JOURNAL OF GEOPHYSICAL
RESEARCH, VOL. 105, NO. B10, PAGES 23,72%23,740, OCTOBER 10, 2000
Experimentson conduitflow and eruption behavior
of basaltic volcanic eruptions
Ralf Seyfried and Armin Freundt
GEOMAR Forschungszentrum,
Kiel, Germany
Abstract:Multiphaseflow in basalticvolcanicconduits
is investigated
usinganalogexperimentsand
theoretical
approaches.
Depending
ongassupply,largegasbubbles
(gasslugs)mayrisethroughbasaltic
magmain regimesof distinctfluid-dynamical
behavior:
ascentof singleslugs,supplied
slugsfedfrom
thegassource
duringascent,
andperiodicslugflow.An annular
flowregimecommences
at thehighest
gassupplyrates.A firstsetof experiments
demonstrates
thatthegrowthof gasslugsdueto hydrostatic
decompression
doesnotaffecttheirascentvelocityand thatexcess
pressure
in theslugsremain
negligible.The applicabilityof theoreticalformulaedescribingslugascentvelocityasa functionof
liquidand conduitproperties
is evaluatedin a second
setof experiments.
A thirdsetof experiments
with continuousgassupplyinto a cylindricalconduitare scaledto basalticconditionsoverMorton,
Eotv6s,Reynolds,andFroudenumbers.
Gasflow rateand liquidviscosityarevariedoverthewhole
rangeof flow regimesto observeflow dynamicsand to measuregasand liquideruptionrates.Foam
generation
by slugbursting
at thesurfaceandpartialslugdisruption
by waketurbulence
canmodifythe
bubblecontentandsizedistribution
of themagma.At thetransitionfromslugto annularflow, when
theliquid bridgesbetweenthegasslugsdisappear,
pressureat theconduitentrancedropsby - 60%
fromthehydrostatic
valueto thedynamic-flowresistance
of theannularflow, whichmaytrigger
furtherdegassing
in a storedmagmato maintaintheannularflow regimeuntilthegassupplyis
exhausted
and theeruptionends abruptly.Magmadischarge
mayalsoterminatewhenmagmaascentis
hinderedby wall frictionin longvolcanicconduits
andtheannulargasflow erodesall magmafromthe
conduit.Suppliedslugsarefoundto reachmuchhigherrisevelocitiesthanunsupplied
slugsandto
collapseto turbulentannularflow uponbursting
at thesurface.
A fourthsetof experiments
usesa
conduitpartiallyblockedby built-inobstacles
providingtrapsfor gaspockets.
Oncegaspocketsare
filled, risinggasslugsdeformbut remainintactastheymovearoundobstacleswithoutcoalescence
or
significant
velocitychanges.
Burstingof bubbles
coalescing
withtrappedgaspockets
causespressure
signalsat least3 ordersof magnitude
morepowerfulthangaspocketoscillation
inducedby passing
liquid.Ourexperiments
suggest
a refinedclassification
of Strombolian
andHawaiianeruptions
according
to time-dependant
behavior
intosporadically
pulsating
lavafountains
(drivenby stochastic
riseof single
slugs),periodicallypulsating
lavafountains(resulting
fromslugflow), andquasi-steady
lavafountains
(oscillatingat the frequencyof annular-flowturbulence).
and ash clouds limited to the troposphere.The eruption
1. Introduction
Through the past decade, there has been a strong research
focus on Plinian eruptions of felsic, highly viscous magmas
involving physical and experimental modeling of the
dynamics of degassing,magma fragmentation,and eruption
column ascent. Magma fragmentation in such eruptions has
been ascribedto bubble overpressure,high elongationrates or
high shear rates associated with the enormous acceleration
driven by gas expansion[e.g., Sparks, 1978; Proussevitchet
al., 1993a; Sugioka and Bursik, 1995; Zhang et al., 1997;
Alibidirov and Dingwell, 1996; Mader et al., 1994; Gardner et
al., 1996; Papale, 1999]. However, -70% of the bulk annual
subaerialmagmadischargeto the Earth'ssurfaceis producedby
basaltic volcanic eruptions, which occur continuously all
around the Earth [Simkin and Siebert, 1994] and are
characterizedby longtime activity but producelow fountains
dynamicsof basaltic magmas,which have a much lower
viscosityand lower gas contentsthan felsic magmas,have
found little attentionsince Wilson and Head [1981] physically
described Hawaiian-style eruptions evolving from
homogeneousdegassingof magma assumedto fragmentupon
reaching a critical threshold vesicularity (70-80%).
Fragmentation
modelsderivedfor highlyviscousfelsicmagma
cannot simply be applied to low-viscosity basaltic magma
becausecomparablyhigh shearratescannotbe supportedand
gasbubblesare free to move and expand.
Wilson and Head [1981] and Parfitt and Wilson [1995]
consider homogeneousgas-magmaflow in the conduit, i.e.,
gasbubblesmovingwith the magmawhile they expandduring
ascent to the surface. Wilson and Head [1988] did, however,
also draw attention to the possibility of bubble coalescence
and the occurrenceof separatedgas-magmaflow, in which
bubbles move relative to each other and to the magma.
Copyright
2000bytheAmerican
Geophysical
Union.
Papernumber2000JB900096.
0148-0227/00/2000JB900096509.00
Vergniolleand Jaupart[ 1986],Jaupartand Vergniolle[ 1989],
and Vergniolleand Jaupart[1990] demonstrated
by experiment
andtheorythat a trappedfoam layer canform underthe roof of
a reservoirby volatile exsolutionfrom the storedmagma,even
23,727
23,728
SEYFRIED
ANDFREUNDT:
CONDUIT
FLOWANDBASALTIC
ERUFFIONS
if a conduit already exists. When exceeding some critical
depth, the foam layer collapsesand releasesa large volume of
gas into the conduit, generatingseparatedgas-magmaconduit
flow.
The distinction between homogenousand separated gasmagma flow is important when considering the gas mass
eruption rate, which is directly coupled with the initial
dissolved magmatic volatile content in the case of
homogeneousflow but is decoupled from volatile content in
separated two-phase flow. This paper investigates basaltic
magma eruption dynamicsbasedon separatedtwo-phaseflow
using the investigationsof Vergniolle and Jaupartas a starting
point. However, the presentstudy focusseson the dynamicsof
separatedtwo-phase flow in the conduit, rather than on its
generation. The experiments of Vergniolle and Jaupart were
not scaled to volcanic conditions, liquid viscosity was not
varied, and slug ascent(slug = large gas bubble almostfilling
the conduitdiameter)was assumedto occuronly in the inertial
regime of single slug ascent where it does not depend on
magma rheology.We will show in the following that separated
two-phaseflow may proceedin different regimes:single-slug
ascentoccursfrom the sporadicreleaseof limited gas volumes
into the conduit; supplied slugs remain connectedto, and fed
from, a gas sourceover the whole time of their ascentthrough
the conduit;slug flow, i.e., a periodic sequenceof ascending
gas slugs,arisesfrom continuousgas releaseat moderaterates;
and turbulentannularflow, in which a centralgasstreamerodes
and mixeswith marginalliquid, formsfrom gasreleaseat high
rates.
