3/19/14 Viscosity Week 5 Lecture Viscosity, viscoelas9city, gela9on Demo: Ice melts to become water-­‐-­‐Water flows Demo: A cube of gela9n gel deforms under shear What happens if you warm the gel-­‐ can you s9ll push it? Liquid cannot sustain a shear—it flows when sheared Resistance to flow depends on viscosity Viscosity Viscosity of oil Oil is more viscous than water Demo: Takes a longer 9me to flow through funnel Demo—you did this in the lab : Drop a ball bearing or chickpea in a tube filled with water, oil, and honey Which liquid does the ball fall slowest, fastest? Rank the 9me of fall in increasing order A material is a liquid if the molecules can move around each other. The fundamental quan9ty that governs this is the !me that it takes for molecules to move around their neighbors. If it takes a long 9me for them to move by each other, the material is very viscous. If it takes a short 9me, the material is less viscous. Molecular viscosity Molecular viscosity Scien9sts typically use two measures of viscosity: ν = l×c
η = ρν
ν = l×c
Size of molecule Velocity of molecule kinema9c viscosity Dynamic viscosity For lay people, the best measure of viscosity is the 9me it takes something to flow. Of course, these three concepts (kinema9c and dynamic viscosity, and flow 9me) are related. €
1 3/19/14 Molecular viscosity Origin of viscosity of water Dimensional analysis gives a rela9on between E and η length2/9me ν = l×c
length length2/9me length/9me η = E ×τ
molecular viscosity: ! = l ! c
Recall: elasticity: E =
k BT
l3
Viscosity = Elas9city 9mes a relaxa9on 9me All fluids are solids at short enough 9mes Times depend on the fluid Short-­‐8me elas8city of a liquid Origin of viscosity of water η = E ×τ
η = ρ ×ν
Dynamic viscosity kinema9c viscosity Just different measures of viscosity h[p://www.youtube.com/watch?v=f2XQ97XHjVw Relaxa8on 8me for water Relaxa8on 8me for water Compare this to ρν
τ=
E
E = kT/ l3 = 2.5 x 1010 g /(cm. sec2) ρ = 1 g/cm3 2
ν = 0.01 €cm / sec
Ques9on: What is the 9me that molecules move by each other? Answer: l
τ=
c
l = molecular size = 5 Angstroms c = 1500 meters/second (room Temperature) €
5 ×10 −8 cm
τ=
≈ 3 × 10-13 sec
150000 cm/sec
τ=
0.01
≈ 4 × 10-13 sec
2.5 × 1010
€
2 3/19/14 Viscosity of hot oil Demo— sugar candy Hot oil flows faster than cold oil Viscosity decreases with increasing temperature Molecules move around each other more easily Sugar syrup thickens –i.e. gets more viscous on hea9ng– Why? η = E ×τ
τ = τ 0 exp (U kT )
η = E ×τ 0 exp (U kT )
U : same interac9on energy as in week 1 Thickeners—viscosity depends on concentra8on •  Very small amount of material increases viscosity a lot— example adding flour to a cream sauce or to a gravy •  Related to thickeners being polymers and gela9on Xanthan Gum makes liquids thicker •  Xanthan Gum (E415): makes food thick and creamy; also stabilizes foods to help solids and liquids stay together SAUCES LOW FAT or NON-­‐DAIRY DRESSINGS water Polymers and Gela8on 0.1% xanthan gum Viscoelas8c gels Example: olive oil with gela9n kT
Equa9ons: η = E ×τ
E = B3
l
Key concepts: Viscoelas9city and 9me-­‐dependence Elas9city of polymer gels Viscosity of polymer solu9ons 3 3/19/14 Viscoelas8city of corn starch (or silly puUy) How does 9me scale affect viscoelas9city? Short 9me: elas9c Viscoelas8city of corn starch How does 9me scale affect viscoelas9city? Long 9me: viscous Short 9me: elas9c Food polymers: starches Chains of polysaccharides glucose sucrose Food polymers: carbohydrates Sugars, starches, pec9n and gums amylopec9n Starch-­‐thickened sauces Granules swell and leak polymers Potatoes Wheat 75% starch 10% proteins amylose Long 9me: viscous mostly long chain amylose molecules Food polymers: proteins Proteins are chains of amino acids alanine tryptophan lysine Higher temperature Examples: roux, gravy 4 3/19/14 Food polymers: hydrocolloids Xanthan gum, guar gum, locust bean gum Protein-­‐thickened sauces Heat denatures the proteins, which then entangle Heat Thickening Curdling Examples: meat stock, sabayon, hollandaise Polymers can cross-­‐link to form a gel Methods: entanglement or ions = polymer strand Spherifica8on: an example of gela8on Green pea ravioli / el Bulli and Alícia Founda9on = bond between polymer strands Spherifica8on—Mango spherifica9on / Alícia Founda9on Spherifica8on: an example of gela8on Form thin layer of gel around droplet Crosslinks are ionic 5 3/19/14 Alginate is a polysaccharide Example of gela8on Calcium ions join together separate alginate strands Ca2+ + 2Alg-­‐ à CaAlg2 Alginate à from seaweed Spherifica8on: Direct Alginate drop forms gels with Ca2+ in solu9on Internal view of spherifica8on Shell thickens with 9me in the Ca2+ bath Ca2+ Alginate Must serve immediately These can not be stored Spherifica8on: Inverse Ca2+ solu9on forms gels with aqueous alginate (F. Sapiña y E. Martinez, Universitat de València)
