for a second reason. As stated before, the relative
expansion rate at the top of the overflowing cylinder
36
dependsonthesurfaceandbulkTheologicalpropertiesof
theliquidunderinvestigation.Dependingontheliquid,
theflowrateandthegeometryofthesystem,thesurface
adaptsitself.Asteady-stateofacertainsurfacetension
andsurfacerelativeexpansionrateisaccomplished.This
meansthatitisnotcertainwhetherthedlnA/dtforall
beers,measuredintheoverflowingcylinder,isequal.The
surfaceviscositycannotbecalculatedunlessthedlnA/dt
foreverybeercanbemeasured.
1
2
distance fromthecenter(cm)
3
Figure 4.15: The dlnA/dt in the overflowing cylinder as a function of the distance from
the center of the inner cylinder. The examined beer was beer D.
Thisisnotarealdrawbackofthemethodforthesekind
ofmeasurementssincethesurfacedilationalviscosityis
not therelevant parameter forthe spreading of surface
active material. The relevant parameter is the dynamic
surfacetension (adyn),whichcaneasilybemeasured.
Intable4.5thedynamicsurfacetensionof7different
beersaregivenasmeasuredwiththeoverflowingcylinder
technique. Itcanbeconcluded that the surface tension
inexpansionforthe7beersisapproximatelysimilar.The
differencesathighexpansionrateshavebecomeverylow.
The large differences between the beers found at lower
expansion ratewith thecaterpillar beltmethod seem to
37
almostdisappearathigherexpansionrates.Nevertheless,
thesequenceofthe7beersremainsverymuchthesame.
Table 4.5: The dynamic surface tension for various beers as measured with the overflowing
cylinder technique. The flow rate was 5.6 r r v V . The dlnA/dt was approximately 2 s~'.
beer
A
B
C
D
E
F
G
(mlMm-7)
(mNm"')
47.4
42.2
43.0
42.8
41.6
41.9
38.0
55.0
52.9
53.0
52.6
52.0
52.1
52.8
The last parameter that can be used to distinguish
between the hydrophobic particle mechanisms and the
spreading mechanism is bulk viscosity. Therefore, the
viscosityofthebeerwasincreasedwithdifferentamounts
ofdextranandemulsiondropletswereadded tothefilm.
80
n
u
E
r
o
f
h
60
î
s
•
TO
•
•
50
CxlC^m"3)
40
30
•
•
-
20
1. 3
•
•
1.5
1.7
1 9
2.1
viscosity <mNsm~z)
Figure 4.16: The number of holes in a fallingfilm of beer Easafunction of the viscosity.
The viscosity was increased by adding dextran.
Thenumberofholesinthefallingfilmisgiveninfigure
38
4.16 asa function ofthebulkviscosity.Thenumberof
holes formed in the film depends very much on thebulk
viscosityofthebeer.Theincreaseofthenumberofholes
can not be explained with the increase in penetration
depth alone (Eg. [4.1]). Apparently, by increasing the
viscosity, the spreading of smaller droplets becomes
effective as well. Because there are increasingly more
smalldropletsgoingfromrighttoleftintherighttail
of the droplet-size distribution, the number of holes
formedinthefallingfilmincreaseathigherviscosityin
aspectacularway.
Table 4.6: The number of holes formed in a free falling beer film for various beers. The bulk
viscosity of the beers is given. The f l o w rate was 1.7x1Cf 5 m 3 s _ 1 , 3 0 ml emulsion of beer E,
2% soya-oil, 1 % Tween 8 0 was added to 3 I beer. The d v s of the emulsion was 9.7 fjm.
beer
T)
(mNsrrT2)
A
B
C
D
E
F
G
1.21
1.34
1.34
1.29
1.34
1.34
1.32
number of holes
(m~3)
13
17
19
15
21
29
16
The number of holes formed int h efalling film apparatus
for different b e e r s , omnibus p a r i b u s , isv e r y differenta s
c a n b eseen i ntable 4.6. However, t h edifferences seemt o
b e influenced mainly b yt h eviscosity oft h ebeer a sc a n
b e seen in figure 4 . 1 7 . Under t h e extreme e x p a n s i o n
conditions i n t h e falling film apparatus t h e beers h a d
v e r y similar dynamic surface tension (table 4 . 5 ) . T h e
dynamic surface tension apparently does n o tinfluencet h e
results obtained with t h e falling film apparatus t o a
large e x t e n t .
39
30
n
u
m
b
?
•F
•
25
o
t
h
o
1
•
20
s
3
Cxl0 m~ 3 )
E
•
C
•
B
D
15
• &
•
•
ft
•
1.2
1.23
1.26
1.29
v i s c o s i t y <mNsm~*>
1.32
1.35
Figure 4.17: The number of holes in afalling beer film asafunction of the bulk viscosity.
The results are given for various beers.
4.5.Discussion
Theresults,obtainedwiththefalling filmapparatus,
cannotbe directly translated intocoalescence inbeer
foam.Thefilmthicknessinfoamsisatleastanorderof
magnitudesmallerthanthefilmthicknessinthefalling
film apparatus, whereas emulsion droplets added to the
filmintheexperimenthaveaboutthesamediameterasin
practice.Therefore,thepenetrationdepth,essentialfor
hole formation in a foam film, will mostly be small.
Consequently,dropletswithaboutthesamediameterasthe
film thickness will, depending on their composition,
initiatecoalescence.Inpractice,thelipiddropletsare
addedexternallytothefoamfilms.Inthatcase,thereis
noupperlimittothedropletsize.Alldropletscometo
the surface. In addition, the film in the falling film
apparatus iscreated at high surface expansion rate.It
maybe anticipated that the film surfaces ina foamare
closertoequilibrium.
40
Anotherobservationmadewiththefallingfilmapparatus
thatcannotbedirectlytranslated tobeerfoam,isthe
resultthathighbulkviscositydecreasesfilmstability.
The effect of bulk viscosity on drainage may be more
pronouncedthantheeffectoncoalescencebythespreading
mechanism.Asaconsequenceofhighviscosity,therateof
drainagewillbeslowerandthefilmthicknessinthefoam
will remain higher over a longer period of time. The
effectofthefilmthicknessonthespreadingmechanismis
moreimportantthantheeffectofbulkviscosityascanbe
seeninEg. [4.1].
Althoughnotallobservationsmadewiththefallingfilm
apparatuscanbedirectlyrelatedtobeerfoam,conclusive
resultswereobtainedtodistinguishwhetherfilmrupture
initiatedby lipidcomponentsisaccordingtothehydrophobic particlemechanism or according to the spreading
mechanism. The emulsion droplets,essential to initiate
coalescenceinthefallingfilmapparatus,musthaveabout
the same diameter as the film thickness. This does not
giveconclusiveevidencethathole formationinaliquid
filmiscausedmerelybythespreadingmechanism andnot
bythehydrophobicparticlemechanism.However,fromall
otherexperiments itbecomesclearthatthespreadingof
surface active material must be responsible for film
rupture.Thedetrimentaleffecttobeerfoamofexternally
addedlipidmaterialisaresultofcoalescence,initiated
bythespreadingmechanism.
One of the indications is that the emulsion droplets
becomesmallerduringthemeasurementinthefallingfilm
apparatus.Hole formation stopsaftera period oftime.
When the flow is decreased the process starts again to
showthesusceptibilityoftheprocessonthefilmthicknessandthedropletsize.Anotherstrongargumentisthat
coalescence by the spreading mechanism depends on the
composition of the droplet.Soya-oil,although itself a
"dirty"system,doesnotspreadonthe(expanded)surface
ofbeer.Experimentsshowthataminimumconcentrationof
emulsifierinthesoya-oilisessentialforfilmrupture.
Theminimumemulsifierconcentrationthatisnecessaryto
41
spreadonaequilibrium surfaceofdilutedbeerisabout
thesameastheconcentrationthatisnecessarytocause
hole formation inthe falling film,whereas the surface
tensioninbothexperimentsisequal.
Yetanotherreasoningisthattheprocessinthefalling
filmapparatusverymuchdependsonthebulkviscosityof
thebeer.Anincreasedviscosity leadstoanincreaseof
the number of holes.This is an additional argument in
favorofthespreadingmechanism.
Becausethedetrimentaleffectofexternallyaddedlipid
componentsisaccordingtothespreadingmechanism,itmay
beconcludedthatthesurfacetensionofthebeermustbe
low to avoid the spreading of surface activematerial.
This does not only apply to equilibrium conditions but
alsototheactualexpansionconditionsoffoamformation
andbreakdown.Fordifferentbeersthesurfacerheological
behaviour inexpansion isdifferent. Inparticular,the
dynamic surface tension may differ for different beers
dependingontheexpansionrateofthesurface.Atlower
expansionratesthedifferencesaremorepronounced.From
thisobservation,itmaybeexpectedthatbeers,thathave
differentsurfacerheologicalbehaviourinexpansion,also
differ intheirsusceptibility toexternallyaddedlipid
components.
Thebulkviscosityofthebeer,althoughitseffectwas
verypronouncedintheexperimentswiththefallingfilm,
is less important in beer foam as far as the spreading
mechanism isconcerned. Inpractice,itmay beexpected
thatthethicknessoffoamfilmsissmallerthantheadded
spreadingdroplets.Consequently,thepenetrationdepthof
thespreadingmotionwill,ingeneral,belargeenoughto
initiatecoalescence.
From these last considerations, it can be concluded
that, inpractice, thecollapseof foam bycoalescence,
initiatedbyexternallyaddedlipidmaterial,canonlybe
avoidedifthefatmaterialdoesnotspreadonthesurface
ofthebeer.Thedynamicsurfacetensionisthereforethe
mostimportantparameter.
42
References
Aronson,M.P.,Langmuir2:653(1986).
Bergink-Martens,D.J.M.,Bos,H.J., Prins,A.,Schulte,
B.C., Submitted to J. Colloid and Interface Sei. (June
1989).
Brown,D.R., J.FluidMech.10:297 (1961).
Culick,F.E.C.,J.Appl.Phys.31:1128 (1960).
Dippenaar,A.,Int.J.Miner.Process.9(1):15 (1982).
Garrett, P.R., J. Colloid and Interface Sei. 69:107
(1979).
Ivanov, I.B., Dimitrov, D.S., "Thin Film Drainage" In:
ThinLiquidFilms.Ed:I.B.Ivanov.pp.379 (1989).
Jackson,G.,J.Inst.Brew.87:242 (1981).
Joos, P., De Keyser, P., "The overflowing funnel as a
method formeasuring surfacedilationalproperties."In:
LevichBirthdayConf.Madrid. (1980).
Kruglyakov,P.M., "EquilibriumPropertiesofFreeFilmand
StabilityofFoamsandEmulsions."In:ThinLiquidFoams.
Ed:I.B.Ivanov.pp.767.(1989).
Lin, S.P.,J.FluidMech.104:111 (1981a).
Lin, S.P.,Roberts,G.,J.FluidMech.112:443:(1981b).
Padday,J.F.,Proc.Intern.Congr.Surf.Activity,London
1:1 (1957).
Piccardi,G.,Ferroni,E.,Ann.Chim.(Rome)41:3 (1951).
Piccardi, G., Ferroni, E., Ann. Chim. (Rome) 43:328
(1953).
Prins, A., "Dynamic Surface Properties and Foaming
BehaviorofAqueousSurfactantSolutions."In:Foams.Ed:
R. J. Akers,Academic Press.London, New York. pp.51.
(1976).
Prins,A.,"TheoryandPracticeofFormationandStability
of Food Foams." In: Food emulsions and foams. Ed: E.
Dickinson, Royal Society of Chemistry, Leeds, pp. 30.
(1986).
Prins,A.,"PrinciplesofFoamStability."In:Advancesin
FoodEmulsionsandFoams.Ed:E.Dickinson,G.Stainsby,
ElsevierAppliedScience,pp.91.(1988).
43
Roberts, K., Axberg, C., Osterlund, R., J. Colloid and
InterfaceSei.62:264(1977).
Ross,S.,J.Phys.ColloidChem.54:429 (1950).
Ross,S.,Hughes,A.F.,Kennedy,M.L.,Mardoian,A.R.,J.
Phys.ColloidChem.57:684(1953).
Van Havenbergh, J., Joos,P., J. Colloid and Interface
Sei.95(1):173 (1983).
VanHavenbergh,J.,Bussmann,H.,Joos,P.,J.Colloidand
InterfaceSei.101(2):462 (1984).
Vrij,A.,Overbeek,J.Th.G.,J.Am.Chem.Soc.90(12):3074
(1968).
Walstra,P.,J.ColloidandInterfaceSei.27(3)(1968).
44
5.DISPROPORTIONATION
5.1.Introduction
Disproportionationisacoarseningprocess,thatisthe
result of inter-bubble gas diffusion, caused by a gas
pressuredifference between bubbles.Ifa singlegas is
present, thispressure difference corresponds to adifferenceinLaplacepressure.Thispressuredifferencemay
bearesultofadifferenceinsize.Accordingtothelaw
ofLaplacethepressureinasmallerbubbleishigherthan
thepressureinalargerbubble,assumingthatthesurface
tensions (a)ofbothbubblesareequal:
*Ptt,-Pi-P2-2a/ri-2a/r2
[5.1]
iPtot beingthetotalpressuredifference,and PxandP2
being the Laplacepressures in thebubbles respectively
withradii rxandr2.Disproportionationmayalsobecalled
Ostwaldripeningorisothermaldestination.
Thepressuredifferencecausesaconcentrationgradient
intheliquidlayerseparatingthebubbles.Asaresultof
thisconcentration gradient,transport of gaswill take
placefromasmallertoalargerbubble.Thelargerbubble
willgrowattheexpenseofthesmallerone.Thesmaller
bubblewilleventuallydisappear.Consequently,coarsening
ofthefoamwilltakeplace.Thedisproportionationrate
depends on several parameters, in particular, the gas
solubility and the film thickness, which may have very
differentvaluesindifferentfoams.
Althoughgas transport in foamsmay bevery important
for the behavior of the foam, limited literature about
thissubjectisavailable.Thisisprobablyaconsequence
ofthefactthataquantitativedescriptionofgastransport in a multibubble system is very complex.However,
although there are some fundamental differences between
gas transport in foams and the dissolution of a single
45
bubble inaninfinite amountof liquid,a lotofunderstanding ongas transport in foamscanbeobtained from
thewelldevelopedknowledgeonbubbledissolution.
Eversinceafirstattempttodescribethedissolution
ofabubblebyEpsteinandPlesset(1950)avastdevelopment and improvement of bubble dissolution theory has
occurred.Scriven (1959)gavetheexactsolution forthe
growthrateofabubbleusingasimilaritytransformation
technique.Unfortunatelythismethodcanonlybeusedfor
bubbleswithzeroinitialradius.CableandEvans (1967)
extended thismethod and used ittodescribe thegrowth
and dissolution of a sphere with finite initial size.
LaterDudaandVrentas (1969,1971)presented newresults
usingfinitedifferencesolutionsandfoundthatprevious
methods using perturbation solutions have only limited
validity.Ingeneralthefinitedifferencemethodpredicts
faster growth and dissolution rates. Ruckenstein and
Davies(1970)solvedtheconvectivediffusionequationfor
radial and translational convection for small Reynolds
numbersandpotentialflowandconcludedthat,invarious
regimes,bothconvectiontermshaveasignificanteffect
onthebubbledissolutionorgrowthrate.Theyalsofound
that,ifsurfaceactivematerialispresent,transportby
translational convection is reduced. This reduction may
be a result of the fact that the surface layer at the
bubble boundary is immobile because the liquid driven
surfacetensiongradientoff-setsthetranslationalliquid
flow(Van'tRietetal(1984)).Tao(1978,1979)described
growthanddissolutionofabubbleinasupersaturatedor
undersaturated liquid. The influence of the surface
tension as a driving force is included into themodel,
thatisbasedonthesolutionifinfiniteseriesoferror
integral functions.VrentasandVrentas (1982)evaluated
the model presented by Tao and concluded that it gives
good results for systems with a low density difference
between thecontinuous and thedispersed phase i.e. for
gas-liquid systems the model is less suitable than for
liquid-liquidsystems.
46
Both model calculations and experimental evidence of
bubbledissolutionwerepresented byWard andcoworkers.
Ward and Tucker (1975)were the first to describe the
dissolutionandgrowthofbubblescontainingmorethanone
diffusinggas,taking intoaccountthevaporpressurein
thebubbleandthegasexpansioneffect,thatisaresult
of the surface tension and the curvature of the bubble
surface.Wardetal (1982ab)extended theirtheoryusing
a first order perturbation analysis of the Schrödinger
equation and the Boltzmann definition of entropy and
concluded thatthediffusionofthegasintheliquidis
rate determining, and not the transition of gas at the
bubbleboundary.Wardetal(1982e)calculatedthevalueof
twopossiblestableequilibriumbubblesizesforabubble
inaclosedvolumeofliquid.Oneunstablecriticalradius
is the result of an equilibrium between the amount of
supersaturationofthegasintheliquidandtheLaplace
pressureinsidethebubble.Ifthebubbleradiusislarger
thanthiscriticalradiusthebubblewillgrow,andifthe
bubble radius is smaller than this critical radius the
bubblewill shrink.Theothercritical radius isstable
andisaresultoftheclosedvolumeofthesystem.Ward
et al (1986) described a diffusion model taking into
accountnon-equilibrium gasconcentrations intheliquid
andthevaporpressureinthebubble.Hegaveexperimental
evidence for the validity of this model using purified
water forthebubbledissolutionexperiments.Theeffect
ofthesurfacetensionclosetoequilibriumsaturationwas
repeated by Cable and Frade (1988)who stated that low
concentrations of impurities inmolten glass may havea
retardinginfluenceonbubbledissolutionbyloweringthe
surfacetension.CableandFrade (1987)alsostatedthat
the presence of traces of poorly dissolving or slowly
diffusinggasesmayhaveaparamounteffectontherateof
bubble dissolution or growth. Also involved in bubble
dissolutioninglassmeltswereWeinbergandcoworkers.Zak
and Weinberg (1980) proposed a model of multibubble
dissolution but they assumed that the average distance
betweenbubblesislargecompared tothediameterofthe
47
bubbleanddescribedthebubblestobeconcentrationpoint
sourcesofgas.Thistheory cannotbeapplied tofoams
because in foamsthe bubbles interferewith eachother.
Weinberg (1981)stated that the surface tension of the
bubbleismoreimportantfortherateofbubblegrowthor
dissolutionthanconvectivetransportaslongasthegas
concentration in the liquid isclose to theequilibrium
value. He also stated that the rate limiting step for
bubbledissolutionisdiffusionintheliquidratherthan
interfacialmasstransfer.SubramanianandWeinberg(1980)
studied the roleof radial convective transport inmore
detailand foundthatitaffectsbubbledissolutiononly
at sufficiently largevaluesof thedriving force.They
concludedthatconvectivetransportmayenhancethebubble
dissolutionrate.SubramanianandWeinberg (1981)useda
short time asymptotic expansion analysis which is less
accurateforlongtimespans.Weinbergetal(1980ab)and
Onoratoetal(1981)repeatedtheimportanceofincorporating the expansion effect in the bubble dissolution
equationsandstressed thatamultigassystemmayhavea
dominantinfluenceontherateofdissolutionorgrowthof
a bubble. Most recently, Yung (1989) gave a review of
papersonthedissolutionofspheresinaninfiniteamount
ofliquid.Hedescribedamodelusinganfinitedifference
method,thatmakesiteasiertoaccountforallsortsof
parameters that other authors have neglected. The gas
expansion effect, the influence of vapor pressure, the
presenceofmorethanonegaswithdifferentsolubility,
radial convection terms, and the surface tension are
includedinthemodel.Anextensivecomparisonbetweenthe
workof'variousotherauthorsismade.