These regimes of separatedtwo-phaseconduit flow involve
distinct formation conditions and ascent dynamics, which
differ from the theoryof Vergniolleand Jaupart [1990]. We use
four different experimental simulations complemented by
theoretical considerationsto investigate the role of these
different two-phaseflow regimesin basalticeruptions.
2. Ascent of Single Gas Slugs
2.1.
Theoretical
Framework
Three dimensionless fluid-dynamical
parameters are
necessaryto derive the terminal ascentvelocity Us] of
buoyantly rising single gas slugs'Froude number,
2
Fr=•,
(1)
gD
which representsthe ratio of kinetic to potential energy,
Eotv0s number,
Eo=pgD2
(2)
which evaluatesgravity force againstsurfaceforce, and
Morton number,
Mo=gg4
(3)
0(73'
which relates viscousto surfaceforces, with g the
gravitational
acceleration,
p theliquiddensity,
I• theliquid
White& Beardmore
(1962) extrapolated
0.4
I
I
inertialregime
0.3
Experimental
conditions
o
ß 0.2
<10-810-4 10-210-1 100
101
lO _
lO3
104
105
106
107
108
o
1=o.1
(7 =0.4 N m -•
•0.05
Ap =2600 kg m'3
:ous regime
g =50-500 Pas
D =1-10
!
0
UsI=O...•
i
at
high (7 ,
101
7b 102
103
104
Eotv6s number, Eo
m
105
106
ß D- 14mm decompression
[] D - 50 mm film thickness
o D - 50mmcontinuous
supply
Figure1. WhiteandBeardmore's
[1962]diagram
forslugascent
velocities
in dimensionless
writing,
extrapolated
to volcanicconditions.
The square
rootof theFroudenumberrepresents
thedimensionless
ascent
velocity.
Eotv6snumber
canbe interpreted
asdimensionless
conduit
diameter.
Mortonnumbers
represent
differentliquidrheologies.
Symbols
give experimental
datafor unsupplied
slugs;arrowspointto
corresponding
velocities
of supplied
slugs
underotherwise
constant
conditions.
Shaded
fieldon theright
outlines
parameter
ranges
for gasslugsin basaltic
magma,
extending
fromtheinertialthrough
thetransitional
regime.
SEYFRIEDAND FREUNDT: CONDUIT FLOW AND BASALTIC ERUl:qlONS
O.
23,729
2.4
=,
O.
g
--2.3
•0.
--2.2
0.1
! Conduit
diameter
D=5m,
•
Magmadensity@= 2600kg/m3
0
• i i ] , , , I , , , I , , , I , , ,
I
0
200
400
I
I
600
800
1000
Magma viscosityg [Pas]
Figure2. Filmthickness
15(leftaxis)from(6) andslugascent
velocity
Usl(rightaxis)from(7) versus
magma
viscosity
• fora basaltic
conduit
diameter
ofD= 5m andmagma
density
p= 2600kg/m
ø.
viscosity,
ando thesurface
tension.
Inertialforcesdominate
at
15
"-41
+ND
-1
M o < 10-6 and Eo > 100, viscosity and surface tension
influencesbecomenegligible,and the ascentvelocityof gas
slugsreaches
thehighest
value,depending
onconduit
diameter
D only[WhiteandBeardmore,1962]as
Usl(i)=0.3455f•D.
(4)
N
Figure 2 showsfilm thickness15as a functionof liquid
viscosityusing (6). Slug ascentvelocityand film thickness
are related as [Brown, 1965]
u=0.3454g(D215
).
No separated
slugrise(Usl= 0) occursfor Eo< 3.4, where
surfacetension is dominant [Wallis, 1969].
(6)
,
(7)
The variationof slug velocity with magmaviscosityafter
TheinertialvelocityUsl(i)from(4) is commonly
assumed
in equation(7) is alsoshownin Figure2. Applicationof (7) is
two-phase flow modeling of basaltic eruptions [e.g.,
Vergniolle and Jaupart, 1990]. However,for a typical
limited
to
rheology of basaltic magma
o=0.4N/m; p=2600kg/m3;•=500Pas;l<D<10m
we obtain
for the surface tension, and to ND > 60 for the viscosity.
0.1 <Frø'5<0.345; 105< Eo 107;105< Mo <1010
2.2.
Slug
Expansion
suggesting
that slug ascentin basalticmagmalies in the
transitionalregimewhereUs•< Us•(i). In the transitional Equations(5)-(7) having been derivedfor engineering
regime,Us• shoulddependon slug lengthand magma applications,assumeconstantslug length during ascent
viscosity. Figure 1 shows slug ascent velocities in through an infinite conduit. In long volcanic conduits,
dimensionless form after White and Beardmore [1962]; we however,rising gas slugswill increasein length,Lsi, dueto
decompression
ofthegas.Gasdensity
pgdecreases
withdepth
extrapolated
thisdiagramto includevolcanicproperties.
The ascentrate of a slugis controlledby the volumeflux of
liquidfromthe bubbleheadto its wake.Hence,a thin liquid
counter-flowfilm wraps the slug. The equilibriumbetween
buoyancy,
viscous,andsurfaceforcescontrolsthe shapeand
z ashydrostatic
pressure
diminishes
andis givenby
pg
(z)=pgz
+Pa'
RT
(8)
rate of the film flow. The elongatedbubblecan be dividedinto
neglecting
excesspressure
effects,wherep is magmadensity,
a convexcap regionand the cylindricalbody,alongwhich
R is gasconstant,
T is temperature,
Pais atmospheric
pressure.
film thickness15=0.5(D-dsl)is constant;
D and dsl are the
Gasslugvolumeandlengthat depthz thenare
conduitandslugbubblediameters,
respectively.
Brown[1965]
related film thicknessto ascentvelocity throughthe parameter
g2'
N=114.5
p2g
(5)
1
mgRT
Ls•
=-•-Vsl=•pgz+Pa
(9)
withmgis gasmass
andA is slugcross-sectional
area.
The
increasein volume with decreasingz is
which evaluates buoyancy against viscous forces, leading to
an expressionthat yields 15from rheologicalparametersand
conduit geometry as
Vs
I =- mgRTpg
=ALsl.
dz
(pgz+Pa)
2
dz
(10)
23,730
SEYFRIED
ANDFREUNDT:
CONDUITFLOWANDBASALTIC
ERUPTIONS
d2Lsl/dZ2
= 10-5,sothatweobtain
theterms
in (11)as
....'........."•h•'
reaches
the
surface
a)_.'""•
lop
of
the
slug
(
Psi(z) = 125,500+956+375+0.5
..,-'
(b)
200
atz=0.5
Lsl
Pa
where the first (hydrostatic)term exceedsthe other terms by
more than 2 magnitudes. This example calculation is
conservative
sinceincreasing
z will decrease
dL/dzandd2L/dz
2
but increasethe hydrostaticpressureterm. Thus, slug-length
increase will follow the hydrostatic decompressionduring
ascent without developmentof significant overpressurein the
400
bubble.
2.3.
