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Transient Interfacial Phenomena in MisciblePolymer Systems
(TIPMPS)
John A. Pojman
University of Southern Mississippi
Vitaly Volpert
Université Lyon I
Hermann Wilke
Institute of Crystal Growth,
Berlin
A flight project in the Microgravity Materials Science Program
2002 Microgravity Materials Science MeetingJune 25, 2002
2
What is the question to beanswered?
Can gradients of composition and temperature inmiscible polymer/monomer systems create
stresses that cause convection?
3
Why?The objective of TIPMPS is to confirm Korteweg’smodel that stresses could be induced in miscible fluidsby concentration gradients, causing phenomena thatwould appear to be the same as with immiscible fluids.The existence of this phenomenon in miscible fluidswill open up a new area of study for materials science.
Many polymer processes involving miscible monomerand polymer systems could be affected by fluid flowand so this work could help understand misciblepolymer processing, not only in microgravity, but alsoon earth.
4
How
An interface between two miscible fluids will be becreated by photopolymerization, which allows thecreation of precise and accurate concentration gradientsbetween polymer and monomer.
Optical techniques will be used to measure therefractive index variation caused by the resultanttemperature and concentration fields.
5
Impact
Demonstrating the existence of this phenomenon inmiscible fluids will open up a new area of study formaterials science.
“If gradients of composition and temperature in misciblepolymer/monomer systems create stresses that causeconvection then it would strongly suggest that stress-inducedflows could occur in many applications with miscible materials.The results of this investigation could then have potentialimplications in polymer blending (phase separation), colloidalformation, fiber spinning, polymerization kinetics, membraneformation and polymer processing in space.”SCR Panel, December 2000.
6
Science Objectives
• Determine if convection can be induced byvariation of the width of a miscible interface
• Determine if convection can be induced byvariation of temperature along a miscibleinterface
• Determine if convection can be induced byvariation of conversion along a miscibleinterface
7
Surface-Tension-InducedConvection
convection caused by gradients in surface(interfacial) tension between immisciblefluids, resulting from gradients inconcentration and/or temperature
high temperature low temperature
fluid 1
fluid 2
interface
8
Consider a Miscible “Interface”
x
y
“interface” = ∂C/∂y
C = volume fraction of A
fluid A
fluid B
9
Can the analogous process occurwith miscible fluids?
high temperature low temperature
fluid 1
fluid 2
10
Korteweg (1901)• treated liquid/vapor interface as a
continuum
• used Navier-Stokes equations plus tensordepending on density derivatives
• for miscible liquid, diffusion is slow enoughthat “a provisional equilibrium” could exist(everything in equilibrium except diffusion)– i.e., no buoyancy
• fluids would act like immiscible fluids
11
Korteweg Stress• mechanical interpretation (“tension”)
k has units of N
σ has units of N m–1
yx
Change in a concentration gradient along the interface causes a volume force
pN − pT = kdcdx
2
= kdc
dx
2
dx∫
FV
= ky
cx
2
12
Hypothesis: Effective InterfacialTension
= k(∆C)2
C
δ
k is the same parameter in the Korteweg model
(Derived by Zeldovich in 1949)
13
Theory of Cahn and Hilliard
= k ∇2∫ C(r)dralso called the surface tension (N m–1)
square gradient contribution to surface free energy (J m–2)
Cahn, J. W.; Hilliard, J. E. "Free Energy of a Nonuniform System. I. Interfacial Free
Energy,"J. Chem. Phys. 1958, 28, 258-267.
k > 0
Thermodynamic approach
g = g0 + k ∇C∫2
Square gradient theory
PN − PT = kdcdx
2
Cahn-Hilliard Theory ofDiffuse Interfaces (1958)
Convection: experiment and theory
Korteweg Stress
Effective Interfacial Tension
= k ∇C∫spinning drop tensiometry
f = f0 + k
1901
Mechanics Thermodynamics
Cahn-Hilliard Theory ofPhase Separation
Nonuniform Materials
PTPNk
simulation
material properties 14
Zeldovich Theory(1949)
van der Waals
1893
15
Why is this important?• answer a 100 year-old question of Korteweg
• stress-induced flows could occur in manyapplications with miscible materials
• link mechanical theory of Korteweg tothermodynamic theory of Cahn & Hilliard
• test theories of polymer-solvent interactions
16
How?