Time scale for spherifica8on Diffusion of Ca2+ ions in water: D = 7 x 10-10 m2/sec 1 mm shell 10 micron shell Alginate 0.1 sec. 20 min. Ca2+ 2
(10−3 m )
L2
t=
=
D 7 ×10−10 m 2 s
t = 0.1sec
t = 1000sec = 20 min
(
These can be stored 2
10 !10"6 m
L2
t=
=
D 7 !10"10 m 2 s
)
6 3/19/14 Polymers can cross-­‐link to form a gel Between cross-­‐links, polymers behave like springs Elas8city of polymers Polymers have a natural cross-­‐link spacing Polymer with N monomers Has an equilibrium length ~ N 1/2 = l Elas8city related to Entropy of polymers Elas8city of polymers Polymers have a natural cross-­‐link spacing Stretching polymers reduces the number of states, reduces entropy l Energy 0 U l Separa9on More states, Higher entropy U ≈ kBT for a gel Entropy of polymers Compressing polymers also reduces number of states, and entropy Equa8on of the week Elas9city of a gel depends on cross-­‐link spacing E=
Fewer states, Lower entropy E kB =
T l k BT
l3
= elas9city [Pa] Boltzmann constant [J/K] = temperature [K] = mesh spacing [m] 7 3/19/14 Equa8on of the week Elas9city of a gel depends on cross-­‐link spacing kT
E = B3
l
[E] =
Mesh size Calculate the spacing between cross-­‐links J
m3
l3 =
k BT
E
l E kB =
T l = elas9city [Pa] Boltzmann constant [J/K] = temperature [K] = mesh spacing [m] Mesh size Calculate the spacing between cross-­‐links l3 =
Mesh size Calculate the spacing between cross-­‐links k BT
E
l k BT
E
4.2 !10"21 J
=
20kPa
= 2.1!10"25 m 3
l3 =
l l = 3 2.1!10"25 m 3
= 6 !10"9 m
= 6 nm
Mel8ng of gels The cross-­‐links in gela9n detach at high temperatures Viscoelas8city of polymers Degree of entanglement determines the behavior Higher temperature 8 3/19/14 Viscoelas8city of polymers Viscoelas8city of polymers Entanglement is like elas8city At short 9mes, polymers can’t disentangle Elas8city of Polymers Lose iden9ty of individual polymers when entangled σ
Degree of entanglement determines the behavior Polymers are constrained under sudden shear σ
This controls the elas9city, E.
Relaxa8on 8me Polymers can slowly untangle à repta9on Relaxa8on 8me Polymers can slowly untangle Repta9on This controls the 9me constant, τ.
This controls the 9me constant, τ.
9 3/19/14 Equa8on of the week Viscosity is related to elas9city by a 9me-­‐scale Concentra8on Dependence Polymers become entangled at high densi9es η = E ×τ
η= viscosity [Pa s] E = elas9city [Pa] τ = 9me-­‐constant [s] Higher concentra9on This sets the elas9city, E, and the relaxa9on 9me, τ.
Shorter polymers don’t entangle as much à lower η
Shear-­‐rate Dependence Polymers can disentangle at high shear rates Viscoelas8city in mouthfeel Elas9city and viscosity determine texture Short 9mes, fast changes Elas9c gels Polymers Higher shear Shear thinning
Example: ketchup
Equa8on of the week Sample calcula9on for honey τ=
η
E
=
τ = 0.5s
Anima9on courtesy Naveen Sinha Shear rate The rate of deforma9on sets the 9me scale. F η = E ×τ
Viscous fluids Long 9mes, slow changes F 103 Pa ⋅ s
2 ×103 Pa
High shear rate Low shear rate Stress determined by viscous component For a liquid, viscosity = stress/ shear rate 10 3/19/14 Solid gel Solid gel kT
E
4.2 × 10 −21
=
1000
= 4.2 × 10 −24
l3 =
l
l=
Thickener is a polymer Polymer forms network in the water This forms the solid gel Thickener is a polymer Polymer forms network in the water This forms the solid gel Viscosity of thickeners The bonds are not permanent Molecules can move Molecules must disentangle to move Spaghev demo 1
3
4.2 × 10 −24
= 1.6 × 10 −8 meters
= 16 nanometers
Viscosity of thickeners η = E ×τ
E=
k BT
l3
L2
τ =τ0 2
l
Viscosity of thickeners η = E ×τ
L2
τ =τ0 2
l
5
1
η = kTτ 0 5 ~ C 3
l
kT
E = B3
l
Very strong concentra9on dependence 11