Insomerespectsthedescriptionofthedissolutionof
a singlebubble inan infinite amount of liquid ismore
complex than thedescription of gasdiffusion infoams.
Howeverinotherrespectsthedescriptionofgastransport
in foams is much more complicated. Non equilibrium gas
concentrationsintheliquidwillpracticallynotoccurin
foams,becausetheconcentrationofthegasatthebubble
boundarywillberapidlyinequilibriumwiththepressure
48
intheadjacentbubbleandthefilmthicknessingeneral
issmall.Inaddition,theradialconvectionproblemdoes
notexistinfoams.
Ontheotherhand,thegeometry andtopologyof (polyhedral)bubbles in a foam is too complex to be solved,
whereasthegeometryofadissolvingsphereisrelatively
elementary. The size and gascomposition of surrounding
bubblesdeterminethegasconcentrationdifferencesina
verycomplexway.Thediffusiondistancevarieswithtime
and location. The dimensions of Plateau borders are
entirely different from thedimensions of films and the
decreaseofthefilmthicknessbetweenbubbleswithtime
canonlybeestimated.Thereforethediffusiondistanceis
notwellknown.
Inspiteofthesedifficultiesresearchworkondisproportionationandgastransportinfoamshasbeenreported
inthelastdecades.Dewar(1917)wasoneofthefirstto
describe the rate of air diffusion through soap films.
Anotherattempttodescribetherateofdisproportionation
was made by Clark and Blackman (1948). They proposed a
simplemodeltodescribethegrowingandshrinkingrateof
bubbles in a foam having respectively a larger and a
smaller radius than the mean bubble radius. They also
calculatedthedecreaseofthespecificsurfaceareaofa
foamoveraperiodoftime,causedbydisproportionation.
Brownetal. (1953)developed anothermodeldescribing
thebubble'radiusasafunctionoftime.Theyemphasized
thattheoryandexperimentdonotalwayshavetocoincide,
because theory doesnot include thepermeability ofthe
adsorbedsurfacefilm,norhighsurfaceviscosityslowing
down theevolution of thebubble.Theeffect of surface
viscosity on gas transport in polyurethane foams was
repeatedbyOwenandKendrick (1968).Princen (1963,1965)
improved the theory presented by Brown et al (1953),
incorporating theexact shapeof abubble situated ata
liquid-gasinterface,thefilmthicknessandchanginggas
composition.Princen(1965)alsostressesthatthepermeability ofmonolayersonboth sidesofthe film playsan
importantroleintherateoftransport,butlaterPrincen
49
etal(1967)gaveevidencethattransportofgasesthrough
solublemonolayersIsgovernedbysimpleFickeandiffusion
(Princen (1967)), that can be described as diffusion
throughporesinanotherwiseinsolublelayer.
Severalothermodelshavebeenproposedtodescribethe
rateofdisproportionation infoams,amongwhicharethe
LSWtheoryandtheDeVriesmodel.TheLSWtheory,named
afterLifshitz,Slyozov(1961)andWagner(1951),predicts
thatthemeanbubbleradiusinafoamwilldecreaseasthe
third root of time. The De Vries model (1958,1972) is
basedonFickeandiffusionandpredictsthatthedecrease
oftheradiusofashrinkingbubbleisproportionaltothe
squarerootoftime,accordingtothefollowingequation:
4RTIDSa
t
[5.2]
Pat„9
wheretistime,r0isthebubbleradiusatt=0,rtisthe
bubble radius at t=t,R is the gas constant, T is the
absolutetemperature, TDisthediffusioncoefficient,S
isthegassolubility, a isthesurfacetension,Patmis
the atmospheric pressure and 6 is the film thickness
between thebubbles.Themodelwasused toestimate the
meanfilmthicknessinfoamsbutgaveerroneousresultsas
discussedbytheauthor.
Gal-or and Hoelscher (1966)calculated unsteady-state
masstransferindispersionswithaMaxwell-Boltzmanlike
modelandincludedtheeffectofthebubble-sizedistribution.Theywereabletocalculatethediffusionrateper
unitareaofinterface.
Thisworkwaslaterreviewed byLemlichandcoworkers.
Ranadive and Lemlich (1979) emphasized the important
effectoftheinitialbubble-sizedistributionondisproportionation and compared the results obtained with the
empirical distribution of De Vries and the theoretical
distribution of Gal-or. They found that the empirical
distribution of De Vries gives the best results. The
50
important effect of the initial size distributions in
foamswasrepeatedbyMonsalveandSchechter(1984)andby
Chengand Lemlich (1985).ThecombinedeffortofLemlich
and coworkers finely resulted in the development of an
apparatus to determine the permeability of thin liquid
films by following the evolution of the bubble-size
distribution of a initially bimodal foam (Rieser and
Lemlich (1988)).Fromtheresultstheyconcludedthatgas
diffusionmaybeenhancedbyconvectionintheliquidfilm
between the bubbles.Cook and Tock (1974)and Haas and
Tock (1975)also determined permeability parameters for
severalgases.Theyemphasizedtheimportantinfluenceof
thegassolubilityonthemigrationrateofgasesandused
thin liquid surfactant films to purify gases based on
theirdifferenceinsolubility.Ramchandranetal (1981)
evaluated gas permeation properties of N2, 02 and C02
throughamonolayeroffoambubbles.Theydescribedthat
a monolayer of gas bubbles can be used to study gas
diffusivities,butthatproblemsmaybeencounteredcaused
bythetime-varyingsurfaceareaofthefoambubbles.The
work was reviewed by Markworth (1985)who comments on
Ostwald ripening and grain growth in foams and gives a
shortreviewonearlierstudies.NarsimhanandRuckenstein
(1986)usedafoamstabilitymodelnotonlycoveringgas
transport,butalsothesizedistributionofbubbles,film
ruptureanddrainageofliquidfilmsandPlateauborders,
in order to be able to describe foam behavior in foam
fractionationexperiments.
Yetanotherapproachtostudygastransportinfoamswas
mentioned recently by Stavans and Glazier (1989). They
appliedVonNeumanslawtodescribetherateofdisproportionation in a two-dimensional foam. Von Neumans law
states thatthedecreaseof thetotal surface areaofa
bubble is proportional to the number of sides of the
bubbleminus6.Thismeansthatbubbleswithsixsidesare
stable,bubbleswithmoresidesthan 6grow and bubbles
withlessthan6sidesshrinkanddisappear.
51
5.2.AimandApproach
Discrepancy between the presented models is clear and
none of the models is completely satisfactory owing to
assumptions made in the course of derivation. Also, in
general,themodelscanbeappliedtomodelsystemsonly.
For practical multicomponent systems the models are
inexact,mostlyoverestimatingtherateofgastransport.
A number of investigators have suggested explanations
fortheoverestimationof thegas transport rate,among
which are: (i) low gas-permeability of insoluble or
solublelayersatthefilmsurfaces,(ii)changesingas
composition,causedbyadifferent solubilityofthegas
components,(iii)nonequilibriumgasconcentrationatthe
bubble boundary, (iv)simplification of the topology of
thebubble,includingshape,effectivesurfaceareaofthe
bubbleand (theevolutionof)thefilmthickness,(v)the
neglectofthevaporpressureoftheliquidsolvent,(vi)
theformationofastructureatthebubblesurface,(vii)
theinfluenceofconvectionofthefilmliquidcausedby
liquiddrainageand (viii)highsurfaceviscosity.
Thestatementthatmostexistingmodelsoverestimatethe
rateofgastransportisalsosupportedbysimpleobservationofbubblessituatedataliquidsurface.Theobserved
radius-versus-timecurvesdonotalwayshavetheshapeof
a moreor less second orthird powerdependence assuggestedbysomeauthors.Instead,thesecurvesmayshowan
inflection point. This inflection point indicates that
transportofgasfromabubblecandecelerate.
A high surface viscosity may be responsible for this
decrease of the rate of disproportionation because the
compression of the bubble surface during the shrinking
processinasurfactantsolutionresults,inprinciple,in
a loweringofthesurfacetensionandthusinadecrease
ofdrivingforce.Anotherreasonfortheappearanceofan
inflectionpointisthepossiblepresenceofmorethanone
gaswithdifferentsolubilities.
Tostudytheeffectonbubbledissolutionofthesurface
dilationalviscosity andofthegascomposition,amodel
52
wasdevelopedandexperimentswerecarriedout.Theradius
ofbubbles,restingatabeer-gasinterface,wasmeasured
asafunctionoftime.Gassesofdifferentsolubilityand
beerswithdifferent surfacedilationalviscositieswere
used. The surface dilational viscosity of beers was
measuredwithaLangmuirtrough.
5.3.Theory
Here a new model is presented to give insight inthe
roleofthesurfaceviscosityandtheroleofchanginggas
compositionintherateofgastransportinfoams.Several
assumptionshadtobemadeinthecourseofthederivation
ofthemodel.Thelocalequilibrium suppositionwasmade
meaningthatthegasconcentrationatthebubbleboundary
issupposed tobeequaltotheequilibrium valueduring
theshrinkingprocessofthebubble.Thevaporpressureof
the solvent was neglected. Ward et al. (1986) clearly
described in which situations and circumstances these
assumptionsmayleadtoerroneousresults.Intheexamples
given here the vapor pressure is small compared to the
totalpressureinthebubbleandtheliquid filmsareso
thinthatthelocalequilibrium suppositioncanbemade.
Therefore, these assumptions have minor effect on the
outcomeoftheexperiments.
Also postulated is that the presence of an adsorbed
monolayer does not form a barrier for gas transport
(Princen (1967))andthatthediffusionintheliquidis
the rate determining step for gas transport through a
liquid film and not thetransition rateof thegasfrom
the bubble into the liquid surface. (Ward (1982b)). If
convectiondoesnottakeplace,transportofgasesthrough
the liquid layer isadiffusion controlled process that
canbedescribedwithFickslaw:
dntot
6c
BA
dt
[5.3]
6z
53
In Eq. [5.3],ntot isthetotalamountofgas,Aisthe
total area,c is the activity of thegas,and z isthe
distance over which diffusion takes place. Now, the
presence of more than one gas is incorporated into the
model.Assumingthatgasesbehavethermodynamicallyideal
and that gases are distributed homogeneously throughout
thebubble,Ficks lawmaybeapplied toeachgas (i)in
thesystem:
dn t
ôCi
= D±A
dt
[5.4]
6z
Forthinfilmstheconcentrationgradientoverthefilm
willbealmostlinear.InanalogytoDeVries(1958)ôc/ôz
canbewrittenas ^ct/i, where i isatopologyfactor.The
value of i depends on the position of the bubble. In
general, five situations can be distinguished: (i) the
bubbleissurroundedbyotherbubblesinafoam,(ii)two
bubbles are separated by a film and surrounded by an
infiniteamountofliquid,(iii)thebubbleiscompletely
surrounded by an infinite amount of liquid, (iv) one
bubblerestsataliquid-gasinterfaceand (v)thebubble
iscompletely surroundedbygas,onlyseparated fromthe
surrounding atmosphere by a thin liquid film. For all
thesesituationsadifferentinterpretationfor i mustbe
made, i thereforeisanadjustableparameter.Forthesake
of clarity fromnow on situation (iv)isdiscussed.The
atmosphere above the liquid is regarded as an infinite
largebubble,inwhichtheLaplacepressureiszero.The
situation canthusbedescribed asatwobubble system.
The i inthis system accounts forthe film thicknessof
thecapof thebubble,i.e. theliquid filmbetween the
submergedbubbleandthesurroundingatmosphere. $isalso
acorrectionparameter fortheeffectivediffusionarea.
Eg. [5.4]becomes:
54
dnt
A
= TD±
dt
iCi
[5.5]
*
With the aid of Henry's law, this last equation can be
writtenas:
dn4
A
BjSj
dt
APi
[5.6]
*
In Eg. [5.6] Sjis the solubility of gas i, and A P 4 is
thepartial pressuredifference ofgas iacross the film.
The value of ±P± depends on the Laplace pressure, the
atmosphericpressure (Patm), andthegascompositioninthe
bubble and in the atmosphere above the liquid. The gas
composition in the atmosphere will practically remain
constantduringthediffusionproces.Therefore,APJcanbe
writtenas:
*Pi=(P.t.+2a/r)(n1/ntot)-k±Patm
[5.7]
where the fraction of gas i in the atmosphere is k±.
Although theLaplacepressure (2a/r)issmallcompared to
theatmosphericpressure (Patm), itcannotbeneglected in
Eg. [5.7]. If the gas composition in- and outside the
bubble isequal (i.e.nj/n,.,,,.=k±)theLaplacepressure is
theonlydriving force forgasdiffusion.Substitution of
Eg. [5.7] in Eg. [5.6], and 4nr2 for the total diffusion
area (A)gives:
Dj Sj,4nx2
dnA
=
dt
[(Patn,+2o/r)(n1/ntot)-k ^ J
[5.8]
*
This equation describes the gas diffusion rate from a
bubble situated at a liquid-gas interface to the atmosphere if the surface tension of thebubble isconstant.
55
InanattempttoaccountfortheTheologicalbehaviorof
thebubble surfacethemodelcanbeextended. Tothisend
a mathematical expression is needed to describe the
rheological behaviorof thebubble surface.The shrinking
of aspherical bubble surface isanall-sided compression
where no shear occurs.To describe this surface behavior
the surface dilational viscosity (i]s)can be used since
thisparameter isvalid forcompression aswell asexpansionEg. [5.9]:
[5.9]
dlnA/dt
whereae is the equilibrium surface tension. Thevalue of
the relative surface deformation rate (dlnA/dt) is then
defined to be positive for expansion and negative for
compression. From experimental results it follows that
thesurfacedilational viscosity ofasurfactant solution
depends strongly onthevalueofdlnA/dt.Highercompression rates result in lower surface viscosities. Surfaces
arethus "shear thinning" (Prins (1976)).
Thesurfacedilationalviscositycanbedetermined using
a Langmuir trough equipped with barriers which can be
movedbymeansofacaterpillarbeltasdescribedbyPrins
(1986). Results from earlier experiments have shown that
forpractical systemssuchasmilkandbeerapowerlawcan
be used to describe the surface rheological behavior in
compression (Prins (1988)):
a =ae-10n(|dlnA/dt|) m t l
[5.10]
The absolute value of the surface dilational viscosity
depends strongly on the value of n. The shear thinning
behavior of thesurface ismainly characterized bym. The
disproportionation model can now be adjusted for dynamic
surfacepropertieswith the aid ofEg. [5.9]and [5.10].
The ideal-gasequationof stateofBoyleand Gay-Lussac
isused todescribe thetotal amountofgas inthe bubble
inrelation to thebubbleradius:
56
3
(P atm(2o/r))(!-nr
)
+
[5.11]
RT
During the derivation of the model, the atmospheric
pressureandtheLaplacepressureofEg.[5.11]gohandin
hand. The Laplace pressure is small compared to the
atmosphericpressureandcanthereforebeneglectedinEg.
[5.11]. The neglect of the expansion effect is also
discussedbyYung (1989).
Eg. [5.8],fordifferentgases,combinedwithEg.[5.9]
and[5.10]andthelawofBoyleandGay-LussacEg. [5.11],
can be numerically solved by an appropriate computer
techniqueinordertoobtainradius-versus-timecurvesand
theprevailing circumstances forshrinkingbubblesunder
differentconditions.
5.4. Experimental
ThesolutionofEg. [5.8], [5.9],[5.10]and [5.11]was
carried out on a VAX 8600 computer using Fortran as a
programminglanguageandstandardIMSLroutinestoperform
numericalintegration.Thenumericalintegrationgivesthe
radius,gascomposition,compressionrate,andthesurface
tensionasafunctionoftimeforgivenvaluesofm,n,r0,
ae, i, gascompositionetc.
ALangmuirtroughequippedwithacaterpillarbeltwas
used todeterminethesurfaceviscosity andthepowerlaw
parametersmandnofEg. [5.10].Thetroughisshownin
figure4.7.Surfacetensionsaresimultaneously measured
in the expanded and compressed area with the Wilhelmy
platetechnique.Therelativecompression rate(dlnA/dt)
wasvariedoverthreedecadesfrom5xl0-1to5xl0"4s"1.
Inadditiontosurfacerheologicalexperimentswiththe
caterpillar belt, single compression measurements were
carried out.Withasinglebarrierasurfaceareaof450
cm2wascompressedtoasurfaceof90cm2usingdifferent
speeds. The experiment was carried out to simulate the
57
compressionofthebubblesurfaceasgoodaspossibleand
to examine whether the predicted low surface tensions
couldbemeasured.(figure4.6).
@/
\
•
CAMERA
GAS
THERMOSTAT
Figure 5.1:Apparatus to measure the bubble radius as a function of time.
Bubble radius-versus-time curves were determined with
theapparatusshowninfigure5.1.Withasyringeneedle
bubbles(radius=±500um)wereproducedinatemperature
controlledvessel.Thesizeofthebubblesituatedatthe
liquid surface ismeasured asa functionof timewitha
macroscope unit and a camera. Gas conditions in the
atmosphereabovethebubbleiscontrolled usingconstant
flowofthedesiredgas,saturatedwithwatervapor.The
temperaturewasmaintainedat20°C.
The surface rheological experiments were carried out
witheightdifferentbeers (beerAto H). Tomeasurethe
bubbleradiuswithtimebeerE,GandHwereused.
5.5.Results
Inorder tobeabletodeterminewhether theobserved
decelerationofthebubbledissolutionandtheoccurrence
58
ofaninflectionpointintheradius-versus-timecurveis
causedbychangesingascompositionorbysurfaceTheologicalproperties,modelcalculationswerecarriedoutwith
severaldifferentgascompositionsandsurfacedilational
viscosities.
300
250
200
r
a
f 150
u
s
< um)
co2
NN2
100
50
4000
0
8000
12000
time ( s )
16000
20000
Figure 5.2: The influence of gas solubility on the bubble dissolution rate.
Figure5.2showsthelargeeffectofthegassolubility
onthebubbledissolutionrateofabubble,situatedata
gas-liquidinterface.Thesolubilityofcarbondioxidein
water is about 50 times higher than the solubility of
nitrogen. The initial bubble radius is 300 um and the
topology factord=10urn.Theequilibrium surfacetension
is40mNm"1.Thegasabovetheliquidsurfaceisidentical
to the gas in the bubble. Surface viscosity has little
effect on both bubbles since the values of m=-0.9 and
n=-1.9 express very low surface viscosity. A carbon
dioxide bubble, situated at a liquid surface under a
carbondioxideatmosphere,disappearsmuchquickerthana
nitrogen bubble under a nitrogen atmosphere. The gas
solubilityclearly isaveryimportantparameter forgas
diffusionprocesses.
59
300
250
200
r
a
d
1
" 150
s
<um)
100
nitrogen content of atmosphere:
50
1 0%
\sx\ i
v
C
200
400..
time
°^^o1 :::ï:: cr a *=^__
( s ) 600
800
1000
Figure 5.3: The influence of the gas composition in the atmosphere on the radius of a
carbon dioxide bubble.
Figure 5.3 illustrates the effect of two gases with
differentsolubilityinthesurroundingatmosphereonthe
disproportionation behavior of carbon dioxide bubbles
havinganinitialradiusof300urn.Theviscosityofthe
bubble surface is very low and does not influence the
shrinking rateof thebubble. Ifnitrogen is introduced
intotheatmosphereabovethecarbondioxidebubble,the
shapeoftheradius-versus-timecurvechangesdramatically. ThedrivingforceinthiscaseisnotonlytheLaplace
pressure,butalsoadifferenceinpartialgaspressure.