600
Decompression
Experiments
Our first set of experimentswas designedto investigatethe
effect of decompressional length growth on slug ascent
velocity. We measured length and velocity from video
recordingsfollowing the ascentof gas slugsalong a 4-m long
vertical perspex tube of 14 mm diameter (Figure 4). A fixedvolume steel tube filled with gas at a controlled pressure
allowed injection of a pre-definedmassof gas into the perspex
tube, which was filled with one of the following four liquids:
-
(a) D = 1 m:Zo= lkm; mg= 20kg
ß
(b) D = 2 m;Zo= 0.5km;mg= 40kg
800
ß
ß
ß
1. Pure water
1000
o
10
20
30
p = 1 mPas' p = 1000kgm-3;Mo = 2.8x10
-ll' Eo= 27.5
40
Lengthof risinggasslugsLsl[ml
Figure 3. Increase in slug length due to decompression
during approachto the surfacefrom (9) for two setsof initial
valuesof conduitdiameter
D, depthof slugoriginz0, andgas
mass
mgcontained
intheslug.
Figure 3 showsthat the length of gas slugsrising througha
volcanic conduit can increase by more than an order of
magnitude from expansionalone and will further increaseif
Perspextube
L=4m
volatilessuchas H20 continueto exsolveduringapproach
to
the surface.Gas slugpressurePsiis the sumof hydrostatic
pressureand excesspressureterms due to inertial, viscous,and
surface tension resistanceto slug expansion [Sparks, 1978;
Proussevitch et al., 1993b]:
Gas
slug
Camcorder
Psl(z)=Pa+Pgz+pmUsl
dz•dz ' k,dzJ
hydrostatic
+
inertial forces
(11)
internal
dLsl•-t-•
4gUsl 2o
-t- •
dz
Lsl
+ viscous
d=14 mm
Lsl
+ surface forces.
However,for basalticmagmarheologyandrelevantvaluesof
UslandLsl(p> 50Pas,andD, L > 2 m) theexcess
pressure
terms remain negligible.
If, for example, we assumeD=2m,
p= 100Pas,
p = 2600kgm
-3,mg=1kg,R= 461Jkg-lK
-1,
z= 1 m,, T= 1400K, Usl=l.5m/s, o = 0.4 kgm-1,
Pressurized steel tube
we obtainLsl= 1.6m from(9) anddLsl/dz=-0.33 from
(10). Since
Figure4. Experimental
setup
to measure
ascent
velocity
and
d2Lsl 492g
2 mgRT
dz
2 =-•• (pgz
+Pa
)3'
decompressional
lengthincrease
of gasslugs.Air is enclosed
under
a defined
pressure
in a steeltubein order
torelease
slug
(12) bubblesof a definedgasmassintotheconduit.
SEYFR]ED AND FREUNDT: CONDUIT FLOW AND BASALTIC ERUt•ONS
23,731
2.4. Analysis of the Counter Flow Film
2. Water-sodium-polywolframate
solution
}a= 1mPas;p = 1400kgm-3;
Mo= 4x10-ll' Eo= 38.5
A secondset of experimentsis usedto analyzeliquid film
thicknessand slug cap geometry.To studythe counterflow
3. Water-cellulose ester solutions
behaviorarounda slug, it was necessaryto use a larger tube
a)g= 13mPas;p = 1000kgm
-3'Mo= 8x10-7;
Eo= 27.5
diameter.We measuredthe liquid film thicknessof slugsin a
b) g= 22mPas'p = 1000kgm
-3;Mo= lx10-5'Eo= 27.5
squareperspextube of width 1= 50 mm, usingtransmitted
light with a schlierensystem.A squaretubeavoidsthe optical
The hydrostatic pressure drop along the tube was distortionof a cylindricaltube, althoughthe resultscannotbe
3.9x104 Pa, (5.5 x 104Pa for liquid 2). The small tube
directlycompareddue to the strongerliquid backflowin the
diameterimpliesa verylow valueof Eo sothattheexperiment tube corners. We performed our calculations using the
is notproperlyscaledto a volcanic
conduit,
butit is sufficient correspondingtube diameter
for thecomparison
of slugascent
ratesunderdecompression
to
thosederivedfrom theoreticalpredictionsgiven above.Slug
D'=
•--4•1
=0.0564
m
ascent behavior in volcanic conduits, where the Eotv6s
numberis muchhigher,will alsobe influenced
by roughwalls
(13)
and we obtain Eo = 455 for all liquidsused,and
and non circular cross section of the conduit, and by the
scavenging
of volatilesfromthemagmaandof smallbubbles
Mo = 2.86X10-ll
Mo=6X10 -7
Mo = 1.45X 10-2
from the conduitwall region into the slug. However,such
phenomena
aretreatedseparately
in section
5.
for 1 mPa s,
for 12mPa s,
for 150 mPa s.
With all four liquids,the ascentvelocityof decompressing
Measurements in a circular conduit D = 50 mm filled with
gasslugsremainedconstant
duringpassage
throughthe 4 m
at Eo = 350 and
long tubealthoughsluglengthsincreased
by up to a factor purewaterwere madefor comparison
Mo = 2.86X10 -ll.
1.4. This observation is attributed to the balance between
The experimentalconditionsare in the inertial regime
increasingbuoyancy(driving force) and increasingslug
surface (resistance force). Ascent velocity did, however, Fr ø.5 = 0.345 except for the highest-viscosity runs
increaseweakly with the initial gas massforced into the (Figure1), which lie in the transitionalregime where a
conduit(Figure5). Slugswith a highergasmassarelonger significantfilm thicknessmay be expected,as shownin
approaches
a valueunmeasurably
thanthosewith a lowergasmassat anypressure
level.Ascent Figure6. Film thickness
liquids(1
velocityincreases
weaklywith sluglengthat a defined smallat the bottomof the capin the lower-viscosity
a constantvalue of 3 mm in
pressure
butit does
notchange
withincreasing
length
of a slug and 12 mPas) and approaches
of constant
gasmass.Considering
thelimitedoverallrangeof the high-viscosityliquid (150 mPas). Film thicknessis
by (6) with respectto measured
data
slugvelocities,
however,deviations
in velocityof < 7% slightlyoverestimated
(Figure
6),
which
will
be
due
to
increased
back
flow
in
the
appear
to benegligible
sothattheexperimental
results
match
cornersof the square conduit. In contrastto theoretical
well withthepredictions
of (6) and(7).
!
130
125 -
120
115-
110-
Exp. p [kg/m
3] g [mPas]Uslfrom(7)
105
- e-- 1
a. 2
--,-.3
100
....
0
50
1000
1000
1400
13
1
1
123 mm/s
124 mm/s
117 mm/s
i
i
100
150
200
Gas mass [rag]
Figure 5. Ascentvelocities
of decompressing
gasslugs,measured
in the setupof Figure4, versustheir
contained
gasmass.
Symbols
distinguish
threesetsof dataforthreeliquids(1 to3) of different
values
of p and
g astabulated.
Lineslabelled
E arelinearregressions
through
experimental
data;noreasonable
regression
was
possible
fordataset3 duetowidescatter.