• photopolymerization of dodecyl acrylate
• masks to create concentration gradients
• measure fluid flow by PIV or PTV
• use change in fluorescence of pyrene tomeasure viscosity
17
Photopolymerization can be usedto rapidly prepare
polymer/monomer interfaces
We have anexcellent modelto predictreaction ratesand conversion
0
50
100
150
200
0 10 20 30 40 50 60
Temperature - model / CConversion - model / %Temperature - exp / C
Tem
pera
ture
(˚C
) or
% c
onve
rsio
n
Time (s)
+
Experimental conversion after 10 seconds exposure
18
Schematic
UV
laser sheet illumination
videocamera
mask
no reaction
reaction1 cm
6 cm
100 W Hg arc lamp
filter (330 - 400 nm)
19
20
Variable gradient
21
Why Microgravity?
• buoyancy-drivenconvection destroyspolymer/monomertransition
2.25 cm
1 g
(Polymer)UV exposure region
22
Simulations
• add Korteweg stress terms in Navier-Stokesequations
• validate by comparison to steady-statecalculations with standard interface model
• spinning drop tensiometry to obtain k
• theoretical estimates of k
• predict expected fluid flows and optimizeexperimental conditions
23
Model of Korteweg Stresses inMiscible Fluids
T
t+ v∇T = ∆T
Ct
+ v∇ = D∆C
vt
+ v∇( )v = − 1 ∇p + ∆v +1
K11
x1
+ K12
x2
K21
x1
+ K22
x2
div v = 0
K11 = kCx2
2
K12 = K21 = −kx1
C
x2
K22 = kC
x1
2
where k is system specific,
Navier-Stokes equations + Korteweg terms
24
Essential Problem: Estimation ofSquare Gradient Parameter “k”
• using spinning drop tensiometry
• use thermodynamics (work of B. Nauman)
25
Spinning Drop Technique
• Bernard Vonnegut, brother of novelist KurtVonnegut, proposed technique in 1942
Vonnegut, B. "Rotating Bubble Method for theDetermination of Surface and InterfacialTensions,"Rev. Sci. Instrum. 1942, 13, 6-9.
ω = 3,600rpm
1 cm
= ∆ 2r3
4
26
Image of drop
1 mm
27
Evidence for Existence of EIT
0
0.1
0.2
0.3
0.4
0.5
0 100 200 300 400 500
EIT (mN/m) 2000 RPMEIT (mN/m) 3000 RPMEIT (mN/m) 4000 RPMEIT (mN/m) 5000 RPMEIT (mN/m) 6000 RPMEIT (mN/m) 7000 RPMEIT (mN/m) 7900 RPM
EIT
(m
N m
–1)
Time (sec)
drop relaxes rapidly and reaches a quasi-steady value
28
Estimation of k from SDT
• estimates from SDT: k = 10–8 N– k = EIT * δ– k = 10-4 Nm–1 * 10–4 m
• Temperature dependence– ∂k/∂T = -10–9 N/k
– results are suspect because increased Tincreases diffusion of drop
29
Balsara & Nauman: Polymer-Solvent Systems
k =Rgyr
2 RT
6Vmolar
Χ +3
1− C
X = the Flory-Huggins interaction parameter for apolymer and a good solvent, 0.45.