Carbon dioxide diffuses outward rapidly, because the
partialcarbondioxidepressureintheatmosphereislower
thaninthebubble.Nitrogendiffusesinwardbecausethe
partialnitrogenpressureintheatmosphereishigherthan
inthebubble.Thediffusionrateofnitrogenhoweveris
much lower than the diffusion rate of carbon dioxide
becausethesolubilityofnitrogenismuchlower.Therefore,initiallythebubbleshrinksrapidlyuntilthegas
compositionsinsideandoutsidethebubblearepractically
equal. Then,the gasdiffusion ratedecreases abruptly,
andtheLaplacepressurebecomestheonlydrivingforce.
60
1400 r
1200
^~~^-^^nitrogen content in the bubble
^^^
"~^-^^^
at t=0:
1000
""•—.
r 800
d
s 600
( um)
—
- - ^ ^ ^ 10055
^—^60%
^"\40%
•B
\20S5
400
^""v\^^
^-v^
^S.
^^
\ 1055
200
v. 555
o%\\i%
i
0
•
i\
. \,
i .
500
i \ i
•
l
i\ i
1000
1500
2000
time <s>
2500
3000
Figure 5.4: Behavior of N 2 /C0 2 bubbles with low surface viscosity under a C 0 2
atmosphere.
Tofurtheremphasizethatthegascompositioninsideand
outsidethebubbleisanimportantparameterfortherate
ofgasdiffusion,figure5.4 showsaradius-timediagram
for a bubble containing varying percentages of carbon
dioxideandnitrogen.Theatmospherecontains100%carbon
dioxide.Thebubblehaslowsurfacedilationalviscosity.
Ifabubblecontainsnitrogenitstartstogrowagainst
theLaplacepressurebecausediffusionofcarbondioxide
inward proceeds much faster than diffusion of nitrogen
outward. (The values of m and n of the powerlaw were
adjusted for expansion inorder todescribe the surface
rheological behavior of the expanding bubble surface).
This process continues until again the gas compositions
in- and outsidethebubbleareequal.Then,the Laplace
pressureremainsasthedrivingforceofgasdiffusionand
thebubblestartstoshrink.
Toillustratetheroleofthesurfaceviscosity ingas
diffusion,examplesaregiveninfigure5.5ofresultsof
calculations on carbon dioxide bubbles situated at a
liquidsurface.Thegasphaseabovetheliquidsurfaceis
alsocarbondioxide.Theinitialbubbleradiuswas300urn.
The surface dilational viscosity is characterized by
61
m=-0.9andthevaluefornvariesbetween-1.9and-1.15.
Theequilibriumsurfacetensionwaschosen40mNm"1.
300 rw
250
•y
\.0« inflectionpoint
200
1
r
a
d
u ISO
s
(pm)
\
100
>-
^ v powerlawn-values!
\
50
• -i
i
9
-1.5
\-l-2
^ s ^
L \-1.25 \
1-1.3\
\
^->^
^-~^
.........1
.
0
500
1000
1500
2000
time(s)
2500
3000
Figure 5.5: Calculated radius versus time curves of carbon dioxide bubbles situated at a
liquid-carbon dioxide interface. The bubbles have different surface dilational viscosities.
Table 5.1:Surface dilational viscosities for given values of n. m=-0.9, dlnA/dt=10 3 s 1.
(mNm -7 )
-1.9
-1.5
-1.3
-1.25
-1.2
-1.15
33.7
24.2
14.9
11.8
8.4
4.5
(rtiNsm"7)
6.3x10 +3
1.6x10+4
2.5x10 +4
2.8x10*4
3.2x10 +4
3.6x10 +4
Intable5.1valuesofthesurfacetensionandsurface
dilational viscosity at dlnA/dt=10
are given for
differentvaluesofn,illustratingthathighervaluesof
n represent higher surface dilational viscosities. The
value n=-1.9 is quite common for a low concentration
proteinsolutionwithsurfacesoflowviscosity.Ascanbe
seen in figure 5.5, the shapeof theradius-versus-time
62
curveisaboutthesameasfoundbyDeVries (1958,1972)
forsurfaceswithlowsurfacedilationalviscosity(n=-1.9
and n=-1.5).Heassumedthatthesurfacetensionremains
constant during the shrinking process of the bubble.
Results given infigure 5.6 show that, forn=-1.9,the
surface tension of the bubble has normal values for
compressed surfaces (25-30 mNm"1) at realistic bubble
sizes.
-
40
s
u
r
t
a
o 30
e
t
e
n
s
i
n 20
powerl«u n-values*
-1.9
—
-1.5,
'
(mN/m)
- 1 . 3 ^ -
10
'
'
•~^*\r^^~—"^Î72__
""^--—" "—~3Ii5——
0
0
50
100
150
radius <um>
200
250
300
Figure 5.6: Surface tension against radius plot of the bubbles presented in figure 5.5.
However, when the surface dilational viscosity is
increased (by means of increasing thevalue ofn),the
surface tension and the dissolution rate decrease. In
figure5.5,wheretheradiusisplottedagainsttime,an
inflection point is found for bubbles of considerable
size.Thesurfaceconditionsattheinflectionpointare
ofgreatinterestbecauseattheinflectionpointdisproportionationstartstoslowdownasshownintable5.2.
Fromthesedataitappearsthatfornvaryingfrom-1.9
to-1.15thevaluefortheradiusattheinflectionpoint
(rt)increasesby4ordersofmagnitude.Forn=-1.9and
n=-1.5 rt issosmall andthesurface deformation rate
(dlnA/dt)tissohighthatthereislittleeffectonthe
life-spanofthebubble.
63
Table 5.2: Conditions at the inflection point, m=-0.9.
n
-1.9
-1.5
-1.3
-1.25
-1.2
-1.15
^i
(dlnA/dtJi
ot
7
(fim)
(s" )
0.03
3.4
34.1
60.6
107.8
191.8
4.0x10 +4
4.0x10 +0
4.0x10" 2
1.3x10~2
4.0x10""3
1.3x10~3
(mNm"')
3.6
3.6
3.6
3.6
3.6
3.6
(T)s)i
(mNsm"7)
9.0x10' 4
9.0x10 +0
9.0x10 +2
2.8x10 +3
9.0x10 +3
2.8x10 +4
For higher values of n the bubble dissolution rate
clearly starts toslow down: (dlnA/dt)£ decreases by8
ordersofmagnitude.Becausethesurface tensionatthe
inflectionpoint (ai) isconstantforallvaluesofnthe
surfacedilationalviscosityattheinflectionpoint (T)S)±
increasesby8ordersofmagnitude.Thesurfacetensionat
theinflectionpointonlydependsonthevaluesofmand
aeandisindependentofthevalueofn,ascanbeseenin
Eg. [5.12]:
m+1
[5.12]
m+2
Although thecompression rate decelerates forhigher
surfacedilationalviscosities,verylowsurfacetensions
are found.Theselowsurface tensionshavenotyetbeen
measuredinpracticalsystems.Thepossibleoccurrenceof
verylowsurfacetensionshoweverwasdescribedearlierby
VandenTempeletal.(1983)andbyBoyleIII(1982).
What happens to the shape of the radius-versus-time
curveiftwogasesofdifferentsolubilityarepresentand
surfaceviscosityishigh,isshowninfigure5.7,where
thegascomposition inthebubbleischosen100%carbon
dioxideandintheatmosphere60%carbondioxideand40%
nitrogen.Theviscosityofthebubblesurfacewasaltered
byvaryingnbetween-1.9and-1.1.Ifthegascomposition
of theatmosphere andofthebubble arenotequalthe
bubblevery rapidly shrinks.Under these conditionsthe
64
250
200
r
a
d
i
u
s150
(um)
enlargement figure 5.8
100
powerlaun-values:
-1.1
50
0L-l
1000
1500
2000
tin»<s>
2500
Figure 5.7: Influence of the surface dilational viscosity on gas diffusion of a C0 2 -bubble
under a 60% C 0 2 and 40% N 2 atmosphere.
110 r
105
>^
'•
'
r
a
d
i
< um)
100
95
90
-
85
-
1.5
2.5
2
3
t i m e <s)
Figure 5.8: Enlargement of the inflection point of figure 5.7, showing that surfaceviscosity
has little effect on gas diffusion when the gas composition i n - and outside the bubble is
unequal.
surfaceTheologicalaspectsdonotplayanimportantrole
ingasdiffusionasshowninfigure5.8,whereanenlargement is displayed of figure 5.7 of the area where the
rapid decrease inbubble radiuschanges abruptly intoa
65
much slower decrease.That isroughly speaking whenthe
bubblewithinaveryshortperiodshrinksfromabout110
umtoabout90pm.Fromfigure5.8itappearsthatinthis
transitionzonethebehaviorofthebubbleradiusdoesnot
verymuch depend on thesurfaceviscosity.When thegas
composition in-and outside thebubble hasbecomeequal
the Laplace pressure becomes the driving force for gas
diffusion and therefore therheological behavior of the
bubble surface determines the bubble shrinking rate.At
longertimes,thesurfaceviscosityplaysaveryimportant
roleinthedecreaseofthebubblesizeascanbeseenin
figure5.7.
Figure 5.9: Surface rheological behavior in compression of beer E,C, and H, determined
with a Langmuir trough equipped with a caterpillar belt, plotted as a powerlaw.
Figure 5.9 shows the results of the caterpillar belt
experiments carried out for threedifferent beers.Over
the three decades measured, the powerlaw adequately
describesthedependencyofthesurfaceviscosityonthe
compression rate. Beer E has a clearly lower viscosity
thanbeerGandHascanalsobeseenintable5.3where
thepowerlawvaluesofmandnaregivenforallbeers.
66
Table 5.3: Powerlaw m and n values for the eight different beers as measured with the
caterpillar belt method.
Beer
A
B
C
D
E
F
C
H
m
-0.97
-0.96
-0.99
-0.95
-0.96
-0.97
-0.90
-0.91
-1.74
-1.80
-1.81
-1.74
-1.78
-1.73
-1.50
-1.48
Figure 5.10: The dynamic surface tension of different beers asa function of compression.
The original surface area of 450 cm 2 is compressed to 90 cm 2 in 4.5 s.
Differences between the surface rheological behavior of
thedifferentbeersbecomeevenmorepronounced withthe
singlecompressionexperimentasshowninfigure5.10.The
surface tension of beer G and H becomes very low in
compression.ThesurfacetensionofbeerH,aftercompressionuntil20%oftheoriginalsurfacearea,isaslowas
8.8 mNirf1.This indicates that the surface tension of a
67
shrinkingbubbleinthisbeersamplemayalsobecomevery
lowincompression.
Infigure 5.11 theshrinking rateof acarbon dioxide
bubble,situatedatabeersurfaceunderacarbondioxide
atmosphereisdisplayed.Theshapeofthecurveforbeer
E issimilar totheshapeofcurves found earlierbyDe
Vries.Theradius-versus-timecurveshowsapproximatelya
squarerootdependency.Thisobservation isinagreement
with theexpectations,becausebeer Ehas alow surface
viscosity andonlyonegas,carbondioxide,waspresent.
Theobserved radius-versus-time curvecanbewellfitted
withthemodelasshowninfigure5.11.Thevaluefor $,
used tofittheobserved radius-versus-time curvewas10
um,whichisoftheexpectedorderofmagnitude.
600
500
r
a
d
i
s 400
^"^"^^w"
(um)
300
BEERE
200
100
\
'
0
200
400
600
time
800
1000
1200
1400
Figure 5.11: Radius versus time curves for a carbon dioxide bubble at a beer-carbon
dioxide atmosphere. The beer has low surface viscosity. I measured values, - model
calculations.
Thedisproportionation rateofacarbondioxidebubble
under anitrogen atmosphere instead of a carbon dioxide
atmosphereisshowninfigure5.12.Thecalculatedradiusversus-time curve can be well fitted on the measured
valueswithlJ=35urn.Asaconsequenceofahighercarbon
68
dioxidegradientoverthefilmbetweenthebubbleandthe
surrounding atmosphere the diffusion of carbon dioxide
fromthebubbleoutward isaccelerated.Atthesametime
nitrogen diffuses into the bubble because there is a
nitrogengradientoverthefilmaswell,onlyinward.The
diffusion of nitrogen however goesmuch slower, because
thesolubilityofnitrogenismuchlowerthanthesolubility of carbon dioxide. The result is that the bubble
initially shrinksrapidly,untilthegascompositioninandoutsidethebubblehasbecomeequal.
600
500
r
a
d
i 4°°
s
(um)
300
1
200
-
iOO
-
\ BEER E
u
0
10
20
30
40
50
60
time <s)
Figure 5.12: Radius versus time curve for a carbon dioxide bubble situated at a
beer-nitrogen interface. The beer has low surface viscosity. I measured values, - model
calculations.
In the case, given in figure 5.12, the bubble, that
initially contained carbon dioxide, within about 10
seconds contains only nitrogen. Thereafter, the bubble
willvery slowlydisappearbecausethenitrogengradient
overthefilmdependsonthesolubilityofnitrogenandon
the Laplace pressure.After ca. 13xl03 s, thebubble is
completelydissolvedaccordingtocomputercalculations.
Thebubbleradiusbelongingtotheplateauvalueinthe
radius-versus-time curve,thatisreached afterabout10
seconds, depends mainly on the gas composition of the
69
bubble and theatmosphere. This iselucidated in figure
5.13,wheretheinitialnitrogenfractioninthebubbleis
plottedagainstthequotientofthevolumeofthebubble
when the plateau value is reached (Ve)and the initial
bubblevolume (V0). Ve/V0 isproportional to the initial
nitrogenfractioninthebubble,givingevidencethat,in
effect, carbon dioxide diffuses outward and nitrogen
diffuses inward and that the diffusion is driven by
partialpressuredifferences.
/
1 r
•
0.6
.
•
0.6
0.4
y /
•
Si
-
0.2
n
•
y^
//•
\S^
0
0.4
0.6
nitrogen fraction
0.2
1
0.8
Figure 5.13: A plot of the quotient of the bubble volume at the plateau value and at t=0
plotted against the nitrogen fraction initially present in the bubble.
Table 5.4: Powerlaw n-values determined by model fitting and by the Langmuir trough with
caterpillar belt method (m=-0.9).
method
model fitting
caterpillar belt
beer E
beer C
beer H
-1.95
-1.82
-1.15
-1.50
-1.10
-1.48
In figure 5.14t h eeffect o f t h esurface v i s c o s i t y o n
g a s d i f f u s i o n i sdisplayed. A c a r b o n d i o x i d e b u b b l e u n d e r
a c a r b o n d i o x i d e atmosphere i nbeer E d i s a p p e a r s i n about
70
1200secondsasdisplayedalsoinfigure5.11.Asimilar
bubbleinbeerGhoweverdisappearsmuchslowerctf=5urn).
600
500
r
a
d
i400
s
\B
(um)
^>v
300
\
•>w
200
N;
1BEER E
100
-
BEERS
\ ^ .•
•
0
2000
4OO0
6000
m
10000
8000
time <s>
Figure 5.14: Radiusversus time curves for carbon dioxide bubbles. Beer Ehas low surface
viscosity and beer C has high surface viscosity. I measured values, - model calculations.
600
500
r
â
'F
i400
s
(um)
300
\
300
•
BEERE
100
N. .
\
i
BEERH
•
•
•
0
0
4000
8000
12000
16000
•
20000
time (s)
Figure 5.15: Radiusversustime curvesfor carbon dioxide bubbles. Beer Ehas low surface
viscosity and beer H has high surfaceviscosity. I measured values, - model calculations.
71
The curve has an inflection point as predicted by the
model forhighsurfaceviscosity.Theshapeofthecurve
changesfromconvextoconcave.Bothcurvescanbefitted
withthemodelcalculations,withdifferentvalues forn
asshownintable5.4.ThebubbleinbeerGshrinksmuch
slower than the bubble in beer E, because the surface
viscosityofbeerGishigherthanthesurfaceviscosity
ofbeerE.AsimilarplotismadeforbeerEandbeerHas
showninfigure5.15.Heretheobservedshapeofthecurve
forbeerHisdifferentfromtheshapeofbeerEandbeer
G. Theobserved shrinking rateof thebubblecannotbe
fitted with themodel,whatever values form and n are
chosen(l)=5 urn).
Figure 5.16: A series of photographs, taken atcertain time intervals, representing the dissolution
of a beer Ebubble and the appearance of a bubble ghost. The size of the ghost is ±25 /jm.
72
Apossibleexplanationforthisunusualbehaviormaybe
thatsomesortofinsolubleskinformationoccursatthe
bubblesurfaceasaconsequenceofsurfacecompression.In
figure5.16 aseriesofphotographsdisplaysashrinking
bubble. It can be clearly seen that by compression an
insolubleskinisformedatthebubblesurface.Theskin
collapses and a bubble ghost appears. This structured
bubbleskinmaydecreasethedriving forceofgastransport.Whenhoweverthebubblesurfaceseparates fromthe
structuredskin,gasdiffusionmayaccelerateagainanda
newskinmaybeformed.Theaccelerationofgasdiffusion
at t=13xl03 scoincides with the first observation ofa
bubbleghostseparatedfromthebubblesurface.Thiskind
ofsurfacerheologicalbehaviorappearstobequitecommon
in multicomponent systems (Sebba (1987)). Anderson and
Brooker (1988)described theoccurrenceofbubbleghosts
in milk and Johnson and Cooke (1980) have carried out
bubbledissolutionexperimentsinseawaterandtheyhave
shownpicturesofbubbleghostsverysimilartothebubble
ghostsfoundinbeer.
5.6.Discussion
Fromtheresultspresentedinchapter5.5,ithasbecome
evidentthatthedifferencesincompositionofatwophase
systemaremostimportantforthedisproportionationrate
inthatsystem.Therateofgasdiffusioninfoamsdepends
mostly on adifference inpartial gaspressures and gas
solubilities. Differences in gas composition in- and
outside bubbles result inrapid gasdiffusion untilgas
compositionin-andoutsidethebubblesbecomesidentical.
UnderconditionsofuniformgascompositiontheLaplace
pressure difference is the only driving force for gas
diffusion.Thisdrivingforcemaybecomeverylowwhenthe
surfacetension decreases farenough asa resultof the
compressionofthebubblesurface.Thesurfacetensionof
the bubble surface becomes very low when the surface
73
dilationalviscosity ishigh.Thismaycause bubblesto
persistmuchlongerthanexpected fromearliermodels.
Even thepresented model however may overestimate the
rateofdisproportionationbecausethepowerlaw (Eq. 5.10)
isnotexactlydescribingtherheologicalbehaviorofthe
bubblesurface.Thepowerlawdescribesthesurfacerheologicalbehaviorofasurfaceundersteady-statecompression
conditionsanddoesneitheraccountforthehistoryofthe
bubblesurfacenorfortheabsolutevalueofcompression.
Thesinglecompressionofabubblesurfaceisatransient
phenomenon,wheresteady-state isneveraccomplished. In
otherwords,notonlythecompressionrateofthebubble
surface isimportant,butalso the total amount ofcompression.Generally,totalcompressionofthesurfaceof
a shrinkingbubbleishighbecausethesurfaceareaofa
bubbleisproportional tothesquareoftheradius.This
mayresultinanevenlowersurfacetensionthanexpected
from the caterpillar belt experiments. Thus, a lower
Laplacepressurewillprevailunderpractical conditions
thanwaspredicted by thepowerlaw. These lastconsiderationsmake itvery likely that the disproportionation
rate of bubbles depends very much on the rheological
behaviorofthebubblesurfaceifthegascompositionis
uniform.