Regression
residuals
R forsets1 and2 areindicated.
Horizontal
lines
labelledT indicatecorresponding
theoretical
velocities
calculated
from(7) whichareindependent
of gasmass.
Measureddata scatteraroundtheoreticalvaluesbut showa weak increasein velocitywith gasmass.
23,732
SEYFRIEDAND FREUNDT:CONDUIT FLOW AND BASALTICERUPTIONS
experiments.Instead,the liquid backflow was laminarwith a
visible film thickness,the slug cap length was longer, and the
film thickness decreased with increasing slug length.
II i constant
sluglength
Ls•=
140mm
However, the collapse of each slug at the conduit exit mixed
small bubblesinto the liquid which were slowly carried down
into the conduit by the back flow of liquid so that a foam film
formed around slugsas the two-phaseconduit flow proceeded
I
=
(Figure 8). With a foamy liquid film, counterflow is weakerso
that slug ascentvelocity is reduced.
I
The admixing of bubbles to the liquid may have some
Io
implications in basaltic volcanic eruptions. Small bubbles
introducedinto the liquid either by turbulent slug wakes or by
ß
slug collapse at the surface and liquid back flow may affect
bubble size distributionsin the liquid as it is frozen in. The
rl
thermal insulation of the conduit is improved by bubbly
marginal magma. At low strainratesthe presenceof additional
i
bubbles increases the effective magma viscosity [e.g.
Vergniolle and Jaupart, 1990], thus reducing slug ascent
i
velocities (equations (4)-(7)). At high strain rates (high
I* ',
'
Capillary numbers), disruption of bubbles along the conduit
i
walls has been proposedto causelubrication and acceleration
I
i
',
...................................................................
•
1 mPas
• of the central conduitflow [Stein and Spera, 1992; Herd and
••6=2.5mm
Pinkerton,
1997]. However, with slug flow velocities in the
i
,
- e12 mPas
Mean film thickness,•S [mm]
0
5
ß
o
*•
0
10
15
20
25
30
ß I•i•
t
e,i
ß
II
. L•
o
(
ß
ß
i
i
i
i
.
.
,J
'
'
,
ß
•
i
I
'
I
range1-5ms-] asdeduced
here,strainrateswill betoolowto
,,
,
• --.--
150mPas -
i
I I I I
• = .•1.
i
ImPas
5=lmm
•
...
1.,
,.I
,...
I..
..I
...
2.5.
,,
', ,
deform the bubblesas can be seenon Figure 8.
,
Supplied
Slugs
150mPas
12mPas ' 5=4.7mm
5=2.2mm
calculated
Figure 6. Measureddecrease
in film thickness
/5 with
distancebelow slugtop for threeliquid viscosities
in a 50mm-wide tube. Film thicknessapproachesa constantvalue
We define a suppliedslug as a large gas bubblethat remains
connected to, and fed from, its source gas reservoir during
passage through the conduit. No backflow occurs and the
ascent velocity is controlled by the rate of gas influx so that
we would expect it to be higher than the ascent velocity of
unsuppliedslugs(equations(4) and (7)). Indeed, suppliedslugs
reachedFrø-5=1.3 (Figure1) in an experimental
tubeof
belowzc, theheight
oftheslugcap.Vertical
linesindicate/550 mm diameter filled
valuesfor eachviscosityafter (6) for comparison.
with pure water (1 mPa s), where the
equilibrium ascentvelocity of an unsuppliedslug would lie on
the limiting asymptoteFrø-5=0.345. Repeating this
predictions,
the experimental
measurements
showthat film
experiment with a thinner tube of 14 mm diameter and more
viscous liquid (5000 mPa s), supplied slugs reached
thickness decreases with slug length at constant liquid
Frø'5= 0.16 (Figure1) compared
to unsupplied
slugswhich
slugsthusreach
viscosity (e.g., g = 150mPa s in Figure 6). Figure 7 wouldhardlymoveat Frø'5= 0.01. Supplied
illustratesthe changein slugshapewith length.Measuredslug 10 times the limiting equilibrium velocity value of unsupplied
velocities in the inertial regime (low-viscosity liquids)
slugs(Figure 1). The columnof denseliquid abovea supplied
correspondcloselyto theoreticallyexpectedvalues,but we slug is pushedout of the conduituntil the slug cap reachesthe
note that publishedtheoreticalapproaches
[e.g. Clift, 1978; surface.When the slug cap burstsat the surface,the slugbreaks
Wallis, 1969] do not addressthe complexrelationships
of slug down into a turbulent two-phase flow and a quasi-steady
ascent in the transitional regime.
fountain of liquid spray is ejected from the conduit. This
Furthercomplications
arisefrom the risingbehaviorof gas behavior was observedin both low- and high-viscosityliquid
slugs.Turbulentliquidbackflowdisrupts
thebottomof a slug experiments.
in the inertialregimeand createsa swarmof smallbubblesin
its wake.Camposand Guedesde Carvalho [1988]foundthatan
axis-symmetric
laminarwake prevailsat Re < 180, and wake
vortex rings start to oscillate at 180 <Re < 300, and
become fully turbulent at Re > 300. We may assume
Supplied slugs in the experiments formed only when the
valve at conduit bottom controlling gas influx was opened
suddenly,that is when the accelerationof the injectedgas mass
flow(dMg/dt)
washigh,andwhen
theinjected
bulkgasvolume
was larger than the conduitvolume. Slow openingof the valve
approximateHawaiian conditionsas a volcanicexample resulting
in lowvalues
of dMg/dt,
i.e.,gradual
acceleration
of
(D= 10m; g=50Pas;
p = 2600 kgm-3) and obtain
the gas mass flux, resulted in the evolution of separatedtworegimes discussedin section 3. The occurrenceof
fully turbulentconditionsunder which slug disruptionand supplied slugs in basaltic volcanoesthus requires the sudden
introduction of small bubbles into the magma may occur as release of a large gas volume, such as in the case of a
observed in the experiments. In the transitional regime catastrophically collapsing foam layer as envisioned by
(higher-viscosityliquid) a bubbly wake did not form in our Jaupart and Vergniolle [1989].
phase flow
Us]= 3.4 ms-] (equation
(4)) andRe= 1768,suggesting
SEYFRIEDAND FREUNDT:CONDUITFLOWANDBASALTICER•ONS
23,733
Slug end
Slug end
Slug end
Liquid viscosity
B = 150 mPas
5
10
15
20
25
30
Film thickness, fi [mm]
Figure 7. (a) Film thicknessversusdepth below slug top as in Figure 6 but for slugs of different lengths in
liquid of constantviscosity. Asymptotic film thicknessdecreasestoward longer slugs. Vertical dashedline
showsfi value from (7) for comparison.(b) Schlierenpicture of two slugsof different lengthsin the 50-mm
conduit.Note train of small bubblesin the wake of the upper slug.