Balsara, N.P. and Nauman, E.B., "The Entropy of Inhomogeneous Polymer-SolventSystems", J. Poly. Sci.: Part B, Poly. Phys., 26, 1077-1086 (1988)
k = 5 x 10–8 N at 373 K
Rgyr = radius of gyration of polymer = 9 x 10–16 m2
Vmolar = molar volume of solvent
30
Simulations
• Effect of variable transition zone, δ• Effect of temperature gradient along
transition zone
• Effect of conversion gradient alongtransition zone
31
We validated the model bycomparing to “true interface
model”
• Interfacial tension calculated using Cahn-Hilliard formula:
• same flow pattern
• Korteweg stress model exceeds the flowvelocity by 20% for a true interface
= k(∆C)2
32
Variation in δ
Korteweg Interface
33
Simulation of Time-DependentFlow
• we used pressure-velocity formulation
• adaptive grid simulations
• temperature- and concentration-dependentviscosity
• temperature-dependent mass diffusivity
• range of values for k
34
Concentration-DependentViscosity: µ = µ0eλc
1
10
100
1000
0 0.2 0.4 0.6 0.8 1
λ = 1λ = 2λ = 3λ = 4λ = 5
Rel
ativ
e V
isco
sity
Conversion
λ = 5 gives apolymer thatis 120 X moreviscous thanthe monomer
35
Variable transition zone, δ, 0.2 to 5 mm
k = 2 x 10–9 N
polymer
monomer
36
streamlines
37
Maximum Displacement Dependenceon k
1=0.2mm; 2=5mm; k1 *106, N =0; 0, Pa*s =0.006;
C =3; T =0; d0*106, kg/(m*s) =0.1; d 1*106, kg/(m*s) =0.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 100 200 300 400 500 600 700 800
seconds
k0 = 1e-7, Nk0 = 1e-8, Nk0 = 2e-9, N
38
Dependence on variation in δIsothermal case with variable transition zone:
k0 *106, N =0.01; k 1 *106, N =0; 0, Pa*s =0.006;
C =3; T =0; d0*106, kg/(m*s) =0.1; d 1*106, kg/(m*s) =0.
0
0.1
0.2
0.3
0.4
0.5
0.6
0 100 200 300 400 500 600 700 800
seconds
epsilon1=0.2mm, epsilon2=5mm
epsilon1=0.2mm, epsilon2=2mm
epsilon1=0.2mm, epsilon2=1mm
39
Effect of Temperature Gradient
Temperature is scaled so T= 1 corresponds to ∆T = 50K.
Simulations with different k(T) -does it increase or decreasewith T?
Simulations with temperature-dependent diffusioncoefficient
40
viscosity 10X monomer (0.01 Pa s)
k0 = 1.3 x 10–7 N
k1 = 0.7 x 10–7 N
41
side heating,δ = 0.9 mm
polymer = 10 cm2 s–1
monomer = 10 cm2 s–1
T0T0 + 50K
Two vortices are observed
42
side heating,δ = 0.9 mm,µ(c) =0 .01 Pa s * e5 c
polymer = 12 cm2 s–1
monomer = 0.1 cm2 s–1
asymmetric vortices are observed with variable viscosity model
43
effect of temperature-dependentD
• k independent of T
• D increases 4 times across cell
• higher T means larger δ• effect is larger than k depending on T even
with viscosity 100 times larger
44
significant flow
T0T1 T0 T1
45
mm =1; k0 *106, N =1.3; k 1*106, N =0; 0, Pa*s =0.1;
C =5; T =0; d0*106, kg/(m*s) =10; d 1*106, kg/(m*s) =40.
0
0.2
0.4
0.6
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
seconds
46
Effect of Conversion Gradient
• T also varies because polymer conversionand temperature are coupled through heatrelease of polymerization
• T affects k
• T affects D
47
9.4
C =1 C =0
monomer
k = 10–8 N
T = 150 ˚C
T = 25 ˚C
polymer viscosityindependent of T
48
with D(T)
C =1 C =0
monomer
k = 10–8 N
T = 150 ˚C
T = 25 ˚C
D=1.2 x 10-5 cm2 s-1 D=1 x 10-6
cm2 s-1
49
Limitations of Model
• two-dimensional
• does not include chemical reaction
• neglects temperature difference betweenpolymer and monomer– polymer will cool by conduction to monomer
and heat loss from reactor
50
Conclusions
• Modeling predicts that the three TIPMPSexperiments will produce observable fluidflows and measurable distortions in theconcentration fields.
• TIPMPS will be a first of its kindinvestigation that should establish a newfield of microgravity materials science.
51
Quo Vademus?
• refine estimations of “k” using spinningdrop tensiometry
• completely characterize the dependence ofall parameters on T, C and molecular weight
• prepare 3D model that includes chemistry
• include volume changes
52
Acknowledgments
• Support for this project was provided byNASA’s Microgravity Materials ScienceProgram (NAG8-973).
• Yuri Chekanov for work onphotopolymerization
• Nick Bessonov for numerical simulations