Therateofdisproportionation ismainlydeterminedby
thegeometry of thebubbles,thegascomposition inthe
bubblesandthesurfacerheologicalaspectsoftheliquid.
The geometry parameter iJ used to fit the measured
radius-versus-time curvesvariesfrom5umforfitsover
a longer period of time to35um for fitsover ashort
periodoftime.Apparently, i isnotconstantaspresumed
inthemodel.Duringtheexperimentthefilmthicknessof
thebubblecapdecreasesmorethantheeffectivediffusion
area. The total effect is that $ decreases with time.
Nevertheless,itappearstobeverywellpossibletofit
observedcurveswiththemodelusinganaverage"#.
74
Theeffectofthegascompositionontherateofdisproportionationasfoundwithmodelcalculation,isconfirmed
experimentally.Thegassolubility isvery importantfor
the rate of gas diffusion. When more than one gas of
different solubility is present in a system, rapid gas
diffusion will take place until the gas composition is
equalthroughoutallgascompartments.Thismayhavegreat
influenceonfoambehaviorandbubble-sizedistributions.
Theeffect,thatsurfacerheologicalparametersmayhave
ontherateofgasdiffusion,isalsoconfirmedexperimentally.TheLaplacepressureisthegoverningdrivingforce
forgasdiffusionifthegascompositionin-andoutside
thebubbleisequal.Thereforegasdiffusionfrombubbles
depends strongly on the surface tension of thebubble.
Duringgasdiffusion,thebubbleshrinksandthesurface
iscompressed.Consequentlythesurfacetensiondecreases.
Thedynamic surfacetensionprevailingundercompression
conditionsdependsonthesurfacerheological properties
of the bubble. Important parameters determining the
dynamic surface tension of the bubble are the surface
dilationalviscosity,thecompressionrateofthesurface,
thehistoryofthebubblesurfaceandtheabsoluteamount
ofcompression.Thethreeexperimentalmethods,described
in this chapter, induce different surface compression
behavior, because the parameters mentioned above differ
foreachmethod.
The surface compression during the actual event of
bubbledissolutionisatransientphenomenon.Thecompressionratevarieswithtimewhiletheabsolutecompression
increases in an unpredictable way until the surface is
completely compressed. Steady-state compression is not
achieved.Thehistoryandtotalcompressionofthesurface
is important in addition to the compression rate. The
deformation of the bubble surface is determined by the
parameters of the system. E.g. high surface viscosity
slowsdownthesurfacedeformationrate.Unfortunatelyit
isnotpossibletodescribethistransientphenomenonwith
mathematicalformula,andthereforeitisnotpossibleto
75
deriveamodelthatcompletelysatisfactorydescribesthe
disproportionationbehaviorofbubblesinafoam.
The single compression experiment carried out in a
Langmuir trough simulates the actual shrinking of the
bubblesurface.Howevertheabsolutecompressionandthe
compression rate are not equal in both situations. The
absolutecompression of abubble surface,generally, is
higher than the maximum absolute compression in the
Langmuirtrough.Respectively100%and80%oftheoriginal
surface is compressed. Therefore, it may be speculated
thatthesurfacetensionofthebubblebecomeslowerthan
canbemeasured intheLangmuirtrough.Inaddition,the
decreaseof the surface tension depends strongly onthe
compressionrate,becausevisco-elasticsurfacesaretime
dependentasaconsequenceofrelaxationprocesses.With
the single compression experiment the barrier is moved
linearly, and therefore dlnA/dt increases during the
experiment.
Inaddition,thecompressionexerted tothesurfacein
the Langmuir trough is not without shear, whereas the
compression of the bubble surface is pure all-sided
dilation. The shear forces might influence the results
obtainedwiththeLangmuirtrough.
From a physical point of view the single compression
experimentisapoorlydefinedexperiment.Amathematical
expressioncannotbegiventhatdescribestherheological
behavior ofvisco-elastic surfaceson thebasis ofthis
experiment.
On the other hand, the caterpillar belt compression
experimentisphysicallyratherwelldefined.Althoughthe
dlnA/dt isnot entirely constant during theexperiment,
becausethebarriersmovelinearlyandbecausetheyarea
certaindistanceapart,astationary-statecompressionis
accomplished. The surface dilational viscosity can be
determinedatvariouscompressionrates,andthepowerlaw
parameters m and n can be calculated. The experimental
results, obtained with the caterpillar belt experiment,
can be used to derive a diffusion model that includes
76
surface Theological aspects as has been proposed in
chapter5.3.
Taking these considerations into account it is not
surprisingthatthepowerlawparametersmandnfoundwith
thecaterpillarbeltexperimentdonotcoincidewiththe
parametersfoundwiththedissolvingbubblemethodandthe
model calculations as shown in table 5.4. The simple
reason for this deviation may be that the powerlaw,
althoughitratherwelldescribestherheologicalbehavior
ofsurfacesinthecaterpillarbeltexperiment,doesnot
accurately characterize the rheological behavior of the
shrinkingbubblesurface.However,combiningresultsfrom
thebubbledissolutionexperiment andmodelcalculations
ithasbeenmadeveryclear that the surface tensionof
the shrinking bubble surface may become very low. In
additiontheformationofaninsolubleskinmayoccurat
thebubblesurfacecausedbythecompressionofthebubble
surface. It can be concluded that gas diffusion from
bubblesmaybeverymuchinhibitedbythesurfacerheologicalbehaviorofthebubble.
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ColloidandInterfaceSei.18:281 (1983).
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EffectsofFoamControlbyDispersed NaturalOilonMass
TransferinaBubbleColumn."Eur.Congr.Biotechnol.3rd,
Volume3,VerlagChemie:Weinheim,WestGermany,pp.521.
(1984).
Vrentas, J.S., Vrentas, CM., J. Chem. Phys. 77:5256
(1982).
Wagner,C , Z.Electrochem.65:581 (1951).
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Ward, CA., Findley, R.D., Rizk, M., J. Chem. Phys.
76(11):5599 (1982a).
Ward, C A . , Rizk, M., Tucker A.S., J. Chem. Phys.
76(11):5606 (1982b).
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53(9):6076(1982°).
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Ceram.Soc.63(7-8):435(1980b).
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80
BEERFOAMPHENOMENA
Thefourphysicalprocesses,bubbleformation,drainage,
coalescenceanddisproportionation,influencethebehavior
ofbeer foaminadifferentway.Inthischapterseveral
foamphenomenawillbediscussedandexplainedintermsof
thesephysicalprocesses.
6.1.Thecreaminessofthefoam
Oneofthefirsteye-catchingphenomenaofbeerfoamis
thecreaminess.Creaminess isafoamcharacteristicthat
is determined by the appearance, by the rheological
propertiesandbythemouthfeelofthefoam.Acreamyfoam
isbelievedtobepreferredbytheconsumer.
Creaminess is a foam property that is difficult to
define.Creaminessisafoamcharacteristic,thatdepends
mainly on the bubble-size distribution, on the liquid
fraction and the whiteness of the foam. A homodisperse
size distribution of small bubbles is desired for a
suitablecreaminess.Inaddition,thefractionofliquid
inthefoammustbehigh,becauseitfacilitatestheflow
propertiesofthefoam.
Thecreaminessofthefoamdoesnotremainconstantwith
time. The initial creaminess is determined by the way
bubble formation takes place. Therefore, creaminess is
mainlydetermined byheterogeneousbubblenucleationand
growthandthemomentofbubbledetachment.Asdescribed
inchapter 2,theparametersthatinfluencethisprocess
are, amongst others, the carbon dioxide content, the
dynamic surface tension of the beer under expansion
conditionsandconvectionduringthedispenseofthebeer.
Thisexplains,amongstothers,thatbeerdispensed froma
tap appears to be more creamy than beer poored from a
bottleorcan.Sincethereismoreconvectioninthetap,
thebubblesproduced fromthetaparesmaller.
81
The creaminessof the foam after a certain period of
time depends on the rate of drainage, coalescence and
disproportionation. As a consequence of these processes
the fractionof liquid inthe foamdecreases and larger
bubbleswillappear.Thebubble-sizedistributionbecomes
widerandthecreaminessofthefoamdecreases.
Abeerfoamwithsmallbubblesisfavored.Thewaybeer
is dispensed influences the size of the bubbles. Beer
shouldthereforebedispensedinsuchamannerthatsmall
bubblesareproduced.
6.2.Theriseofthefoam-liquidinterface
Theriseofthefoam-liquid interfaceis,primarily,a
resultofdrainage.Coalescenceanddisproportionationdo
notdirectlyaffecttheriseofthefoam-liquidinterface.
However,theseprocessesincreasetherateofdrainageand
therewith indirectly the rate of the rise of the foamliquidinterface.
Simple calculation gives insight in the importance of
thisphenomenon.Thesituationisconsideredthattheonly
processoccurringinthefoamisdrainage.Supposethata
foaminitiallyis3cmhigh,andcontains60%gasand40%
liquid. For fresh beer foam these figures are quite
realistic.Alsosupposethatasaresultofdrainagethe
foam contains 90% gas and 10% liquid after a certain
periodoftime.Then,thefoamheightis2cm.Thetotal
foamheighthasdecreasedbyathird.Thedecreaseinfoam
heightmaytakeplaceinabouttwominutes,dependingon
variousparameters,liketheviscosity.Thismeansthatby
drainage alone, the foam volume can partly disappear
whereasthetotalbubblevolumeremainsthesame.
6.3.Theinfluenceoftemperature
Beerfoamismorestableatlowtemperaturesasmeasured
withaRudintube(figure8.2).Thisphenomenoncannotbe
82
easily explained since the influence of temperature is
many fold. The temperature has a dominant effect on
variousotherparametersthatinfluencestherateofthe
fourphysicalprocesses.Atlowtemperaturethesolubility
ofthegasishigher,theviscosityofthebeerishigher,
the(dynamic)surfacetensionishigherandthedensityof
gasishigher.
The nucleation of bubbles is greatly affected. As a
result of a higher solubility of the gas the number of
bubbles that nucleate becomes less. In addition, the
bubbleswillbecomesmallerbecausethebubblegrowthrate
decreases.
Drainageisinfluenced bythechangeinviscosity.The
drainagerateisbelievedtobeinverselyproportionalto
viscosity (Eg.[3.1])andthereforedrainagewillproceed
sloweratlowertemperature.Ascanbeseeninfigure8.3
thedrainagerateasmeasuredwithaRudintubeisproportional to theviscosity, ifviscosity ismanipulated by
varyingtemperature.
Thedirecteffectoftemperatureoncoalescenceisnot
well known. When film rupture occurs according to the
spreadingmechanism,coalescenceisincreasedasaresult
of the increase of bulk viscosity. In addition, the
surfacetensionofbeerishigheratlowertemperatureand
therewith the spreading of surface active material and
thusfilmrupturemaybeenhanced (seechapter4).
The effect of temperature on gas diffusion is by its
indirecteffectonthedensityofthegas,thesolubility
of thegas,and thesurfacetension.Thedensity ofthe
gasisinverselyproportionaltotheabsolutetemperature
andwillthereforehardlycontributetodifferencesinthe
rateofgasdiffusion.Thevariations insurfacetension
asaresultofvariationsintemperaturearerathersmall
comparedtothevariationsingassolubility.Asaresult
gas diffusion and disproportionation will proceed more
rapidlyatlowertemperatures.
Themostimportanteffectoftemperatureisbelievedto
betheeffectonbulkviscosity.Atlowtemperaturesthe
viscosityoftheliquid ishigherandthereforedrainage
83
proceeds slower. Consequently, the beer-foam interface
risesslowerifthetemperatureislower.Inaddition,the
films between the bubbles remain thicker. This brings
about thatcoalescence becomes less likely and that the
rate of disproportionation decreases. Summarizing the
aboveconsiderations,theconclusionmaybedrawnthatat
lowertemperature lessfoamappears,butthatitismore
stableagainstbreakdownprocesses.
6.4.Thecoarseningofthefoam
Coarsening of the foam means that the bubbles in the
foam become larger. Consequently, the appearance of the
foambecomeslessattractive.Coarseningofthefoamcan
becausedbyeithercoalescenceorbydisproportionation
within the foam. These processes however have to occur
withinthefoam,becauseiftheyoccuratthetopofthe
foamcoarseningdoesnottakeplace.Insteadthefoamwill
collapseasdiscussedinchapter6.5.
Thecoarseningofthefoambycoalescencewillproceed
somewhatdifferentthanthecoarseningbydisproportionation. As a result of coalescence only larger bubbles
appear, while as a result of disproportionation also
smaller bubbles appear.The smaller bubbleshowever can
hardly be seen by the naked eye and consequently the
general impression of thecoarsening phenomenon will be
equalforbothphysicalprocesses.
Drainage only influences the coarsening of the foam
indirectly. By drainage the film becomes thinner and
therefore the chance that coalescence occurs increases.
Disproportionation willproceedmorerapidlyasaresult
ofdrainage,becausethediffusiondistancedecreases.
6.5.Thecollapseofthefoam
Foam collapse is the reduction of foam height. Foam
collapse ismainly theresult oftheescapeofgasfrom
84
the foam. Gas escapes from the foam either when gas
diffuses from theupperbubble layer tothe surrounding
atmosphereorwhenthefilmbetweenabubbleintheupper
layerandthesurrounding atmosphereruptures.Thefinal
resultinbothcasesisthatthefoamheightreduces.
By simple observation of the upper bubble layer, it
appears that,under normal conditions,coalescence does
notmuchcontributetofoamcollapse.Thebubblesinthat
layerappeartobestableagainstcoalescence.Onlywhen
external surfaceactivematerialisadded (chapter4)or
whenlargerairbubblesrisetothetoplayerofthefoam
(chapter 6.7) coalescence may occur.However, innormal
situations,thisdoesnothappenveryoften.
Incontrast,gasdiffusionfromthefoamtothesurrounding atmosphere takes place rapidly. As described in
chapter 5forasinglebubble,thedriving forceforgas
diffusion fromtheupper layerof the foam ishigh asa
consequenceofthedifference ingascompositionbetween
theinteriorofthefoamandthesurroundingatmosphere.
Partialgaspressuredifferencesashighas1Bardominate
the gas diffusion process because initially the bubble
containsonlycarbondioxideandtheatmospherecontains
practically only nitrogen and oxygen. Therefore, carbon
dioxide will diffuse outward and nitrogen and oxygen
inward.However,thesolubilityofnitrogenandoxygenis
much lower than the solubility of carbon dioxide.Since
thediffusionrateisalsodeterminedbythesolubilityof
thegas,carbondioxidediffusesoutwardmorerapidlythan
nitrogenandoxygeninward.Theresultisthatthebubble
intheupperlayerofthefoamshrinkstoabout2%ofits
originalvolume.Thisshrinkingprocessdoesnottakemore
than several seconds (figure 5.12). Thereafter, thegas
composition in and outside the bubble is the same.The
only driving force for the diffusion of nitrogen and
oxygenoutwardagainistheLaplacepressure.TheLaplace
pressurehoweverisverylowbecausethesurfacetension
ofthebubblehasbecomeverylowasaconsequenceofthe
shrinking process. In addition, an insoluble layer of
surface active material may be present at the bubble
85
surface(figure5.16).Forthesereasonsthegasdiffusion
outward will proceed very slowly. The small air bubbles
in the top layer of the foam will be relatively stable
againstgasdiffusionoveralongperiodoftime.
Asaconsequenceoftheshrinkingofbubblesinthetop
layerofthefoam,bubblesfromthenextlayercancometo
the surfaceof the foam. Thesebubblesare subjected to
exactly the same diffusion process and they shrink to
about2%oftheiroriginalvolumeaswell.Thisseriesof
eventswillrepeatitselfoverandoveragain,untilall
bubbleshaveshrunken,oruntilthetoplayerisentirely
filledwithsmallairbubbles.
Gas diffusion from the top layer to the surrounding
atmosphereisnottheonlygasdiffusionthattakesplace
as a consequence of partial pressure differences. In
addition,upwardcarbondioxideanddownwardairdiffusion
from and tothe layersunderneath thetop layeroccurs.
Thepartialpressuredifferenceswillpenetratethefoam.
However,thediffusionofgasthroughvariouslayers,and
thus through various liquid films,will proceed slower
than diffusion from the top layer to the surrounding
atmosphere.
Anorderofmagnitudecalculationcangiveinformation
abouttheimportanceofgasdiffusion fromthetoplayer
ofthefoamforthecollapseofthefoam.Supposethatgas
diffusion is the only process that takes place in the
foam,andthatcoalescencedoesnotoccur.Afoamof3cm
height,inaglasswithadiameterof6cmisconsidered.
Supposethegasfractionisinitially0.6andallbubbles
haveaninitial radiusof 200urn.Inthatcasethefoam
contains approximately 1.5 million bubbles distributed
overabout100layers.Ifthebubblesinthetoplayergo
throughthediffusionprocessuntiltheirvolumeisabout
2%oftheiroriginalvolume,thentheareatheyoccupyin
thesurfacebecomesaboutl/14thoftheoriginalarea.This
meansthat,after14layersofbubbleshavebeensubjected
to the diffusion process, the surface is completely
occupiedwithshrunkenairbubbles.Thebubblesoriginally
presentin14layersare,afteracertainperiodoftime,
86
presentinthetoplayer.Afterthat,diffusionofgashas
totakeplaceoveralongerdistanceandthroughmorethan
one liquid film and will therefore proceed slower. The
process will repeat itself over and over again for all
bubble layers,but the rate of gas diffusion decreases
becauseinthecourseoftheprocessdiffusionhastotake
placethroughmoreandmorelayers.Whenallbubbleshave
gonethroughthediffusionprocessthefoamwillconsist
ofabout7layersofbubbleswitharadiusofabout50um.
Theheightofthefoamwill thenbe0.4 mm,taking into
accountthatthegasfractioninthefoamhasbecome0.9.
Theultimateresultofthisdiffusionprocessisverymuch
inagreementwiththepracticalobservationthataftera
certainperiodoftimethefoamhascollapsed,butthata
singlelayerofverysmallbubblesappearstopersiston
topofthebeer.
Fromthesecalculationsitcanbeconcludedthatabeer
foam canalmost completely collapse as aconsequenceof
gasdiffusion.Itisamazingthatithappenswithoutthe
disappearance of a singlebubble.Thenumber of bubbles
does not change and remains 1.5 million bubbles in the
abovegivenexample.
Iftherapidcarbondioxideandairexchangethrougha
single foam film takes 1 second (chapter 5.5),and if
every14layersoffoambubblesbecomesonelayerinthe
courseofthediffusionprocessinaconsecutiveway,the
100layersofbubblescollapseinabout400seconds.This
is a result of the fact that layer after layer goes
throughthediffusionprocess.Thetotalcollapsetimeof
thefoam isthe sumofthediffusion timesrequired for
alllayers.Itbecomesapparent,thatthetotalcollapse
timeofthefoam isvery susceptibletotherateofthe
diffusion process through a single film.An increaseof
0.1 second indiffusiontimeforasinglebubbleresults
inanincreaseofabout40secondsinfoamcollapsetime
intheabovegivenexample.Itmaybeconcluded thatthe
collapseproceedswithintheaverageconsumptiontimeof
theconsumer.