3. Continuos Gas Supply
film regionwrappingthe slugs.In contrastto single-slug
ascent,where film liquid just circulatesaroundthe bubble,in
3.1. Theory of Slug flow and annular flow
A continuousgas stream injected into a liquid column is
known to be unstable and transforms into various types of
separatedtwo-phase flow [Wallis, 1969]. In the slug flow
regime a continuousgas stream breaks up into a chain of
equallyspacedslugbubblesof ascentvelocityUsf, whichis
greaterthanthe velocityof corresponding
isolatedslugs,Usi,
bythemean
gasvolume
fluxQg[Wallis,
1969]such
that
+Usi ,
Us
f= Qg
A
(14)
the slug-flowregimethereis an effectivetransportof film
liquiddownward
in theconduit
asobserved
in ourexperiments
The downwardflux of liquid dependson liquid viscosity
through the film thicknessfl.
Slug flow transformsinto annularflow when the liquid
bridgesbetweenthe gasslugsdisappear
with increasing
gas
influx. Coalescence
of gas slugsthen is facilitatedby
increasingturbulencein the liquid bridges.Wallis [1969]
reportsa criterionfor the transitionfrom slugto annularflow
thatdepends
onthefluxof liquidQI:
Qg=0.4+0.6
•. QI
The mean velocity of the bulk mixture acrossthe cross
AUsf
sectionalarea of the conduit, A, is constantfrom continuity,
j= Qg+QI
A
(15)
ß
Here, Q• is the netupwardflux of liquidwhichreflectsthe
difference between the upward transportedliquid betweengas
slugsand the liquid flowing downwardthroughthe marginal
3.2.
Experiments
(16)
AUsf
With
Continuous
Gas Supply
Having investigatedthe ascentof slugsintroducedsingly
into the conduit,we now addressthe two-phaseflow dynamics
that result from a continuousgas supply. This third set of
23,734
SEYFRIED AND FREUNDT: CONDUIT FLOW AND BASALTIC ERUlqlONS
1977] that eruptsgas and liquid at a massratio
M•
k m =•,
(18)
Mg
where
MgandM•arethemeasured
erupted
mass
fluxes
ofthe
two phases.The densityof the mixture,Pancanbe obtained
from
Pan=
Pg+ krnPl
l+k m
ß
(19)
For typical experimentalvalues of M 1= 25 g/s and
Mg=0.Sg/s (km=50), we obtainRe2p=4000,
thatis
higherthanthe minimumvaluerequiredfor turbulentflow. The
two-phase
flownumber
satisfied
N2p> 100forexperimental
liquid viscosities< 400 mPas. However, we did not observe
significant changes in flow behavior at viscosities
> 400 mPa s and therefore we also include results for higher
viscosity values in our discussion.For volcanic conditions
.•:•%'....... ..:
(assuming
g= 100Pas,p•= 2600kgm-3, D=Sm, and
km=50), Re2pvarieswith depthin the conduitbut
..½..•'•...-•.:.:,
.>....•:
..
"?.)•.
":,.•,•
ß
•.:
•.
•
'•....
Re2p
> 2300if J> 18ms
-1isa condition
easily
satisfied
at
...•. .-•:
.•.•..
•..•.
•.•
leastat upperconduitlevels.Usingthe sameg andp• values,
•.•. .• .....
•.....• •.
•
the volcanictwo-phase
flow numberis N2p> 100 if
D > I m (e.g., N2p= 910 for D = 5 m). Again, no
. •.2.
significantchangesin flow regimeoccurwith furtherincrease
..•. '.•.. ..•. ß ..•
.h. .•
.::.•
..
ofeither
Re2p
orN2paslongasthelimiting
values
fora given
flow regime are satisfied. The same holds for the Morton
number(equation(3)), which is much higher in the volcanic
than in the experimentalsystem(Figure 1), but the dominance
•-, •:
.
ß
.•.
of viscousover surface forces is maintainedin both systems.
3.2.2. Experimental setup. The experimental setup
Figure 8. Photographof bubbly liquid back flow partly
obscuring
the risinggasslugin the centerof the pipe.Width
of pictureis 50 mm.
experiments was designed to measure the mass balance of
liquid and gas ejectedfrom the conduitand to determinethe
pressure changes within, and at the transitions between,
different tlow regimes. These experiments were scaled to
natural
basaltic
volcanic
conditions.
3.2.1. Scaling of the experiments. Under volcanic
conditions,gravity forcessurmountsurfaceforcesby ordersof
magnitudeif we considerthe scale of the conduitflow profile
rather than the behavior
of individual
bubbles.
experimental Eotv6s numbers Eo--335
Our choice of
ascertains that
gravity forces surmount surface forces by more than 2
magnitudes.EotvOs numbersfor volcanic conduitswould be
higherat Eo > 105,but higherEo valueshaveno effecton
the tlow behavior as long as the critical value for gravitydominance
is exceeded.
Scalingin the annular11owregime usesthe two-phaseflow
Reynolds number,
Re2p
=JDPa-•--•-n
,
(17)
(Figure 9) consistsof a liquid-filled perspcx tube of 1 m
length with 50-mm-wide squarecrosssectionconnectedto a
liquid reservoirof 100 L. Compressed
air is injectedvia four
nozzles at the base of the conduit to establishtwo phase flow
over the whole lengthof the conduit.Liquid exhaustedfrom the
top of the tube was sampled in a containerdivided into
concentricring-segments,
whichallowedus to determineradial
liquid massdistributionfrom experimentaleruptions.In most
experiments,
however,eruptedliquid wasallowedto flow back
into the large reservoir in order to maintain steady-state
conditions.Bubbly flow, slugflow, and annularflow couldbe
producedin the conduitwithoutsignificantchangesin liquid
level and hydrostaticpressure.Flow behavior, bubble sizes,
and velocities were determinedfrom video recordings.Liquid
viscosity was varied logarithmically from l to 1200 mPa s
by dissolvingcelluloseester in water. Basal pressurein the
conduit was measured 100 mm above the gas injection level.
Gas volume flow was measuredbefore the injection and could
be converted into mass flow using measuredtemperatureand
pressuredata. An inductive, viscosity-independent
liquid mass
flow meter was placed betweenreservoirand conduit.In these
experiments the gas-inlet valve was opened slowly (low
dMg/dt)
toavoid
formation
ofsupplied
slugs.
3.2.3. Liquid-friction
effects. Liquid mass flux from
the conduit was controlledby the two-phaseflow dynamicsat
low liquid viscosities, but friction in the liquid plumbing
system limited the flux at high viscosities. Most of liquid
friction
occurred in the narrow
cross section of the flow meter
which
mustbeRe2p
> 2300to maintain
turbulent
conditions,
andthetwo-phase
flownumber,
N2p,introduced
by Wallis (Din=10mm). Conditionsof Re < 600 withinthe pipeallow
[1969],whichprovides
a lowerlimitN2p> 100to annular the friction coefficient •, to be determinedfrom the Hagentlow formation. In the annular tlow regime, the central tlow is
a particle-laden
gasjet of viscosity
gan= 10-4Pas [Kieffer,
Poiseuille law,
;k = 64/Re.