87
The observation that smaller bubbles give better beer
foambehaviorcannoweasilybeexplained.After14layers
ofsmallbubblesshrunkento2%oftheiroriginalvolume
less gas has diffused out of the foam than when the
bubbles would have been larger. In other words, a foam
that contains smaller bubbles also containsmore layers
andthereforethesameamountofgasmustdiffusethrough
morelayersifthefoamcontainssmallerbubbles.
Thepracticalobservation,thatthebubblesinthetop
layer of the foam are much smaller than the bubbles
underneath,canbeunderstoodwiththeknowledgeofthis
gasdiffusionprocess.
Nowalsotheobservation,thatanitrogenfoamismuch
morestableagainstcollapsethanacarbondioxidefoam,
canbeexplained. Gasdiffusion from anitrogen foamto
thesurrounding atmosphereproceedsmuchslowerthanthe
diffusionofcarbondioxide,becausethepartialpressure
differences and the solubility of nitrogen are much
smaller.Infact,ifthefoamcontains100%nitrogenand
the surrounding atmosphere is air (80% nitrogen, 20%
oxygen), the foam expands. In that case, the partial
pressure differences for oxygen and nitrogen are equal
(0.2P atm ),butthedirectionofthegradientisopposite.
Thesolubilityofoxygenisabouttwicethesolubilityof
nitrogen.Therefore,twotimesmoreoxygendiffusesinward
than nitrogen outward. Consequently, the size of the
bubblesinthetoplayerinitiallyincreasesandthefoam
level rises.Thisphenomenon cannotbeobserved bythe
nakedeye,becausetheincreaseisverysmall.
A little amount of nitrogen in apredominantly carbon
dioxidefoamalreadygreatlyimprovesthestabilityofthe
foamagainstcollapse.Ifnitrogenispresentthebubbles
shrinkmoreslowly.Inaddition,thebubblesdonotshrink
rapidly until 2% of the original volume. Instead, the
transition from rapid gas diffusion, driven by partial
pressuredifferences,toslowgasdiffusion,drivenbythe
Laplacepressure,willbeatalargervolume.Thismeans
thatlessareawillbecomeavailableforthelayerunderneaththetoplayertocometothefoamsurfaceandalso
88
thatitwilltakelonger.Therefore,theoverallcollapse
of the foam will be significantly slowed down. This
explainswhy theaddition ofnitrogen tobeer issucha
successful way to improve head retention times,Carroll
(1979), Kuzniarski (1983), Butterworth (1983), Hedderick
(1984).
Acarbondioxidefoamunderacarbondioxideatmosphere
ismorestableagainstcollapsethanacarbondioxidefoam
underanitrogenatmosphere.Ifacarbondioxideblanket
coversthebeerfoam,thediffusionofcarbondioxideis
driven only by the Laplace pressure and not by large
partialpressuredifferences.Therefore,gasdiffusionis
comparatively slow, and the foam ismore stableagainst
collapse.Thebubblesinthetoplayerofthisfoamremain
larger than when the surrounding atmosphere contains
nitrogen(comparefigure5.11and5.12).Theappearanceof
the foam therefore is lessattractive if carbondioxide
coversthefoam.
A last observation gives evidence that foam collapse
takes place by the described gas diffusion mechanism.
Afterfoamcollapse,amonolayerofsmallbubblesremains
on the beer surface for a long period of time. If foam
collapsetakesplacebycoalescence,asforexampleisthe
case if spreading material is added to the foam, all
bubbles disappear. In that case, the monolayer of very
small airbubbleswill notremainonthesurfaceofthe
beer.Thebeerthenappearstobecompletely flat.Thus,
a very easy distinction between foam collapse by gas
diffusionandbycoalescencecanbemadethisway.Bygas
diffusion bubblesbecome smaller and remain on thebeer
surface. By coalescence the bubbles become initially
largerandthendisappearcompletely.
Coalescence does apparently not takeplace in thetop
layerofthefoam.Thisconfirmsthehypothesispostulated
inchapter4,thatcoalescencemainlytakesplaceiffilms
areexpandedandthedynamicsurfacetensionishigh.The
compressed bubble surfaces inthe top layerof thefoam
arenotverysusceptibletocoalescence.
89
6.6.Cling
Clingisthephenomenonthatapartofthefoamadheresto
thewallwhentheupperlevelofthefoamdecreases.The
firstobservationmadeisthatthegasdiffusionprocess
ofcarbondioxideoutwardandairinwardisessentialfor
the deposition of cling. The small bubbles at the foam
surfaceadheremorestronglytothewallthanlargerones.
Theabilityofbubblestoadheretothewallandtostick
togetherappearstobedependentontheshrinkingofthe
bubble.Thisisconfirmedbyanexperimentcarriedoutby
Glenister at al (1966). When a glass is covered with a
glass plate and the foam is allowed to collapse, no
bubblesadheretotheglasswall. Inanequalglassthat
isnotcoveredandcontainsthesameamountofbeerfoam,
clingisformed.
Whenasipistakenfromtheglass,theshrunkenbubbles
in the upper layer turn to the wall. Apparently, they
sticktogether.Somewhereatsomearbitraryplacebreakage
occursinthetoplayer.Thebondbetweenthebubbleand
theglasswallseemstobestrongerthanthebondbetween
bubbles.
As a result of cling the foam collapses in an uneven
way.Next totheglasswall aring-shaped depression in
the layer of small air bubbles appears as a result of
cling.Thereforegasdiffusionofcarbondioxidefromthe
foamislocallyacceleratedthere.Asaconsequence,foam
collapses more rapidly near the glass wall than in the
middle of the glass. Consequently, a small heap-shaped
buildupoffoammayappearinthecenteroftheglass.
6.7.Theinfluenceofairentrapment
Asdiscussed inchapter2.1foambubblescanbeformed
by agitation. While dispensing beer into a glass, a
plungingmotioncanbeproduced.Asaresultairbubbles
comeintothebeerfoam.Ingeneraltheseairbubblesare
largerthanthecarbondioxidebubbles.Asimilarpartial
90
pressuredifferencebetweentheairbubblesandsurrounding carbon dioxide bubbles is present as between the
surrounding atmosphereandthecarbondioxidebubblesin
the top layer of the foam.Consequently, carbondioxide
diffusion takes place into the air bubble. Very minor
amountsof air diffusestothebubbles inthe immediate
periphery of the air bubble. The air bubbles suck the
carbon dioxide from the surrounding bubbles and become
larger.Thebuoyancy forceoftheselargeaircontaining
bubbles increases and consequently they may risetothe
surface. As a result the foam becomes less attractive.
Also these bubbles may coalesce. In this manner gas
escapes from the foam. Entrapped air bubbles can thus
contributetofoamcollapsebytransportingcarbondioxide
totheatmosphereabovethefoam.Therefore,thewaythat
beer ispoured outcanmakealotofdifference forthe
behaviorofthefoam.Asarule,airentrapmentshouldbe
avoided.
6.8.Theinfluenceofchemicalcomposition
Foams, with the same chemical composition, may have
differentfoambehavior.Theessenceofthisstatementis
thatinafoamthechemicalcomponentsmaybedistributed
throughout the foam in a different way. Three examples
willbegiven.
Two foamswith exactly the samechemical composition,
but with different bubble-size distributions may behave
different.Thecreaminessof the foam and thereforethe
appreciationoftheconsumerwillbedifferent.Ingeneral
thefoamwiththesmallerbubblesisfavored.Inaddition,
the foam with smaller droplets is more stable against
collapsebygasdiffusionasexplainedinchapter6.5.
Twofoamswiththesamechemicalcomposition,containing
thesameamountofnitrogen,canhaveadifferentcollapse
behaviour. The onlydifference between the foamsmaybe
that in one foam all nitrogen in enclosed in a single
bubble,whereasintheotherfoamthenitrogen isevenly
91
distributedthroughoutthebubbles.Thecollapseofafoam
containing a single nitrogen bubble can be enhanced as
explained in chapter 6.7. When all bubbles contain the
sameamount of nitrogen however,the foam is stabilized
againstcollapse.
When two foamshave thesamechemical composition and
contain the sameamount of lipid material,thenegative
effectofthislipidmaterialonthebehaviorofthefoam
may be different. This difference can be caused by the
fact that the lipid material inone case is present as
droplets,andintheothercaseismolecularlydissolved.
Lipid dropletscaninitiatecoalescenceandthusenhance
foamcollapseenormouslyasexplained inchapter4.When
lipid material is dissolved a relatively small negative
effectonfoambehaviorcanbeobserved.
References
Butterworth,M.J.,TheBrewer69:407 (1983).
Carroll,T.C.N.,Tech.Quart.MBAA16(3):116 (1979).
Hedderick,J.B.,TheBrewer70:116 (1984).
Kuzniarski,J.N.S.,TheBrewer69:362 (1983).
Glenister,P.R., Segel,E.,Koeppl,K.G.,ASBCProc.pp.
150 (1966).
92
BEERFOAMSTABILITY
Thepoordefinitionoffoamstabilityhasoftenleadto
misunderstandingsandconfusionoftongues.Thereforethe
need of an appropriate and straightforward definition
arose soonafter thebeginning of thisresearch work on
beerfoam.Howevertheefforttoredefinetheconceptof
foam stability has failed. The main reason for this
failure is that the word stability can only be used in
relationtoasingleproperty,i.e.amomentarymeasurable
characteristic,ofasystem.Therefore,itispossibleto
define the stability of a single foam property. Foam
itself is not a property but a system that has various
propertieslike:(i)totalvolume(ii)theamountofgas,
(iii)theamountofliquid,(iv)bubble-sizedistribution,
(v) distribution of bubbles throughout the foam, (vi)
optical properties likecolour and shine, (vii)several
rheological properties like viscosity and elasticity,
(viii)organolepticalproperties,and(ix)temperature.
Aqueousfoams,onceformed,areinthermodynamicterms
unstable.Consequently thephysicalprocesses,drainage,
coalescenceanddisproportionationtakeplace.Thismeans
thatthefoampropertieswillvaryasafunctionoftime.
Everysinglefoampropertyhasitsownstability.
Thestability ofabeerfoamproperty indicateshowthis
propertyvariesasafunctionoftime.
Afoammayhaveverystableandunstableproperties.It
isimpossibletodefinefoamstability.Stability,itself
isnotapropertyeither,becauseitcannotbemeasured
momentary.Therefore,foambehaviorcannotbeexpressed
withasinglefoamnumber.Unfortunately,different foam
numbersmustbemeasured toobtainacompletepictureof
the behavior of the foam. This will be discussed in
chapter8inmoredetail.
Itmaybedifficulttoacceptforthebrewing industry
thatfoambehaviorcannotbeexpressedwithasinglefoam
93
number.Ofcourse,thedesireforsimplicitydominatesin
thedaytodaypracticeofbrewing.
A way to elucidate the argument, that a single foam
number cannot expresstheoverall foambehavior, isto
comparefoambehaviorwithtaste.Itisgenerallyaccepted
that a single taste number can not be given. Always a
singletasteproperty,likelightstruck flavour,bitterness,oroneofthenumerousothertastes,ismeasuredand
presentedseparately.Anenormouseffortismadebylarger
breweriestotestthetasteofbeerinallitsaspectsand
detail. The use of taste panels is common practice.
Chemical analysis are continuously carried out on many
identifiedtastecomponentswithsophisticatedequipment,
likeGLCandHPLC.Eveniffoambehaviorisnotascomplex
astastetheanalogyisperfect.Theonlydifferenceis,
that it is not generally accepted that for the proper
characterizationoffoamasimilareffortshouldbemade.
Inaddition,theinterpretationoftastenumbersismore
orlesscommonknowledge,while,incontrast,theinterpretation of different foam numbers is not. In other
words,theavailableknowledgeaboutfoambehaviorisvery
limitedcomparedtotheknowledgeabouttaste.
94
8.MEASUREMENTOFFOAMBEHAVIOR
8.1.Introduction
Inchapter 6 and 7 itwas concluded that theoverall
behavior of a foam can not be measured with a single
apparatus,norcanitbeexpressedbyonefoamnumber.An
argument in favorof this statement isthat anenormous
amount of methods and procedures have been proposed to
determinefoamcharacteristics.Inpractice,beerfoamis
measuredwithseveralreadilyavailablemethods.TheBlom
method,theRudintubeandtheNibemfoamstabilitytester
areamongthemostwellknownexamples.
The method described by Blom (1934)is based on the
measurementoftherateofliquiddrainagefromthefoam.
With this method degassed beer is put in a separation
funnel and carbon dioxide is diffused into the beer
throughaporcelaincandleinordertoproduceacertain
amountoffoam.Theseparationfunnelisthenplacedona
balance.Theliquidthatdrainsfromthefoamisseparated
from the foam and directed away from the balance to a
separatecontainer.Thedecreaseoftheweightofthefoam
ismeasured atcertaintimeintervals.Blom (1934)found
that the rate of drainage can be described as a first
orderkinetic.Afterashortlagperiod,thelogarithmof
theweightofthefoamisproportionaltotime,following
thenextempiricalequation:
Wt=W0e"kt
[8.1]
With theobtained results ahalf-life timeof the foam
canbedetermined:
ln2
t%=
[8.2]
whereWtistheweightofthefoamafteracertaintimet,
W0istheinitialweightofthefoam,kisaconstantand
95
t^isthefoamhalf-lifetime.
TheBlommethodisimproveduponandautomatizedinthe
CarlsberglaboratoriesasreportedbyRasmussen(1981)and
Rosendal and Rasmussen (1982). The apparatus can run a
measuringandrinsingprogramforthedeterminationof50
samples during normal working hours. The initial foam
volume and half-life timeof the foam are automatically
obtained.Oneoftheimprovementsmadeisthatthefoamis
nolongerproduced bydiffusingcarbondioxidethrougha
brittle porcelain candle. The candle is difficult to
replace by a candle that gives the same reproducible
results. Instead the foam is formed by pressing the
carbonatedbeerthroughanozzlewithwelldefineddimensions.Thefoamisthusproducedinasimilarwayasbya
tapinabar,and therefore itmaybeexpected thatthe
initialbubble-sizedistributionand thegascomposition
isalmost the sameasinpractical situations.With the
automated apparatus, different initial foam volumes are
produced and therefore also a "foamability" number is
obtained.The "foamability"numberdependsmainlyonthe
carbondioxidecontentofthebeer.Theinitialheightof
the foamand therising of the foam-liquid interfaceis
measuredwithaconductivityprobe.However,theprobemay
interfere with the physical processes occurring in the
foam.Forexample,theprobemayinducecoalescence.Ina
second generation apparatus,developed at the Carlsberg
research laboratories, the foam measurement with the
conductivity probe is replaced by anoptical technique.
Also the sampler has been improved upon. Nowadays, the
samples can be directly drawn from a large variety of
bottlesandtins.
TheRudintube,developedanddescribedbyRudin(1957),
isbasedonamethoddescribedbyRossandClark (1939).
ThesimilaritybetweentheRudintubeandtheBlommethod
is that with both measurements the rate of drainage is
obtained.TheRudintubeisalongtubeofsmalldiameter.
At the bottom of the tube there is a sintered glass
filter, through which a gas (e.g. nitrogen or carbon
dioxide)canbespargedintotheprimarilydegassedbeer.
96
The time, that elapses while the foam-liquid interface
risesbetweentwomarksatthelowerend of thetube,can
be taken as a characteristic foam number. Also a foam
half-life time or Head Retention Value (HRV) can be
defined. Instead of the weight of the foam (Eg. [8.1]),
theheight oftheliquid-foam interfacecanbetakenasa
measure of the drained liquid. Ross and Clark (1939)
defined a S-value for the rate of drainage from a foam.
Thedefinition of the2-valueisbased onthe logarithmic
relation between theamount ofdrained liquid andtime:
E=
[8.3]
2.303 log((a+b)/b)
where aisthevolumeof beerdrained from the foam and b
isthevolumeofbeerthatremained inthefoamattimet.
The E-valueisequal to1/k (Eg. [8.1]and [8.2]).
A Foam Flashing Value (FFV) was defined by Hudson
(1960). Afterthefoamwasproducedbyexpandingbeerwith
anorifice thedrainage of 200ml of foamwas measured.
200 (B2 - B J
FFV =
[8.4]
J
B,
2
whereBAistheamountofbeerthatdrainsfromthefoamin
90sand B 2isthetotalamountofliquid inthe foam. The
FFV is not often used in the brewing industry as a beer
foam characteristic.
Pierce and Pursell (1959) closely investigated the
validityoftheempiricalrelation [8.1], [8.2]and [8.3].
They found that these equations can only be used after a
certain time-lag, and within certain limits of time,
especially ifother gasses thancarbondioxide are used.
An explanation for the unusual behavior of different
gassesintheRudintubewasgivenbyBishopetal (1975).
He stated that the half-life time value of the foam is
very susceptible to impurities inthecarbondioxidegas.
The influence of these impurities can be explained with
97
differences ingas solubility (seechapter 6.5) andnot
withtheoccurrenceofoxidation.
Another explanation fordeviations of the logarithmic
relation between the rate of drainage and the time is
suggestedbyRossandCutillas(1955).Theystatethatthe
decrease of the total interfacial area in a foam as a
resultofgasdiffusionislogarithmicallyrelatedtotime
as well. The rate of liquid drainage depends on the
progressofthethreephysicalprocessesinvolved inthe
breakdownofthefoam,drainage,coalescenceanddisproportionation.Itmaybearguedthatinitiallydrainageis
themainprocess,and that at a later stage coalescence
and disproportionation become more important. The most
dominantprocessdetermineswhethertheempiricalrelation
of Eq. [8.1] or Eg. [8.3] is valid. Consequently, the
validity of theseequationsmayvery muchdepend onthe
timeintervalthatisusedtomeasurefoamdrainage.Ross
andCutillas(1955)explainedthatwithalighttransmissionmethodaseparationcanbemadebetweentheeffects
ofdrainageofliquidinfoamfromthatofgasdiffusion,
which causes a decrease of interfacial surface area.
SimilarresultswereobtainedbySegeletal (1967).They
stated that,assuming first-order kinetics,twostraight
lines can be drawn to fit a logarithm-of-drained-beer
versus time curve and two reaction constants can be
determined.Theyconcludedthatthetworeactionconstants
mustreflectonseparateprocesses.
AreviewontheRudindrainagetubetechniqueisgiven
byBamforth (1985). Herepeated thestatementofKlopper
(1954),thatresultsofdrainagemeasurementsmustbeused
with reservation because theconsumer assesses the foam
itselfandnotthedrainagerate.
TheuseoftheRudintubeorothermethodsbasedonthe
rateofdrainagehaveseveraldisadvantages.Thesedisadvantagesaremainlythatthefoamandthemeasurementare
verydifferentfromthepracticalsituationasobservedby
theconsumer.
(i)Thebeer isdegassed previous tomeasurement.The
samplesarethenspargedwithadifferentgasandfoamis
98
produced.Thegascompositioninthefoammaybedifferent
from thegascomposition inthepractical situation.In
thatcase,ameaningfulfoamnumberwillnotbeobserved,
even if the same phenomena could be assessed as the
consumerdoes.Forexample,theeffectofnitrogenationon
therateofbeer foamcollapsecannotbemeasured with
theRudintube.
(ii)IntheRudintubethebubblesareproducedthrough
aporousglassfilter.Therefore,theinitialbubble-size
distributioninthefoamis,amongstothers,determinedby
thegasflowrateandthesizeofthepores.Thisinitial
bubble-size distribution may bevery different from the
initial sizedistribution inpractice and therefore the
progressofdrainage,coalescenceanddisproportionation,
andthusthebehaviorofthefoammaybeinfluenced.The
effect of the initial bubble-size distribution on beer
phenomena, like creaminess and foam collapse,havebeen
described respectively inchapter 6.1 and 6.5. E.g. The
effectoftheinitialbubble-sizedistributionontherate
ofgasdiffusionwasalsodiscussedbyLemlich(1978)and
RanadiveandLemlich(1979).Bamforth(1985)alsostressed
that the method is very susceptible to the size of the
pores in the filter used to sparge gas bubbles in the
beer. Apparently, the initial bubble size in the Rudin
tubehasagreateffectondrainage.Thedrainagerateof
a foamwithsmallerbubblesappearstobelowerthanthe
drainagerateofafoamwithlargerbubbles.
(iii)Another drawback of the Rudin tube is that the
geometryofthetubeisverydifferent fromthegeometry
of a normal beer glass.Wall effects may influence the
breakdownof the foam. Therateofgasdiffusion tothe
atmosphere above the foam will be lower than in the
practical situation because the surface area is very
small.Thatthegeometryofthetubeisveryimportantfor
the obtained results is confirmed by Ross and Suzin
(1985), who carried out experiments incylindrical-and
conical-shapedvessels.
(iv)Thecompositionoftheatmosphereabovethefoamin
the Rudin tube will be different. The rate of carbon
99
dioxidediffusionfromthefoamtothesurroundingatmosphere as described in chapter 6.5. will be influenced.
Therefore,thefoamwillnotcollapseasinpractice.In
fact,thecollapseofthefoamisnotevenassessedwith
thismethod,sinceonlytherateofdrainageisobserved.
(v)IntheRudintubemuchfoamisproducedfromasmall
amountofbeerincomparisonwiththepracticalsituation.
Thismaymeanthatthesurfaceconcentration inthefoam
ofadsorptedsurfaceactivematerialissmallerthanina
practicalsystem.Thedepletionofsurfaceactivematerial
will influence the reliability of the measurement in a
negativeway.
TheRudintubetechniqueisthemostwidespreadmethod
used in the brewing industry nowadays. However, each
breweryhasmadeitsownmodificationanddefineditsown
procedures.Therefore,thenumberscannotbecomparedto
eachother.
Not allbeer foammeasurement techniques arebased on
the rate of drainage of liquid from the foam. Three
methods have been put forward that are based on the
measurementoffoamcollapse.Oneofthemethodsisknown
as themethod of De Clerck and De Dijcker (1957). With
this method foam is dispensed into a glass at standard
conditions. Afterwards, the collapse of the foam is
measuredbyfocussingamicroscopeontothefoamsurface.
Thesecondmethodisbasedonthemeasurementofvertical
transmissionoflightthroughthefoam.Withthismethod,
amongstothers,reviewed byWilsonandMundy (1984),the
total height of the foam is measured, because both the
riseofthefoam-liquidinterfaceandthecollapseofthe
foamcontributestoagradualincreaseoflighttransmission. A similar apparatus was described by Savel and
Basaravâ (1989) who used an optical glass detector to
measurethetransmissionoflight.Bymovingthedetector
theycouldseparatelymeasurethelevelofthefoam-liquid
interface and the foam height. They claimed that the
breakdown of foam can be described by a rather complex
empiricalrelation,thatwillnotberepeatedhere.
Themostwellknownmethodtomeasurefoamcollapseis
100
theNibemfoamstabilitytester.Themethodwasdeveloped
byKlopper (1977)andKlopperandVermeire (1977ab). The
foam is produced in a glass with a foam flasher. The
flasherworksverysimilartoatap,andisavailablefor
bottlesandtins.WiththeNibemfoamstabilitytesterthe
collapse of the foam in the glass is measured with a
conductivityprobe.Theprobefollowstheupperfoamlevel
asafunctionoftime.Thetimeelapsefrom1cmto4cm
below the top of the glass is measured every cm. In
generalthetotaltimeelapsefrom1cmto4cmistaken
as a measure for foam behavior. The method gives only
information about thecollapse of the foam. Information
about other beer foam phenomena is not obtained. In
general,thereproducability oftheresultsoftheNibem
foamstabilitytesterislowerthanthereproducabilityof
foam numbers obtained with the Rudin tube, although
controversial standard deviations are presented in the
literature(PiendlandLegat(1980),WackerbauerandGreif
(1980),Ulimann(1982)andWeyh (1988)).Fromexperience,
the reproducability of the Nibem foam stability tester
dependsmostlyonthecontrolofthetemperature,ofthe
cleannessoftheglassandofthegascompositionofthe
atmosphere surrounding theglass.Thetemperatureofthe
sampleispreconditionedat20°Cbuttheapparatusisnot
temperature controlled, and therefore the laboratory
temperaturecaninfluencetheoutcomeofthemeasurement.
Since the collapse of the foam is measured, the gas
diffusionfromthetoplayertothesurroundingatmosphere
andcoalescenceinthetoplayerofthefoamaremeasured.
Thecleannessoftheglassmayinfluencethecoalescence
rate, and therewith the collapse time as discussed in
chapter 4. The gas composition above the glass isvery
importantfortherateofgasdiffusiontotheatmosphere.
During foamcollapseacarbondioxideblanket settleson
topofthefoam.Asaresult,thegasdiffusionratefrom
the foam decreases.When the carbon dioxide blanket is
disturbedbyairturbulence,thecollapserateisaltered.
This effect on the foam collapse rate is so pronounced
thatthereproducabilityofthemeasurementmaydependon
101
the slamming of adoor, theopening of a window orthe
occasionalpassingbyofacolleague.
The Nibem foam stability tester was compared to the
Rudin tube method by Weyh (1987). In the same study,a
comparisonofbothmethodswithadispensetest,described
byPlank (1963),wasmade.Thismethodisverysimilarto
themethoddevelopedbyDeClerck andDeDijcker (1957).
Thedispensetestisbasedonthecontrolled,motor-driven
dispenseofbeerintoaglass,followedbythemeasurement
offoamcollapsewithamicroscope.TheE-values,obtained
withtheRossandClarkmethod,poorlycorrelatewiththe
Nibem number. The correlation depends very much on the
kind ofbeersthatareexamined. Thisisnot surprising
since,withthetwomethods,differentfoamsanddifferent
phenomena are measured under different conditions. A
somewhat better relation appears to exist between the
Nibemnumbersandtheresultsofthedispensetest.This
canbeexplainedbecause,inprinciple,thesamephenomena
aremeasured.Stillthecorrelationbetweenthemethodsis
notasgoodasmighthavebeenexpected.Thewaythebeer
ispoured intotheglassseemstoinfluencethecollapse
rateofthefoam.
Clingcanbemeasured with aphotocell that scansthe
glasswall,whereuponclingwaspreviouslyproducedunder
welldefinedconditions.Amethodbasedonthisprinciple
wasdescribedbyKlopper (1973).Aphotographictechnique
waspresentedbyGlenisterandSegel(1964)whoalsocame
upwiththeconceptofprimaryandsecondarycling.They
defined primary cling as the first ring obtained in a
glasswherebeerwaspreviouslysuckedoutatsuccessive,
regular intervals. Secondary cling is defined as the
consecutive rings. Although the first ring is always
largerthantheothers,ascanbeunderstoodfromchapter
6.6, there is no fundamental basis for the distinction
betweentwokindsofcling.Yetanothermethodtomeasure
clingwaspresented by Jackson and Bamforth (1982). The
cling can be produced in a similar way as described by
GlenisterandSegel (1964).Theclingisthenrinsedfrom
theglasswithwaterandtheabsorbanceat230nmofthe
102
resulting solution is then taken as a measure for the
totalamountofcling.
Althoughtheabovementionedmethodsandtechniquesgive
ampleinformationonfoamcharacteristics,evenmorebeer
foampropertieswerestudiedbyGlenisteretal(1966)and
Segelet al (1967). Theydiscussed methods toassesthe
whiteness of a foam, the density of a foam, the foam
strengthandthefoamviscosity.Thewhitenesscansimply
bemeasuredwithareflectometer.Thedensityofthefoam
isdefinedastheratiooftheliquidinthefoamandthe
foamvolume.Thedensityofthefoamisthereforeequalto
the liquid fractionof the foam and can be measured in
variousobviousways.Foamstrength (orrobustness)isa
measureforresistanceofafoamagainstexternallyadded
surfaceactivematerial.Understandardconditions,cetyl
trimethylammoniumbromidewasaddedtothebeerandfoam
characteristicsweredeterminedasnormal.Glenisteretal
(1966) measured the viscosity of the foam by dropping
glassbeadsthroughafoamcolumnandapplyingStokeslaw
asalsodescribedbyWaniskaandKinsella (1979).Forall
sortsofreasons,notdiscussedhere,theproperviscosity
of a foam isnotmeasured with thistechnique (see e.g.
Princen (1983)).However,theresultofthismeasurement
mayverywellbeagoodcharacteristicforthecreaminess
ofafoam.
Other method to establish foam characteristics are
described. However, they are not commonly used for the
characterization of beer foam.With thesemethods other
foampropertiesthandrainagerateorcollapseratecanbe
measured.
OneofthesemethodswasdescribedbyNishiokaandRoss
(1981,1983),Nishioka (1986).Themethod isbasedonthe
measurementofthepressurebuild-upinaconfinedvolume,
thatisaresultofthecoarseningofthefoam.Theloss
of total surface area with time can be related to the
pressureincreaseasdescribedbytheauthors.Therefore,
with these results quantitative information is obtained
about the combined progress of disproportionation and
coalescence.
103
Other methods are based on the measurement of the
conductivity of a foam.Chang and Lemlich (1980)stated
thattheratiooffoamconductivitytoliquidconductivity
isproportionaltotheliquidhold-upinafoam.Agnihotri
and Lemlich (1981) and Datye and Lemlich (1983) later
added that this relation is mostly independent of the
surfactantusedandtheinhomogeneityinbubblesize.The
sizeofthebubblessomewhatinfluencestheconductivity
of the foam. The conductivity of a foam with smaller
bubbles is lower than the conductivity of a foam with
largerbubbles.
Substantial research work hasbeendone on thedetermination of bubble-size distributions in aqueousfoams.
Thebubble-sizedistributioninfoamscanbedeterminedin
variousways. Forbeer foam,Glenister et al (1966)and
Segel et al (1967) described a method to measure the
bubble-sizedistribution.Thebubble-sizedistributionwas
measured from photographs takenof thetopof thefoam.
Thismethodmayadequatelygivethesizedistributionof
the bubbles in the top layer of the foam, but, as was
discussed inchapter 6.5,underpracticalconditionsthe
bubblesinthetoplayerofthefoamaremuchsmallerthan
the bubbles inside the foam. Therefore, the bubble-size
distribution of bubbles in the top layer by no means
represent the size distribution of bubbles inside the
foam.
Othermethodstomeasurethebubble-sizedistributionin
a foam are based on the measurement of observed bubble
diameters in a cross section of the foam. This cross
sectioncaneitherbeobtained byphotographing thefoam
throughaglasswallorbyfreezingandcuttingthefoam
(DeVries (1972)). Seleki and Wasiak (1984)described a
different method. With this experiment the foam is led
through a capillary, and the distance between the foam
films in that capillary is taken as a measure for the
bubble size.The method was used by Rieser and Lemlich
(1988)todeterminethegasdiffusionrateinafoamfrom
theevolutionofaninitiallybimodalbubble-sizedistribution.Thedeterminationofthebubble-sizedistribution
104
of a foam by measuring the chord length distribution
obtainedrunningaconductivityprobethroughagas-liquid
dispersion was described by Lewis at al (1984). They
calculated the bubble-size distributions from the chord
lengthdistribution,usingastatisticalmethodofThang
andDavies(1979).
8.2.AimandApproach
Withthemethods,describedabove,foamnumberscanbe
obtained. Here a modified Rudin tube, a modified Nibem
meterandtheoriginalNibemmeterwereused.Thesefoam
numbersgiveinformationabouttheprogressofoneormore
foamphenomenaasafunctionoftime.Insomecases,total
drainageismeasured,inothercasesfoamheight.However,
thesefoamnumbersareareflectionoftheoccurrenceof
oneormorephysicalprocesses.Sincetheprogressofthe
physical processes depends on the apparatus used, and
since different properties are measured with different
methods,thefoamnumbers,thatareobtainedwithdifferentmethods,do notnecessarily have tocorrelatewith
eachother,norwiththeconsumersassessmentofthebeer
foam behavior.With themethods formeasuring beer foam
characteristicsafoamnumberisobtainedthatisaresult
of some total effect of bubble formation, drainage,
coalescenceanddisproportionation.Ifitwerepossibleto
measuretheprogressofthefourphysicalprocessesina
foamseparately,abetterinsight inthecharacteristics
ofafoamcouldbeobtained.
Strictly,thereisonlyoneobjectivemethodtomeasure
foam behavior and that is to measure the bubble-size
distributionasafunctionoftimeandplace.Themeasurementoftheevolutionofthebubble-sizedistributionshas
not yet been used to make a distinction between bubble
formation,drainage,coalescence anddisproportionation,
although theoretically itmust bepossible.The initial
bubble-size distribution gives information about the
bubble formation process.Themeasurement of thevolume
105
fractionofliquidinthefoamasafunctionoftimeisa
measure for therateofdrainage.A distinction between
coalescence and disproportionation can be made because
there isa fundamental difference between theeffectof
coalescenceanddisproportionationontheevolutionofthe
bubble-sizedistribution.Onlylargerbubblesappearasa
resultofcoalescence,whereasdisproportionationresults
in both larger and smaller bubbles. Hence, a bimodal
distributionisobtainedinthelattercase.Adistinction
can be made between coalescence and disproportionation
usinggasesofdifferentsolubility.Therateofdisproportionationdependsverymuchonthegassolubility.By
usinggasesofdifferentsolubilitylikenitrousoxideor
carbondioxideontheonehandandnitrogenoroxygenon
theotherthedisproportionation ratecanbeinfluenced.
Coalescence willmostly be independent of theusedgas.
Therefore,usinggaseswithverydifferentsolubilities,
anestimatecanbemadeofthecontributionofdisproportionation and coalescence to the evolution of the size
distributioninafoam.
Inthischapteranewmethodtoassessanumberoffoam
phenomenawillbeintroduced.Themethod isbasedonthe
simultaneousmeasurementofthebubble-sizedistribution,
the levelof the foam-liquid interface and the levelof
thefoamheightasafunctionoftime.Thedrainagerate,
thechangesinthegasfraction,thefoamcollapserate,
andthechangesinfoamvolumearethusobtained.Inorder
tomeasureallthesefeaturesanopticalglass-fibreprobe
waspiercedthroughthefoamatconsecutiveintervals.The
resultsobtained with thenewmethod werecompared with
thebubble-sizedistributionsmeasuredwithaphotographic
method.
8.3.Experimental
Thecharacteristicsofbeerfoamwereassessedinthree
different ways. A Rudin tube, a Nibem foam stability
tester and a new method to measure amongst others the
106
bubble-sizedistributioninafoamwereused.
The Rudin tube was made of a temperature controlled
PharmaciaChromatographycolumn(600x25mm).Atthebottom
oftheinnertubeaG2-glassfilterwasmelted.Withthis
filterbubblesofapproximatelythesamesizeareproduced
aswhenabeer isdispensed fromabottle.Thebeerwas
degassedbyshakingregularlyinair.Priortomeasurement
thecolumnwas filledwiththesamegasasthegasthat
was used during the actual measurement. Then, 50ml of
beersamplewasputintothecolumnandfoamwasproduced
bysparginggas(C02orN2)intothecolumnuntilthetotal
systemhadreachedaheightof33cmabovethefilter.The
gasflowratewasmaintained at2.1xl0"6 m3s_1. Thetime,
thatelapseswhenthefoam-liquidinterfacerisesbetween
twomarks on the column (at 3and 8cm above theglass
filter), wasmeasured. Measurements were carried out at
25°C, unless indicated otherwise. The S-value, HRV, or
half-lifetimewerenotcalculated.
TheNibem foam stability testerwasused in twoways.
The firstway isexactly asdescribed by Klopper (1977)
andKlopperandVermeire (1977ab).Themodification,that
was also used, was made to enable the measurement of
previouslydegassedbeersamples.Inaglass,ofthesame
dimensionsasusedforthestandardmeasurement,100mlof
degassed beer was added. The foam could be produced by
diffusing gasthroughaporousG2-glassfilter.Only C02
wasused,becausethenitrogenfoamistoostableagainst
collapsetoallowreproduciblemeasurement.Thecollapse
rateofthefoamwasmeasuredwithaconductivityprobeas
usual,withtheexceptionthatduringthemeasurementthe
glass was covered with a small container to avoid air
turbulenceandtherewithtoimprovethereproducabilityof
themeasurement.
Thebubble-size distribution, the foam height and the
level of the foam-liquid interfaceweremeasured witha
newlydeveloped technique.Theapparatusisbasedonthe
useofanopticalglass-fibretechniquedeveloped atthe
TechnicalUniversity ofDelft,TheNetherlands (Frijlink
etal(1986)andFrijlink (1987)).Theapparatusconsists
107
of threemajorparts,asshowninfigure 8.1: firstlya
mechanism formoving the fibre up and down the foam at
knownspeed,secondlythefibreitselfcombinedwiththe
opto-electronic unit, and thirdly equipment for data
acquisition and for the calculation of the bubble-size
distributionsandotherfoamproperties.
MOTOR
GLASS-FIBRE
TTL SIGNAL
OPTO-
DATA
ELECTRONIC
ACQUISITION
UNIT
PROCESS1NG
Figure 8.1 : The optical probe method to determine bubble size distributions.
Fromtheopto-electronicunitlightisemittedintothe
fibre. The end of the fibre consists of a very small
rounded tip of diameter ca. 20urn,the diameter of the
fibreitselfbeing 200um.Theessenceof themethod is
thattheamountoflightreflectedatthetipofthefibre
dependsontherefractiveindexofthemediumsurrounding
thetip.Iftherefractiveindexofthemediumisapproximately the same as the refractive index of the glass
almostnolightisreflected.However,iftherefractive
index of the medium is much lower than the refractive
index of the glass, part of the light is reflected.
Therefore,whenthetipissurroundedwithgas,morelight
is reflected than when the tip is in liquid. A beam
splitterseparatesthereturningbeam;halfisreturnedto
108
thesource and lostand theotherhalf isreceived bya
light-sensitive cell and converted into an electronic
signal.Theopto-electronicunitalsocontainsaanaloguedigitalconvertertomakedataacquisitioneasier.
Onmovingthefibrethroughafoam,thatwasproduced
inanidenticalwayasforthemodifiedNibemmethod,an
alternating signal corresponding to gas and liquid is
obtained. If the speed of the probe is known (ca. 10
cms"1),thetimeintervalsofgasandliquidareameasure
forthebubble-sizedistributioninthefoam.Eitherthe
analogueorthedigital signalcanbeused tocalculate
thebubble-sizedistribution.
Withthecalculationofthebubble-sizedistributiona
problem similar to the 'tomato salad' problem is to be
solved.Theobservedone-dimensionalgaslengthsarenot
equaltotheactualthree-dimensionalbubbleradiibecause
a cross sectionofabubbleishardlyevermadethrough
two polar ends. Furthermore, bubbles of large diameter
have a greater chance of being pierced by the optical
probe than bubbles of smaller diameter. A statistical
method can be used to calculate the three-dimensional
bubble-size distribution from the one-dimensional chord
length distribution. Several methods are available for
this purpose (Thang and Davies (1979), Kawakami et al
(1988), Clark and Turton (1988), Ruan et al (1988)). A
method described by Weibel (1980) was used here. The
method makesuseof thegas fractionof the foam,which
follows from the measurement of the upper level of the
foam and the levelof the foam-liquid interface. Ifthe
experiment iscarried out atconsecutive time intervals
the rate of drainage, the collapse of the foam and the
changes in foam volume are detected in addition to the
evolutionofthebubble-sizedistribution.