(20)
SEYFRIEDANDFREUNDT:CONDUITFLOWANDBASALTICERUPTIONS
23,735
Sampling
container
Back
,pie
flow
tube
Conduit
Pressure
transducer
MI
Qg
.pie
Figure 9. Setup for experimentswith continuousgas supply consistingof a liquid-filled perspextube of 1 m
length with square cross section of 50 mm connectedto a liquid reservoir of 100 L. Exhaustedliquid was
sampledin a container,and could flow back into the liquid reservoirto provide constantflow conditionsfor
long
timemeasurement.
Massfluxof liquidM1,andvolume
fluxofgasOg,weremeasured
attherespective
entries.
For constantliquid densityand pipe geometry,k increases the conduitwasobserved)
up to 2 gs-I (whereannularflow
with viscosityand is indirectlyproportionalto the massflow. commenced).Liquid was allowed to mix with bubblesin these
Hence,anasymptote
formsasMl tendsto zerosothat
k=16nDin
g--•--,
longer-lastingruns, and data were recordedat 20 Hz.
For both series, electronically recorded data were used to
(21)
andthepressure
lossAp alongthelengthLinof theinletpipe,
MlLin
Ap
=128g
p•Dp
n.
1.2-[•""
......
• "*'•••:•'••'i•'•:•"ø'•v:;;'i•iiiii•iii'i!•ii!iii•i::•ø'C•fi',;•"•
0300mPas
• 1200mPas
(22)
0.8
The pressureloss (Ap) increasesfrom only 40 Pa for the
lowestviscosityof _=1 mPas and M1= 50gs-l up to
104Pafor_=1200mPas
andM1= 10gs-1.
...........
: ........
0.4
When the pressureloss approaches
the hydrostaticpressure
valueof 7000 Pa in the reservoir,the rate of liquid supplycan
no longerbalancethe rate of liquid ejectionby the two-phase
flow and the conduitis emptiedof liquid as the experiment
I
I
I
......
i"'"'"'
.......' .......
I ...........
•..............
•............
•:•::"'
.................
::::::.:•
proceeds.
3.2.4. Experimental results. A steady gas supply
injectedinto a liquid columnmay breakup into an unsteady,
pulsatingflow in the conduitdependingon the gas flow rate
[Wallis, 1969]. With increasing gas supply we observed
gradual changesin flow regime in our experiments,from
bubbly flow throughslug flow to annularflow for higher
viscosities.
The transitions
in flow regimeshiftedto lowergas
supply rates at higher liquid viscosities.In the slug flow
regimethelengthof eachbubbleincreased
with the rateof gas
supply but decreased with increasing liquid viscosity.
•100
-
0
0.2
0.4
0.6
0.8
1
1.2
Quantitativeresults varied with the way gas was introduced
Gasmassflow [g/s]
into the conduit and with the durationof the experiments.
Experimentscould be run only for a limited time before the Figure 10. Resultsof series1 experimentswith continuous
effects of longtime mixing, making the liquid foamy (see gas supply,terminatedbefore significantmixing of bubbles
into liquid occurred.Variation of (a) normalizedpressure
section2.4, Figure 8), beganto disturbthe flow pattern.
In a series1 of experiments,gas supplywas kept constant pm/P0
, (b) measure
of turbulence
Tu, and(c) mass
ratiokm
for at least20 s after unsteadyinjectionto measurestationary
flow conditions. Experiments were terminated before liquid
mixed with gas bubbles.Data collectedat a samplingrate of 10
Hz provided-- 200 data pointsfor each parameter.
In a series (2) of experiments, gas supply was slowly
withgasflux.Noliquid
could
beexhausted
over
thetOl•
ofthe
conduitand km = 0 at gas massflow rates<0.5gs-L Note
howflow regimeboundaries
shiftwith respectto thegasflux
scale as liquid viscosityincreases.Lines are visual fits to the
data. Vertical dashedline indicatesWallis' [1969] criterion
increased
from0.5 gs-l (wherefirstexhaustion
of liquidfrom (equation(17)) for the slug flow to annularflow transition.
23,736
SEYFRIED AND FREUNDT: CONDUIT FLOW AND BASALTIC ERUPTIONS
evaluate
mean
pressure
Pm'mean
gasmass
flowMg,andmean the
transition from slug to annular flow, followed by a
in km towardannularflow dueto increased
friction
liquidmassflow Mi. The relationbetweenstandard
deviation, decrease
Op,and meanpressure,
Pm is usedas a measure
of the
turbulence
as
Tu =
100 [%].
(23)
Pm
Results from series 1 pressuremeasurementsare shown in
(equation (19)) limiting the liquid supply so that it cannot
balance liquid loss by ejection. At 1200 mPa s, the viscous
frictiondominates
andthemassratiokm becomes
independent
of the gas supply rate (Figure 10c). Such high experimental
liquid viscosities are, however, out of the scaled range for
comparison with basaltic volcanic conduits (see section 5.3.).
Figure10a. PressurePmis normalizedto hydrostatic
pressure The actualratiokm of a basalticeruptionin the annularflow
(P0) in the liquid columnbeforeonsetof the experiment
in regime will depend on the effective liquid friction, i.e., on
liquid viscosityand length of the conduit.
Series 2 experiments,in wl•ich admixing of small bubbles
changesof the liquid columndue to ejectionof liquid:Pm
increasesduring the change from bubbly to slug flow in low- into the liquid was allowed,producedsignificantdifferencesin
viscosity liquids (g < 100 mPas) due to the elevation of the the eruptive behavior. Such mixing dampensturbulence,and
liquid column by the volume of the gas phase.In the slug flow gas and liquid mass fluxes becomelinearly coupled (Figure
order to eliminate pressurechangesarising from small length
regime,Pmdid not changesignificantly,
but a rapiddecrease
in
pressure occurred as turbulence increased with approach to
slug-annular flow. The transitional region between slug and
slug-annular flow narrows with increasing liquid viscosity,
which is best seenby the rapid pressuredecreaseat a gas flux
11).Theincrease
in M• withMgdecreases
asliquidviscosity
increases,
andthere
islittlechange
inM•overtherange
ofMg
at viscosities greater than 800 mPa s. The erupted mass ratio
kmin the annularflow regimeis about2-3 timeslowerthanin
comparable series 1 experiments without mixing. Mixing
of 0.5 gs-1 for the highest-viscosity
liquid (1200mPas; with gas bubbles increasesthe effective viscosity [Prandtl et
Figure 10a). Wallis' [1969] criterion, equation (16), for the
transition from slug to annular flow is independent of
al., 1990] and friction at the conduit wall, which reduces the
viscosity
andliesat 0.55gs-1 for thegivenconditions.
decreasingthe gas mass flux producesa hysteresisin the
Two-phase turbulence increases continuously with
increasing gas supply rate and liquid viscosity (Figure 10b),
and pressurebecomescontrolledby the dynamic force of the
turbulent two-phase flow, rather than by the hydrostatic
pressure gradient, when the liquid bridges between the slugs
disappearduring transitionfrom slug to annularflow. As liquid
flow resistance increases with viscosity, the pressure drop
forcing the flow upward also increases,resultingin an increase
in Tu (equation (23)) that promotesmixing of small bubbles
into the liquid.
The massratio km of eruptedliquidto gastendsto zeroat
very low gas supply rates (Figure 10c) as the gas flow cannot
ejectliquidfromthe conduit.A maximumin km is reached
at
liquid output (lower value of km). Increasingand then
variation
of M• withMg(Figure
12)whichis probably
caused
by a continuousincreasein viscositywith mixing time, thus
reducingthe liquid transportrate. Eruptiondurationthus has
an influenceon the massbalanceof eruptedgasandliquid.
4. Flow in a Rough-Walled Conduit
Naturalvolcanicconduitsare not smoothcylindricaltubesof
constant diameter as assumedin modeling and used in
experimentsbut are rathercharacterized
by lateral and vertical
changesin diameterand axislocationresultingfrom complex
crack propagationthroughthe multiple layers of a volcanic
50
'
40-
•
-
0 •0
•_.%.4•
0•
'
•o
-
o,,
-
,
30-
20-
10-
_
-.•'••
• ....
0.5
•
• ....
• .5
• ....
2
2.5
Gasmass
flow,Mg[g/s]
Figure 11. Resultsof series2 experiments
with continuous
gassupply,allowingfor mixingof bubblesinto
liquid.
Liquid
fluxM1varies
linearly
withgasfluxMg,andtheslope
decreases
toward
higher
liquid
viscosities.
SEYFRIED AND FREUNDT: CONDUIT FLOW AND BASALTIC ERUPTIONS
Pressure fransducer
Pressure fransducer
23,737
2
I
Figure 12. Experimentalsetupto investigategas slug propagation
througha partiallyblockedconduit.
Pressuretransducers
mountedinside trappedgas pocketsrecordtheir oscillationstimulatedby the passing
liquid.
ordersof magnitudelesspowerfulthanthoseproduced
in thc
first experimentsdiscussedabove. There, strong pressure
fluctuationswere causedby rapidformation,coalescence,
and
expansion
of slugbubblesandby turbulentmixingof liquid
are the dominant
couldbe trapped
allowed
usto recordoscillation
of thegas and gas.We concludethat theseprocesses
edifice [e.g. Ryan et al., 1981]. We useda perspextube with
built-in obstacles (Figure 12) to experimentally investigate
the propagation of slug bubbles through a partially blocked
conduit. Pressuresensorsmounted below obstacleswhere gas
pockets stimulated by the passingliquid.
A first series of experiments used the partially blocked
conduit filled with liquid of 850 mPa s viscosity connectedto
a large liquid reservoir. Gas injection began in the slug flow
regime and was then driven into the annular flow regime. Gas
pockets formed below the obstaclesin the conduit, but when
these were filled, the core flow of liquid and gas slugsmoved
around the obstacles(Figure 13). Gas slugs then deformedbut
remained intact during passagethrough the conduit, and no
significant deviations in slug ascent velocity compared to a
sourcesof volcanic tremor, rather than the much less powerful
oscillationof trapped gas pockets.
smooth
vaporizationat the conduitwall or releaseof trappedgas
pocketsby volcanicshocks.Singleslugsrise and burstat the
conduit
could be observed.
In a second set of experiments, gas was initially injected
into the conduit wall pockets.Gas-freeliquid was then pumped
through the conduit, and the signals of two pressure
transducersplaced inside the gas pockets were recorded at a
sampling rate of 11,025 Hz to detect the resonance
5. Eruption Phenomena
Each of the flow regimes in the experimentalconduit
producesa differentstyleof eruption.
Single slug ascentcan only developfrom single,sudden
incidentsof limited-volumegas releasewhich, in the volcanic
environment, may occur, e.g., by local ground-water
surfacecausingshorteruptionpulsesseparated
by irregular
timeintervals.
We referto thistypeof activityassporadically
pulsatinglava fountains.The collapseof slug bubblesat the
surfacein ourexperiments
wasrecorded
on 16mm highspeed
frequencies.
Thesepressuresignalsdid not rise significantly film with up to 2000 frames per second.The pictures
above the noise level in all experiments. Furthermore, the (Figure 13) clearly show a rather quiet process,involving
signals producedby gas pocket oscillation were at least 3 little fragmentation,where slug collapse took place at the
23,738
SEYFRIED AND FREUNDT: CONDUIT FLOW AND BASALTIC ERUIYFIONS
I
2
3
:f'""•'
...... ß..............
•.....................
.:•'•'.
,;•...'
.....
•.•i..:•..:.•:
....:.•.,..
.:
...-:•%•::•.
•.,.•
..2,
......
'..........
'...........................
.....
''.........
:'
ß.... -....:,.•&:
:}
..............
., "......•::
•: ....:•.-.
?..,•;•,. •' ,
: %•g?'
;.........
......• Q•L.
'•.•.-'
'".',I:
:.•' Eg•
.. •:::::•'•'•'•.;
½e,
•...... :..."•:::•::•E:•};
'.:'
•:':•:-•
:•'"'
,.-•:.%.,
'•"•
'}:; ...
:'•:-•*•'
,..-•'[7'*';
..... •::'5-.*t•:: : ;:
........ ß•. •.
•.•,•
..:,::::..:
:.?•.:::r•
.•:.
:.•.• .... g.•
..
a)
•'
.
....
•
g•.-...-.?-.:..., ?,/&
•
.}•-•::--•...
•. :xc..
.-
.../.../':
..•'•.•g;:::.
•.•?½.::.•?........:.. .
::.-?;'
:......
......:.........,•.•.
.....
. ....
.
.. •:•.
.....
..
:½?-..:...,
• ...::.,ß
' ".:.:::'
.,:-"?X-•:,:..[
,..'-.;.':2'.4:;
;:•:" .:
:,•'• ' ,•......•.•
'k
...
Time
differenece
between
the frames At • 0.1 s
Figure 13. (a) Picturestaken at At = 0.1-s intervals from an experimentwith the setup in Figure 12 showing
the core of the slug flow movingaroundthe obstacleswhich are alreadyfilled with trappedgas.(b) Sequenceof
picturesin the samesetupshowingburstingof bubblesinto trappedgas pocketsduringcoalescence.
liquidlevelinsidetheconduit.Whentheliquidlevelwasin the with single slugs, the mode of bubble disruption in the slug
reservoiratopthe conduit(Figure14) as in a lava-filledcrater, flow regime dependson whether it occursinside the conduit or
however, bubble bursting and liquid ejection were more
at the free surface.
Supplied slugs rise much taster through the volcanic conduit
vigorous and resembledstrombolianexplosions.Because
singleslugascentproduces
little mixingof gasandliquid,and than single slugs and effectively push the overlying liquid
thus does not significantly expand the liquid by foam effusively out of the conduit. When the slug cap burstsat the
formation,a slugformedby a quickpulseof gasinjectionhad surface,the suppliedslug breaksdown into annular flow.
Annular flow thus can result from either a gradualincreasein
to be sufficientlylong to pushout any of the overlyingliquid
gas flux out of the slug-flow regime or from the collapseof a
supplied slug. Annular flow always creates a fountain-like
eruption
with strongpulsationsof higher frequency,reflecting
regular time intervals; we call this type of activity a
periodicallypulsatinglava fountain..However,whetheror not the turbulencefrequencyof the conduit flow. Fragmentationof
liquid is exhausted
from the conduitduringslugflow depends liquid is more efficient than in the slug flow regime,
on the depthof the staticliquid level belowthe conduitexit generating more and finer droplets. We refer to this style of
before disruption(Figure 15).