The results of the optical glass-fibre method were
compared with a photographic method. In that case,the
bubble-sizedistributionswereobtained bymeasuringand
counting bubbles on a photograph taken through a glass
wall. The photographic method has several disadvantages
e.g. (i)theglasswallmight distort thebubbles, (ii)
109
the glass wall might enhance coalescence, (ill) the
bubblesat theglasswall arenotrepresentative ofthe
foambubbles,and(iv)themethodisverytimeconsuming.
Althoughthephotographicmethod hasthesedisadvantages
anorderofmagnitude comparison of bothmethodscanbe
made.
8.4.Results
Infigure8.2thedependenceoftheRudinfoamnumberon
temperature is displayed for beer E. It can be clearly
seenthatthefoamnumber,asmeasuredwiththismethod,
increaseswithlowertemperatures.
340
f
° 320
m
C 30O
E
r 280
'
-
(i>
260
240
'•
220
•
200
':
0
5
10
IS
20
temperature <°C)
25
30
Figure 8.2: The foam number asa function of the temperature measured with the Rudin
tube.
This is incorrespondence with expectations.With the
Rudin tube drainage is measured. Because the rate of
drainageisproportionaltobulkviscosity(Eq.[3.1])and
becausebulkviscosityincreaseswithlowertemperatures,
analmostlinearrelationshipbetweenthetemperatureand
theRudin foam number canbeexpected. From thisresult
theconclusioncanbemadethatthefoamnumberobtained
110
withaRudintubeverymuchdependsonthebulkviscosity
ofthebeerunderinvestigationandonthetemperatureof
themeasurement.
340
r
t
0
a
m
n
m
b
e
r
0 >
300
0 /
...«"
(s)
260
220
/o
• - * ' '
1.2
/
1.4
1.6
1.8
2
v i s c o s i t y (mNsm~2>
2.2
2.4
Figure 8.3: The foam number as a function of the viscosity, measured with the Rudin
tube. The viscosity was adjusted with temperature (•••) and with dextran (—).
Inordertoestablishwhethertemperatureisrelatedto
theRudinfoamnumberbyitseffectonbulkviscosityonly
or by its effect on other parameters as well, thebulk
viscositywasalsoincreasedwithdextran.Thefoamnumber
ofthesampleswasagainmeasuredwiththeRudintube.In
figure 8.3 the results are given. As can be seen the
relation between the foam number and thebulk viscosity
shows a linear correlation when the bulk viscosity is
variedbymeansofthetemperature.Thelinearrelationshipbecomes lesspronounced when thebulk viscosity is
increasedbyaddingdextran.Inadditiontheslopeofboth
linesisdifferent,givingevidencethatmoreparameters
than only the bulk viscosity influences the rate of
drainage. In addition, there is not a good correlation
betweenthebulkviscosityandtheRudinfoamnumberwhen
measuredwithdifferentbeersascanbeseenintable8.1.
However,thelinesinfigure8.3 showmorethanenough
similaritytoconcludethatthebulkviscosityofthebeer
111
is a very important parameter for the foam number
determinedwiththeRudintube.Theobservationthatbeer
foam is more stable at lower temperatures can thus be
explained (seealsochapter6.3).
Intable8.1thefoémnumbersobtainedwith7beersare
displayed asmeasured with theNibemmeter andwiththe
Rudintube,usingcarbondioxideandnitrogen.Inaddition
thebulkviscosityofthebeersisgiven.
Table 8.1:Foam numbers for various beers asdetermined with the Rudin tube with C 0 2 and
N 2 and with the standard and modified Nibem foam stability tester.
beer
A
B
C
D
E
F
C
Rudin C 0 2
Rudin N 2
(s)
(s)
142
235
206
250
241
293
273
643
757
633
715
727
654
722
1
(mNsm"2)
1.21
1.34
1.34
1.29
1.34
1.34
1.32
Nibem
modifiedNibem
(s)
(s)
175
215
224
254
278
137
92
108
165
163
176
285
422
Thereappearstobeaverylargedifferencebetweenfoam
numbersdeterminedwithcarbondioxideandnitrogen.With
nitrogen much higher foam numbers areobtained.Mostly,
drainage and coalescence appear to occur in a nitrogen
foam.Disproportionation willproceed very slow,because
the solubility of nitrogen is low. In a carbon dioxide
foamdisproportionation willcontribute significantly to
the amount of liquid drainage, because gas diffusion
proceeds rapidly as a result of the high solubility of
carbondioxide.Consequently,muchlowerfoamnumbersare
foundforcarbondioxidefoams.Apparently,disproportionationcontributesindirectlytodrainageandistherefore
animportantprocessforthefoamnumberasmeasuredwith
theRudintube.TheupperlevelofthefoamintheRudin
tuberemainsthesameformostbeers.Therefore,coalescence does not seem to be an important process inbeer
foam.
The foam numbers, determined with the modified Nibem
112
foamstabilitytester,arelowerthanthenumberswiththe
standard Nibem meter. This must be a consequence of the
difference in bubble formation. The bubbles produced by
the foam flasher are smaller than the bubbles produced
with the porous glass filter. The difference may also be
explained by a difference in gas composition. With the
standard Nibem method the foam contains the original gas
of the beer, whereas with the modified Nibem method
purified carbon dioxide isused.
Thebeersallhaveapproximately thesamebulkviscosity
exceptbeerA and toalesserextent beer D. Thismust be
one of the main reasons that the foam numbers for beer A
are low compared to the foam numbers of theotherbeers.
From the obtained foam numbers, in particular from the
numbers obtained withtheRudintubeusing carbon dioxide
and the standard Nibem method, it may be concluded that
theoverall behaviorof the foamof beerA isverypoor.
Beer B very rapidly collapses as can be concluded from
the results obtained with both the standard and the
modified Nibem foam stability tester. Even in the Rudin
tube foam collapse can be observed for beer B. In the
Rudintubetheupper levelof thefoamof theother beers
remains almost atthe initial height.TheRudinnumber of
beerB,measuredwithnitrogen,isextremelyhigh,meaning
that coalescence does not contribute to the collapse of
the foam toa largeextent.Therefore, therapid collapse
measured, when carbon dioxide was used, must be a result
ofgasdiffusion.ThefoamnumberofbeerB,obtained with
thestandard Nibem foam stability tester ishigh compared
to the number, obtained with the modified Nibem foam
stability tester. This can only be explained if the
original gas of beer B contains less soluble gas, that
stabilizes the foam againstcollapse.
The foam behavior of beer C is comparatively poor. In
particular, thefoam number,obtained with theRudin tube
using nitrogen, is lower than the foam numbers of the
other beers.Thismustbearesultof coalescence and not
of drainage, because the bulk viscosity of beer C is not
lower than the bulk viscosity of the other beers. It
113
appearsthatinthefoamofbeerCmorecoalescenceoccurs
thaninthefoamoftheotherbeers.
The foam numbers of Beer D and E are rather normal,
although the standard Nibem foam number for beer D is
somewhatlow.Thismaybearesultofthecompositionof
theoriginalgas.ThebulkviscosityofbeerDissomewhat
lowerthanthebulkviscosityofbeerE.
ThenumbersofbeerFarealsorathernormalalthoughit
appears that more coalescence and less gas diffusion
occursinthisfoamthaninthefoamsofbeerDandE.
BeerGhasunusual high foamnumbersasmeasured with
bothNibemmethods.Thiscanbeexplained bytheextreme
highsurfacedilationalviscosity incompressionandthe
abilitytoformbubbleghostsasexplainedinchapter5.5.
AfterbeerGwasdegassed,thebeerwassomewhatturbid.
Thisphenomenonwasnotobservedbyusingtheotherbeers.
TheliquidofbeerGcancompletelydrainfromthefoamif
thefoamisprotectedagainstcollapsebyacarbondioxide
blanketontopofthefoam.Inthatcase,adry,aerated
structure remains after drainage.Thecreaminessof the
foambecomesvery lowand thecolorof the foambecomes
grey-brownwithinashortperiodoftime.Thecollapseof
thefoamisunevenandtheappearanceofthefoamisnot
very attractive. In the case of beer G, the high foam
numberscertainlydonotrepresentgoodfoambehaviorfrom
aconsumerpointofview.
Figure8.4showsthebubble-sizedistributionofafresh
beer E foam generated by sparging nitrogen through a
G2-glassfilterwithwelldefinedpores.Thefoamisalmost
homodisperse directly after generation and the bubbles
haveameanradiusofabout100pm (notethatthenumber
ofbubblesisplottedonalogarithmicscale).
Figure8.5showsthesamefoam,butthreeminuteslater.
The bubble-size distribution has widened and the mean
bubbleradiushasincreased.Mostimportantistheobservationthatnobubbleshavebecomesmaller,meaningthat
disproportionationdidnotoccur.
Usingcarbondioxideinsteadofnitrogenpracticallythe
samebubble-sizedistributionisobtained directly after
114
generationofthefoam (figure8.6).Afterthreeminutes
howeveracompletelydifferentpictureisobtained.Avery
largenumberofsmallerbubblesthaninitiallypresentwas
measured. From figure 8.7 it isclear that bubbleshave
shrunkenasaconsequenceofgasdiffusionandthebubblesizedistributionhaswidenedmuchmorethanwhenthefoam
containednitrogen.Itisevidentthatdisproportionation
hastakenplace.
250 450 650 850 1050
RADIUS (xl0-Bm)
Figure 8.4: Bubble size distribution of a
nitrogen beer foam at t=0 min.
250
450 650 850 1050
RADIUS Ocl0-6m)
Figure 8.6: Bubble size distribution of a
carbon dioxide beer foam at t=0 min.
50
250 450 650 850 1050
RADIUS (xl0-6m)
Figure 8.5: Bubble size distribution of a
nitrogen beer foam at t=3 min.
250 450 650 850 1050
RADIUS (X10"B1)
Figure 8.7: Bubble size distribution of a
carbon dioxide beer foam at t=3 min.
The distributions determined with the photographic
method on the same foams are presented in figures
8.8-8.11. The discrepancy between the two methods is
smallerthanappearsfromthedistributions,becausethe
numberofbubblesisonalogarithmicscale.Ingeneral,
somewhat larger bubbles are observed with the optical
probemethod thanwiththephotographicmethod.Thismay
bearesultofthefactthatlargerbubblesarenotseen
attheglasswallwiththephotographicmethod,orbecause
the optical probe method induces some coalescence. In
115
addition, the initial bubble-size distribution iswider
whenmeasuredwiththeopticalglass-fibreprobemethod.
Theexplanation forthisobservation ismostlikelythat
thebubble-sizedistributionasmeasuredwiththeoptical
glass-fibreprobemethodisarepresentationoftheentire
foam, whereas the bubble-size distribution, measured
photographically,givesthebubble-sizedistributionata
specific foam height.All inall,theconclusion maybe
drawnthatthedistributionsdeterminedwiththeoptical
glass-fibre probe method and the photographic method,
correspondqualitativelyandquantitativelyverywell.
6
w5
ai 4
ft
Iff,
CG 3
w
CO
x: ?6
E=
S3
§H
250
450 650
850
RADIUS (Xl0- 6 m)
Figure 8.8: Bubble size distribution of a
nitrogen beer foam at t=0 min.
250
450 650 850 1050
RADIUS (Xl0-6m)
Figure 8.10: Bubble size distribution of a
carbon dioxide beer foam at t=0 min.
-J
0
50
11
tju
650
850
RADIUSi k
(H0-Bm)
Figure 8.9: Bubble size distribution of a
nitrogen beer foam at t=3 min.
250 450 650 850 1050
RADIUS (xl0-Bm)
Figure 8.11: Bubble size distribution of a
carbon dioxide beer foam at t=3 min.
8.5.Discussion
Themeasurementof foambehaviorisnotasimpletask.
Althoughitisnotdifficulttomeasuresomekindofbeer
foam characteristic with one of the described, readily
116
1050
available, methods that have been developed within the
lastdecades,theobtainedresultsmaybeverymisleading.
Thesebeerfoamnumbers,ingeneral,donotgiveagood
impressionofthefoambehaviorasitisassessedbythe
consumer. The methods do not correlate with each other
either.Apparently,onlypartofthetotalinformationis
obtained.Agoodexampleofthelatterisgivenintable
8.1,whereseveralmethods,tocharacterizebeerfoam,are
compared.Atthemost,atendency canbe found thatthe
behavior of the foam increases from beer A to beer G.
Although these beers are very extreme in their foaming
behavior, the ranking for the beers is different for
different methods. The main reasons are that; (i)with
mostmethodsthefoamisnotproduced inthesamewayas
in practice, and therefore the initial bubble-size distribution is different, (ii)in some methods beers are
degassedpriortomeasurementand foamedwithagasofa
different composition. In that case, effects of gas
composition and concentration in theoriginal beerscan
not be measured, (iii) the geometry of the measuring
cylinderdoesnotcorrespondwiththepracticalsituation,
(iv)forsomemethods,thecompositionofthesurrounding
gasatmosphere isnotidenticalwiththenormaldrinking
conditions.Inthatcase,thecollapsebygasdiffusionis
notmeasuredcorrectly,althoughthisisthemainprocess
forthebreakdownofthefoaminpractice, (v)theratio
beertofoamisoftendifferent,resultinginadifferent
depletion of surface active material, (vi)mostly, the
temperature during the measurement is not the drinking
temperature,(vii)lastbutnotleast,differentphenomena
areobserved, e.g. drainageinsteadofcollapse.
A better impression of the foam behavior is obtained
when more sophisticated experiments arecarried out.In
addition, to the rise of the foam-liquid interface and
collapse the foam, the bubble-size distribution can be
measuredasafunctionoftimetoobtainmoreinformation
about the foaming behavior. Gasses with a different
solubility, preferentially nitrogen and carbon dioxide,
canbeusedtodiscriminatebetweendifferentprocessesas
117
described.Additionally,theviscosityofthebeercanbe
measured tofindoutwhetheradistinctivebehaviorofa
foamcanbeexplainedbyadifferenceindrainagerateor
bytheprogressofotherprocesses.Ifatypicalbehavior
isfound,thatcannotbereadilyexplained,thecompositionofthedissolvedgasinthebeermayberesponsible.
Therefore,foamcharacteristicswiththe"natural"gasand
thegascompositioncanbemeasured.Ifalltherelevant
experimentsarecarriedoutacompleteimpressionoffoam
characteristicscanbeobtained.
Nevertheless,itremainsdifficult tomakeaquantitativedistinctionbetweenthedifferentphysicalprocesses
occurring inthe foam.Thequantitative distinction can
notbegivenbecausethefourphysicalprocesses,bubble
formation, drainage, coalescence and disproportionation
areinterrelated.Theinterrelationsarecomplicated.
Theinitialbubble-sizedistributioninfluencestherate
ofdrainage,coalescenceanddisproportionation.Drainage
willproceedslowerifsmallerbubblesarepresentbecause
therearemoremotionlesssurfacestoslowdowndrainage.
Whensmallerbubblesarepresentcoalescencewillnotbe
asdestructiveaswhenlargerbubblesarepresent,because
there aremuchmore filmstorupture.Theeffect ofthe
initialbubble-sizedistributionongasdiffusionfromthe
top layerof the foam tothesurrounding atmospherehas
beendiscussedbeforeinchapter6.5;afoamwithsmaller
bubbles ismore stable against outward gasdiffusion.A
wide bubble-size distribution will enhance disproportionation inside the foam, because the Laplace pressure
differences in that case are larger. As a result of
drainagethefilmthicknessbetweenthebubblesdecreases
withtime,andthisingeneralresultsinfasterdisproportionation and more coalescence. If coalescence or
disproportionation occurmoredrainagewillbeobserved.
Inaddition,coalescencewill acceleratedisproportionation because, owing to coalescence, the bubble-size
distribution becomes wider and the Laplace pressure
differencesincrease.Furthermore,disproportionationmay
enhancecoalescence.Asaconsequenceofdisproportiona-
118
tion film rearrangements in the foam may lead to an
increaseincoalescence.
These are only a few of the possible interrelations
between bubble formation, drainage, coalescence and
disproportionation.Becauseoftheseinterrelationsitis
impossible to distinguish between these processes in a
quantitative way. However,agood qualitative orevena
semi-quantitativedistinctioncanbemade.
Themeasurementoftheevolutionofbubble-sizedistributionsinfoamswithgassesofdifferent solubilitycan
makeacontributiontoaspecifieddeterminationoffoam
characteristics.Therefore,theopticalglass-fibreprobe
techniquemaycontributetotheassessmentoffoamcharacteristics.Forbeerfoamitisagoodworkingmethodthat
givesrapidandconclusiveinformationabouttheprogress
ofthefourphysicalprocesses.Inaddition,themethodis
comparativelyeasytooperate.
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Sei.84(1):42 (1981).
Bamforth,C.W.,J.Inst.Brew.91:370 (1985).
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81:131 (1975).
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Clark,N.N.,Turton,R.,Int.J.MultiphaseFlow14(3):413
(1988).
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(1983).
DeClerk,J., DeDijker,G.,EBCProc.Copenhagenpp.43
(1957).
DeVries,A.J., "Morphology,CoalescenceandSizeDistributionofFoamBubbles."In:AdsorptiveBubbleSeparation
Techniques.Ed:R.Lemlich,Ac.Press,N.Y.London,pp.7.
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(1972).
Frijlink, J.J., van Halderen, P.A., Hofmeester J., Warmoeskerken,M.M.CG.,I2-procestechnologie3:19 (1986).
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Reactors,PhD.Thesis,TechnicalUniversityDelft,Netherlands(1987)pp.119.
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150. (1966).
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London (1960).
Jackson,G.,Bamforth,C.W.,J.Inst.Brew.88:34 (1980).
Kawakami,M.,Tomimoto,N.,Kotazawa,Y.,Ito,K.,Trans.
Iron.Steel.Inst.Jpn.28(4):271 (1988).
Klopper,W.J.,J.Inst.Brew.60:217 (1954).
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Klopper,W.J.,TheBrewersDigest52(1):51 (1977).
Klopper,W.J.,Vermeire,H.A.,Brauwissenschaft30(9):276
(1977").
Klopper,W.J.,Vermeire,H.A.,Voedingsmiddelentechnologie
10(3):7 (1977b).
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Nishioka, G., Ross, S., J. Colloid and Interface Sei.
81(1):1 (1981).
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123(1):299 (1988).
- Rosendal,I.,Rasmussen,N.J.,MBAATech.Quart.19(4):153
(1982).
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(1939).
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121
9.CONCLUSIONS
The appearance of the foam is one of the important
aspects of beer quality. The appearance of the foam is
foremostdeterminedbytheprogressoffourphysicalprocesses,i.e.bubbleformation,drainage,coalescenceand
disproportionation.
Bubble formation is an important process because it
initiallydeterminescreaminess,theamountof foam,the
bubble-size distribution in the foam, the bubble wall
compositionandthegascompositionthroughout thefoam.
Bubble formation depends on beer properties, like the
dynamic surface tension under expansion conditions, the
wettingproperties,thegascontentandthegascomposition.Thisprocessalsodependsontheconditionsduring
thedispenseofthebeer.Averyeffectivewaytoimprove
beerfoambehaviorisbydispensingthebeerinsuchaway
thatsmallcarbondioxidebubblesareformed.Inaddition,
apropercontrolofthegascompositionandthetemperature is essential. Large hydrodynamic shear forces and
small nucleation siteswith good wetting propertiesmay
contributetotheformationofsmallbubbles.Theentrapment of air during the dispense of the beer should be
avoided. The bubble formation process isvery important
forfoambehaviorbecausetheinitialfoampropertiesvery
much influence theprogress of thethree other physical
processes.
Drainage and disproportionation appear to be themost
importantprocessesforthedisappearanceofthefoam.The
drainagerateismainlydetermined bybulkviscosityand
thereforethetemperatureofthebeerisoneofthemain
parameters,thatinfluencesthebehaviorofthefoam.For
disproportionationtwodifferentsituationscanbedistinguished. If gasdiffusion occurs inside the foam, large
bubbles grow at the expense of smaller bubbles. This
coarsening process proceeds rapidly as shown in chapter
8.4.Ifgasdiffusesfromthetoplayerofthefoamtothe
surrounding atmosphere, the foam collapses.This isthe
122
mostimportantprocessforthebreakdownofthefoam.If
thisdiffusionprocesscanbesloweddownforjustasmall
periodoftimeforeachbubblelayer,thefoamwilllast
muchlonger.Thisisaresultofthefactthatthewhole
diffusionprocesselapsesinatimethatisequaltothe
sum of the time required for each bubble layer in the
foam. Improvement of the stability of the foam against
collapse can be made effectively by nitrogenation as
explainedinchapter6.5.Gasdiffusioncanalsosignificantly be slowed downby surfaceviscosity. The surface
tensionincompressionmustbelowinordertodecelerate
gasdiffusion,becausetheLaplacepressureisthedriving
forceforgasdiffusionifthegascompositionthroughout
the foam isuniform. The formation of insoluble surface
layersincompressionappearstogohandinhandwiththe
decreaseofthesurfacetension.However,forthedecelerationofgasdiffusion,alowsurfaceviscosityisless
effective than nitrogenation. In addition, the initial
bubble-size distribution is important. A narrow initial
size distribution of small bubbles is in favor of good
foambehavior.
Coalescencedoesnotcontributetothecollapseofbeer
foamtoalargeextentundernormalconditions.However,
coalescencebecomesaverydominatingprocessifexternal
spreading material is added to beer foam. Dirty beer
glasses or consumer lips may be a source of spreading
material, that can initiate coalescence. The effect on
beerfoambehaviorcanbedisastrousfortheappreciation
oftheconsumer.Normally,acollapsed foammaystillbe
appealingbecauseamonolayerofsmallbubblesremainson
topofthebeer.Ifcoalescencetakesplacethebeerlooks
completelyflat.Theonlywaytoavoidcoalescencebythe
spreading mechanism appears to be to avoid spreading.
Therefore, the beer must have a low surface tension in
expansion. However, beers have very similar surface
rheological behavior inexpansion, especially at higher
expansion rates. Therefore, beer foam will remain very
susceptibleforspreadingmaterial.
123
LIST OF SYMBOLS
Roman symbols
a
= drained beer volume
[m 3 ]
A
= area
[m 2 ]
b
=beervolume ina foam
=drained beervolume in90 s
[m 3 ]
B2
= total drained beer volume
[ml]
c
= activity
[ m o l e m"3]
Ci
= activity ofcomponent i
[ m o l e m"3]
d
= thickness of the spread layer
=volume/surfacemean diameter
[m]
dlnA/dt
= relativedeformation rate
[s"1]
(dlnA/dt^
=dlnA/dt at inflection point
[s"1]
m
[mV1]
ID,
=diffusion coefficient
= IDofcomponent i
F
= force
[N]
FFV
= Foam Flashing Value
[-]
g
HRV
= gravity
= head retention value
[ms" 2 ]
k
[s"1]
m
= constant
= fraction of gas iinthe atmosphere
= slit length
=powerlaw parameter
[-]
n
=powerlaw parameter
[-]
= amount of gasi
[mole]
= total amount of gas
[mole]
K
1
n
tot
[ml]
[m]
[mV1]
[s]
[-]
[m]
0
=perimeter ofbubble attachment
[m]
P
P
=penetration depth
[m]
[Nm"2]
Pc
= atmospheric pressure
=capillary pressure
Pi
=partial pressure of gas i
[Nm" 2 ]
Ptot
[Nm"2]
Pi
= total pressure
=pressure inbubble1
p2
Q
=pressure inbubble 2
= flow rate
[Nm"2]
r
= radius
[m]
r„
= bubble radius at t =0
[m]
= bubble radius att =t
[m]
124
[Nm"2]
[Nm"2]
[m 3 s" 1 ]
=radiusof bubble1
m]
=radiusof bubble 2
m]
R
= initial radiusof a droplet
m]
R
=gas constant
Jmole^K"1]
S
=gas solubility
m o l e m" 3 ]
Si
=gas solubility ofcomponent i
m o l e m" 3 ]
t
= time
s]
*%
=half-life time
s]
t«,
=critical drainage time
s]
T
= temperature
K]
u
=bursting velocity
ms"1]
v
= velocity
ras-1]
v0
= initial velocity
ms-1]
V
=bubble volume
m3]
=bubblevolumeatplateau value
m3]
v0
w0
wt
=bubblevolume att =0
m3]
=weight ofbeer foam at t =0
m]
=weight ofbeer foam at t =t
m]
z
=diffusion distance
m]
Greek symbols
= Mach a n g l e
-]
=bulk viscosity
Nsm" 2 ]
= surfacedilational viscosity
Nsm" 1 ]
TT
=disjoining pressure
Nm" 2 ]
f
a
= density
kgm" 3 ]
= surface tension
Nm"
o,dyn
=dynamic surface tension
Nm"
ae
=equilibrium surface tension
Nm"
a
°i
=o at inflection point
Nm"
°o
=o intheoil phase
Nm"
= interfacial tension oil-water
Nm"
= spreading tension
Nm"
= a in thewater phase
Nm"
o„
= foam characteristic (Eg. [8.3])
s]
e
= film thickness
m]
ec
= initial film thickness
m]
ec
=critical film thickness
m]
i
=topology factor
m]
125
SUMMARY
Thefoamingbehaviorisoneofthemainqualitycharacteristicsofbeer.Theappearanceandbehaviorofthefoam
has to be in accordance with the expectations of the
consumer. The foam characteristics of beer foam are
determined by the progress of four physical processes,
viz. bubble formation,drainage,coalescenceanddisproportionation.
Inbeerfoamtwokindsofbubblesareinitiallypresent.
The first kind of bubbles is formed by heterogeneous
nucleation from the supersaturated beer solution. These
beer bubbles are comparatively small and contain carbon
dioxide. Homogeneous nucleation does not take place in
beer,becauseanenormoussupersaturationwouldbenecessaryforthespontaneousformationofbubbles.Thesecond
kindofbubblesisformedinbeerbyairentrapmentduring
the dispense of the beer. These bubbles are in general
largerthanthecarbondioxidebubblesandcontainair.
Drainageoccursinbeerfoam.Therateofdrainageisa
resultofacomplexinterplayofgravity.Plateauborder
suction,geometry aspects and balancing parameters.The
parameters that slowdowndrainage arebulk and surface
viscosity.
Coalescence in beer foam can be caused by externally
added lipid components. The two mechanisms that may be
responsible for this phenomena are thehydrophobicparticlemechanism andthespreadingmechanism.Anumberof
parameters can be used to distinguish between these
mechanisms. In the case of the hydrophobic particle
mechanismthesizeofalipiddropletthatinitiatesfilm
rupture must be at least equal to the film thickness,
whereas the droplets may be smaller in the case of the
spreadingmechanism. Inaddition,thespreadingparticle
mechanism canonly work when the spreading condition is
met.Therefore,thecompositionofthelipiddropletand
theprevailing,dynamicsurfacetensionofthefilmmust
allow spreading.Theviscosity of the film liquid isan
important parameter todistinguish between the two film
126
rupture mechanisms, because at a higher bulk viscosity
coalescence is more easily initiated by the spreading
mechanism andmoredifficultbythehydrophobicparticle
mechanism. A falling film apparatuswas used toexamine
thestability of a freefalling beer film under various
conditions.Emulsionsofdifferentcompositionanddroplet-size distribution were added to stable free falling
beer films.Some emulsionscaused hole formation inthe
falling film. The number of holes formed in the film
dependedondropletsizeanddropletcomposition.Droplets
ofapproximately thesamesizeasthefilmthicknesshad
to be put in the beer and a certain minimum amount of
emulsifier had to be added to the emulsion in order to
cause hole formation.A number of spreading experiments
andvarioussurfacerheological experimentswerecarried
outinordertostudytherelationbetweenthespreading
of surface active material and the (dynamic) surface
tension. A good correlation between the spreading of
surface active material and hole formation in the free
falling filmwasfound.After sometimeofoperationthe
droplet-sizedistributionoftheaddedemulsionappeared
toshifttosmallerdropletswhenholeswereformedinthe
falling film. An increase of the bulk viscosity of the
beer resulted in an enormous increase of the number of
holesthatwereformedinthefilmperunitoftime.Thus,
from these results arguments in favor of the spreading
mechanismwereobtained.
Theradius-versus-timecurvesofbubbles,thatshrinkas
a result of gas diffusion, often showed an inflection
point. Therefore,theeffect of thegascomposition inandoutsidethebubblesandtherheologicalaspectofthe
bubble surface on the rate of disproportionation was
examined.Agasdiffusionmodelwasdeveloped,including
thepossiblepresenceofgaseswithdifferentsolubilities
andincludingapowerlawthatdescribesthedependenceof
thesurfaceviscosityonthesurfacedeformationratein
compressionandexpansion.Experimentswerecarriedoutto
measure anumber of surface rheological aspects incompression. The dissolution rateof bubbles wasmeasured.
127
Largepartialpressuredifferencesappeartodictatethe
rateofdisproportionation.Additionally, thesolubility
ofthepresentgasesdeterminesthegasdiffusionrateto
a largeextent.When thegascomposition throughout the
foam isuniform therateofdisproportionation isdeterminedbythesurfacedilationalviscosity ofthebubble.
Experimentalresultsareverymuchinagreementwithmodel
calculations, unless an insoluble skin formation takes
place atthebubble surface asaconsequence of surface
compression. As a result of insoluble skin formation,
bubbleghostsmaybepresentinbeerafterfoaming.
Severalbeerfoamphenomenacan,atleastqualitatively,
be explained with the knowledge of the four physical
processes. The creaminess of the foam, the rise of the
foam-liquid interface,theinfluenceoftemperature,the
coarseningofthefoam,foamcollapse,cling,theinfluenceofairentrapmentandtheinfluenceofthecomposition
of beer aredescribed. Thedisappearance of the foam is
mainly caused by liquid drainage and gas diffusion from
thetoplayerofthefoamtothesurroundingatmosphere.
Only when externally added spreading material initiates
filmrupture,coalescencecontributestofoamcollapse.
Because there are so many beer foam phenomena and
properties, anoverall foam stability number cannot be
given. Consequently, different methods must be used to
measuredifferentfoamphenomenainordertofullycharacterize beer foam behavior. A newly developed optical
glass-fibreprobetechniquewasusedtomeasurethebubble
sizedistribution,theheightofthefoamandthelevelof
thefoam-liquidinterfaceasafunctionoftime.Withthis
techniqueandtheuseofgasesofdifferentsolubilitya
qualitative distinction can be made between the four
physicalprocesses.
128
SAMENVATTING
Hetgedragvan het schuim iséénvande belangrijkste
kwaliteitskenmerkenvanbier.Hetuiterlijkenhetgedrag
vanhetschuimmoetenzijnzoalsdatdoordeklantwordt
verwacht.Hetschuimgedragwordtbepaalddoorhetverlopen
vanvier fysischeprocessen.Dezeprocessenzijnbellenvorming,drainage,coalescentieendisproportionering.
In pas gevormd bierschuim komen twee soorten bellen
voor. De eerste soort bellen ontstaat door heterogene
kiemvorming in een oververzadigd bier.Deze bellen zijn
betrekkelijk klein en bevatten koolzuur. Homogene kiemvormingvanbellenkomtinbiernietvooromdateenenorme
oververzadiging nodig isvoorspontanebellenvorming.De
tweede soortbellen inbier ontstaat door de inslagvan
lucht tijdens het inschenkenvanbier.Deze bellen zijn
inhetalgemeengroterdandekoolzuurbellenenbevatten
lucht.
Desnelheid,waarmeedrainageplaatsvindtinbierschuim,
ishetresultaatvaneeningewikkeldewisselwerkingtussen
dezwaartekracht,dezuigingvandePlateauzomen,compenserendeparametersengeometrischeaspecten.Deparameters
die drainage tegenwerken zijn o.a. de oppervlakte- en
bulkviskositeit.
Coalescentieinbierschuim kanwordenveroorzaaktdoor
van buiten toegevoegde, vetachtige deeltjes. De twee
mechanismen, die verantwoordelijk kunnen zijn voor dit
verschijnsel, zijn het hydrofobe deeltjes mechanisme en
hetspreidingsmechanisme.Eenaantalparameterskanworden
onderzocht om onderscheid te kunnen maken tussen deze
mechanismen. In het geval van het hydrofobe deeltjes
mechanisme moet de diameter van het deeltje minstens
gelijkzijnaandefilmdikte,terwijlhetdeeltjekleiner
magzijninhetgevalvanhetspreidingsmechanisme.Daar
komt nog bij dat aan de spreidingsconditie moet worden
voldaan om het spreidingsmechanisme te laten werken.
Daarom moet de deeltjessamenstelling en de heersende,
dynamische oppervlaktespanning dusdanig zijn dat het
spreiden van oppervlakte-aktief materiaal kan optreden.
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Ookdeviskositeitvandefilmvloeistofiseenbelangrijke
parameter waarmee onderscheid kan worden gemaakt tussen
beide mechanismen, omdat bij een hogere viskositeit
filmbreukmakkelijkerkanwordenveroorzaaktinhetgeval
van het spreidingsmechanisme en moeilijker inhetgeval
vanhethydrofobedeeltjesmechanisme.Eenvallendefilm
apparaat werd gebruikt om de stabiliteit van een vrij
vallende bierfilm te onderzoeken onder verschillende
condities.Emulsiesvanverschillendesamenstellingenmet
eenverschillendedeeltjesgrootteverdeling werdenaande
stabiele vallende bierfilm toegevoegd. Sommige van die
emulsiesveroorzaaktengatvormingindevallendefilm.Het
aantalgatendatwordtgevormdindefilmisafhankelijk
van de grootte en de samenstelling van de deeltjes.
Druppels van ongeveer dezelfde grootte alsde filmdikte
moesten aanhet bierworden toegevoegd om gatvorming te
veroorzaken. Bovendien moest aande druppels een zekere
hoeveelheid emulgator worden toegevoegd. Een aantal
spreidingsproeven en oppervlaktereologische experimenten
werd uitgevoerd om het verband tussen het spreiden van
oppervlakte-aktiefmateriaalendedynamischeoppervlaktespanning tebestuderen. Eengoede correlatie tussenhet
spreidenvanoppervlakteaktiefmateriaalenhetoptreden
vangatvormingindevrijvallendefilmwerdgevonden.De
deeltjesgrootteverdeling van de toegevoegde emulsies
blekenteverschuiveninderichtingvankleineredeeltjes
wanneer gaten werden gevormd in de vallende film. Een
verhogingvandebulkviskositeitvanhetbierresulteerde
ineensterketoenamevanhetaantalgatenindevallende
film per tijdseenheid. Het coalescentiemechanisme in
bierschuim, dat optreedt wanneer vetachtige componenten
vanbuitenafwordentoegevoegd,blijktdushetspreidingsmechanismetezijn.
De straal-tegen-tijdcurvesvan bellen die krimpen als
gevolgvandisproportioneringvertonenvaakeenbuigpunt.
Daaromisdeinvloedvandegassamenstellinginenbuiten
debellenendeinvloedvandereologischeeigenschappen
van het beloppervlak op de disproportioneringssnelheid
onderzocht.Eengasdiffusiemodelwerdontwikkeld,waarbij
130
rekening is gehouden met de mogelijke aanwezigheid van
tweegassenmeteenverschillendeoplosbaarheidenwaarbij
een machtwet is gebruikt om de afhankelijkheid van de
oppervlaktedilatatieviskositeitvandevervormingssnelheid
in zowel compressie als expansie tebeschrijven. Enkele
experimenten zijn uitgevoerd om een aantal oppervlaktereologischeaspectenincompressietebepalen.Desnelheid
waarmeebellenoplossenwerdgemeten.Partiëlegasdrukverschillenblijkendedisproportioneringssnelheidinbelangrijkematetebepalen.Bovendienisdeoplosbaarheidvan
deaanwezigegassenbepalendvoordegasdiffusiesnelheid.
Wanneer degassamenstelling inhet gehele schuim gelijk
iswordt de disproportioneringssnelheid bepaald door de
oppervlaktedilatatieviskositeit vandebel.Deverkregen
experimenteleresultatenkunnengoedwordenbeschrevenmet
modelberekeningentenzijinhetbeloppervlakeenonoplosbare laag wordt gevormd door de oppervlaktecompressie.
Wanneer onoplosbare lagen worden gevormd tijdens de
compressie van het bieroppervlak kunnen "bubbleghosts"
inbiervoorkomennadathetbierheeftgeschuimd.
Verschillendeverschijnselendievoorkomeninbierschuim
kunnenwordenverklaard metbehulpvandekennisvande
vier verschillende fysische processen. De romigheid van
hetschuim,hetoptrekkenvanhetvloeistof-schuimgrensvlak,deinvloedvandetemperatuur,hetvergrovenvanhet
schuim,hetinzakken,cling,deinvloedvandeinslagvan
luchtendeinvloedvandesamenstellingvanhetbieris
beschreven.Hetverdwijnenvanhetschuimblijktvooralte
komen door drainage en gasdiffusie vanuit de bovenste
bellenlaag van het schuim naar de atmosfeer boven het
schuim. Alleen wanneer vetachtige componenten, die van
buitenafwordentoegevoegd,hetbrekenvanfilmsveroorzaken,draagtcoalescentiewezenlijkbijtothetinzakken
vanhetschuim.
Omdater zoveelverschillendeverschijnseleneneigenschappenvanbierschuimzijn,ishetnietgoedmogelijkom
destabiliteitvanschuiminééngetaluittedrukken.Dit
heefttotgevolgdatverschillendemethodesmoetenworden
gebruikt en verschillende verschijnselen moeten worden
131
gemeten om het schuimgedrag volledig te karakteriseren.
Eenoptischeglasvezelkabeltechniekisgebruiktombellengrootteverdelingeninschuim,dediktevandeschuimkraag
endehoogtevanhetvloeistof-schuimgrensvlak tebepalen
alsfunctievandetijd.Metgassen,dieeenverschillende
oplosbaarheid hebben, is een kwalitatief onderscheid
gemaakttussendevierverschillendefysischeprocessen.
132
CURRICULUMVITAE
A.D.Ronteltapwasbornonthe12thofNovember1957in
Pladju,Indonesia.HewasraisedinHollandwherehe
graduated fromhighschoolin1976.Afterspendingone
yearatthe"VrijeHogeschool"inDriebergen,hestarted
tostudyFoodTechnologyattheAgriculturalUniversity
inWageningenin1977.Inthefinalyearsofhisstudy
hespecialized inFoodchemistry,Biochemistryand
ProcesTechnology.Aftergraduatingin1985,hestarted
theresearchworkonbeerfoamofwhichthisthesisis
thefinalresult.
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