The periodicityof slug flow causeseruptionsto occur at
beforegas injection,the liquid viscosity,andthe durationof
gas supply. In our experimentsusing water (1 mPa s), the
conduit
had to be filled
to the exit level
to have measurable
amounts of liquid ejected. At a viscosity of 100 mPa s, gas
bubbles mixed into the liquid could escape only slowly and
thus expandedthe liquid columnuntil the mixture reachedthe
conduit exit from where it mainly flowed out effusively. As
eruption as a quasi-steadylava fountain. Experimental
eruptionsdrivenby annularflow with higher-viscosity
liquids
suffered waning liquid eruption rates in responseto the
friction-limited liquid supply (see section3.2.3.), eventually
resulting in ejection of gas only from the conduit. Our
experimentssuggestthat when a quasi-steadyfountainis
preceded
by Strombolian-type
explosions,
gasreleaseat depth
SEYFRIEDAND FREUNDT:CONDUITFLOWANDBASALTICERUP•ONS
23,739
Single gas slugs can form in a volcanicconduitby sudden
releaseor generation(e.g., by water vaporization)of a limited
gas volume. The ascentvelocity of single gas slugsthen lies
in the transitionalregime at 0.1 < Frø-5<0.345. Ascent
velocityis independentof decompressional
sluggrowthduring
ascentbut dependson liquid viscosityand weakly on the gas
masscontainedin a slug. The staticmagmalevel in the conduit
has to reach the vent exit to producesignificantStromboliantype eruptions from single slug ascent. A steady gas release
into the conduitat moderateratesbreaksup into the slugflow
regime, where liquid trapped between periodic gas slugs is
carried upward and ejected as the bubblesburst at the conduit
exit. Eruptions due to single-slugascentoccur irregularly in
time, in contrast to rhythmical Stromboli0n-like eruptions
that are due to slug flow. We therefore distinguishbetween
sporadically pulsating lava fountains and periodically
pulsatinglava fountains.Backflow of liquid alongthe margins
of gas slugs drives convectionin the conduit. Liquid mixed
with small bubbles, generatedeither in the turbulent wake of
large slugsor during slug disruptionat the surface,is thereby
transferredinto deeperregionsof the conduit.Such processes
may significantly modify bubble size distributions in the
resulting volcanic rocks.
A suppliedslug forms when a large volumeof gas (greater
than the conduit volume) is suddenlyreleasedinto the conduit
Figure 14. Photograph of a narrow fountain of strongly and remains connected to, and fed from, its gas reservoir
fragmentedliquid eruptedfrom the conduitduring slug-annular throughout its ascent. Supplied slugs reach much higher
flow. Liquid viscosity is p = 125 mPas and gas flux is velocities (Frø-5=0.15-1.6 in the experiments)than
unsupplied slugs. No backflow of liquid takes place, and
Mg=0.8 g/s.
overlying magma is driven effusively out of the conduit until
the slug cap bursts at the surface and the supplied slug
wasmoregradual,
whereas
whenit is preceded
bylavaeffusion, collapsesto a highly turbulenttwo-phaseflow in the conduit.
gaswasreleased
rathercatastrophically
to forma supplied Turbulent annularflow generatesquasi-steadylava fountains
slug.
in which the mass ratio of liquid to gas is lower than in the
Our experimentsprovide no a priori characteristicto relate slug flow and is controlledby the transportcapacityof the gas
the eruption style to a certain sourcemechanism(processof stream. The mass ratio can decrease with time even at constant
gas releaseor generation)of the separatedtwo-phaseflow in gas flux when the friction-controlled supply rate of liquid
the conduit.Dedicatedexperimentswouldbe neededto identify cannotkeep pace with the eruptionrate of liquid. Annular flow
distinguishing features, such as perhaps differences in the can form either by increasingthe gas supply rate above the
grain size distributions resulting from the different
range for slug flow, or by collapseof suppliedslugs.In both
fragmentation mechanisms.
cases,the transition to annular flow involves a change from
the hydrostaticto the much lower dynamicpressuregradient,
reducing pressure in the reservoir and promoting further
6. Conclusions
degassingof the magma which may maintain fountaining
Our experimental
studycomplements
earlieranalyses
of activity until the gas reservoiris exhausted.
homogeneoustwo-phaseflow in basaltic volcanic conduits
In general,the eruptedmassratio of magmato gas depends
[WilsonandHead,1981]by considering
separated
two-phaseon the rheologyof the magma,the flow regimein the conduit,
flow phenomena.
Scalingof theexperiments
allowsto apply viscousfrictionin the plumbingsystem,andthe mixingtime
ourresultsto basalticeruptions
whennaturalcomplexities
at a
givenvolcanoare adequatelyconsidered.
of magmaand gas during ascentand eruption.Our resultsare
not apparently sensitive to conduit shape and roughness.
Figure 15. Fourframesat At = 2 mstimeintervals
from 16-mmhigh-speed
film recording.The collapseof a
gassluginsidethe conduitcan be seenas a quietprocesswithoutoscillationor significantfragmentation.
23,740
SEYFRIEDAND FREUNDT:CONDUIT FLOW AND BASALTICERUPTIONS
Slugs remained stable without coalescenceand significant
velocity change during ascentin a partially blocked conduit.
Bubble burstsduring coalescencewith gas pocketstrappedin
the corners of the blocked conduit appear to be a prominent
source of volcanic tremor because they produced at least 3
orders of magnitude more powerful pressuresignals than gas
pocket oscillationinducedby passingliquid.
Notation
A
cross-section
area.
C
bubble
concentration.
D
conduit
diameter.
D'
H
correspondingtube diameter.
height of the magma chamber.
J
flux.
K
Karman's constant (K = 0.4).
L
length.
M
mass flow.
N
Q
R
S
T
T
dimensionlessparameterrelating film
thicknessand ascent velocity of slugs.
bulk volume flux.
specific gas constant [J/Kg/K].
spring constantof a gas slug.
temperature.
temperaturedifference.
Tu
turbulence.
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m
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fi
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)•
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0
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damping factor.
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Wallis,G.B., OneDimensionalTwo-Phase-Flow,1408pp., McGraw-
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•
dimensionlessfilm thickness.
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Wilson,L., andJ.W. Head,Ascentanderuptionof basalticmagmaon
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g
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I
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m
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Woods,A., andA. Cardoso,
Triggering
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sf
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Acknowledgments. This work was funded by the Deutsche
Forschungsgemeinschaft
(DFG) throughgrantsFr947/3-1andFr947/3-2
to A. Freundt. We wish to thank K. Cashman,L. Wilson, and A. Woods
for theircommentson thispaper.
1997.
R. Seyfried
andA. Freundt,
GEOMARForschungszentrum,
Wischhofstr.1-3, D-24148 Kiel,
Germany.(rseyfried@geomar.
de)
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