A micro-macro simulation algorithm for the calculation of polymeric flow is developed and implemented. The algorithm couples standard finite element techniques to compute velocity and pressure fields with stochastic simulation techniques to compute polymer stress from simulated polymer dynamics. The polymer stress is computed using a microscopic-based rheological model that combines aspects of network and reptation theory with aspects of continuum mechanics. The model dynamics include two Gaussian stochastic processes, each of which is destroyed and regenerated according to a survival time randomly generated from the material’s relaxation spectrum. The Eulerian form of the evolution equations for the polymer configurations is spatially discretized using the discontinuous Galerkin method. The algorithm is tested on benchmark contraction domains for a polyisobutylene solution. In particular, the flow in the abrupt die entry domain is simulated and the simulation results are compared to experimental data. The results exhibit the correct qualitative behavior of the polymer and agree well with the experimental data.

1.
Laso
,
M.
, and
Öttinger
,
H. C.
, 1993, “
Calculation of Viscoelastic Flow Using Molecular Models: The CONNFFESSIT Approach
,”
J. Non-Newtonian Fluid Mech.
0377-0257,
47
(
1
), pp.
1
20
.
2.
Feigl
,
K.
,
Laso
,
M.
, and
Öttinger
,
H. C.
, 1995, “
The CONNFFESSIT Approach for Solving a Two-Dimensional Viscoelastic Fluid Problem
,”
Macromolecules
0024-9297,
28
(
9
), pp.
3261
3274
.
3.
Hua
,
C. C.
, and
Schieber
,
J. D.
, 1996, “
Application of Kinetic Theory Models in Spatiotemporal Flows for Polymer Solutions, Liquid Crystals and Polymer Melts Using the CONNFFESSIT Approach
,”
Chem. Eng. Sci.
0009-2509,
51
(
9
), pp.
1473
1485
.
4.
Bell
,
T. W.
,
Nyland
,
G. H.
,
Graham
,
M. D.
, and
de Pablo
,
J. J.
, 1997, “
Combined Brownian Dynamics and Spectral Method Simulations of the Recovery of Polymeric Fluids After Shear
,”
Macromolecules
0024-9297,
30
(
6
), pp.
1806
1812
.
5.
Hulsen
,
M. A.
,
van Heel
,
A. P. G.
, and
van den Brule
,
B. H. A. A.
, 1997, “
Simulation of Viscoelastic Flows Using Brownian Configuration Fields
,”
J. Non-Newtonian Fluid Mech.
0377-0257,
70
, pp.
79
101
.
6.
Öttinger
,
H. C.
,
van den Brule
,
B. H. A. A.
, and
Hulsen
,
M. A.
, 1997, “
Brownian Configuration Fields and Variance Reduced CONNFFESSIT
,”
J. Non-Newtonian Fluid Mech.
0377-0257,
70
, pp.
255
261
.
7.
Van Heel
,
A. P. G.
,
Hulsen
,
M. A.
, and
van den Brule
,
B. H. A. A.
, 1999, “
Simulation of Doi-Edwards Model in Complex Flow
,”
J. Rheol.
0148-6055,
43
(
5
), pp.
1239
1260
.
8.
Keunings
,
R.
, 2004, “
Micro-Macro Methods for the Multiscale Simulation of Viscoelastic Flow Using Molecular Models of Kinetic Theory
,”
Rheology Reviews 2004
,
D. M.
Binding
and
K.
Walters
, Eds.,
British Society of Rheology
, pp.
67
98
.
9.
Feigl
,
K.
, and
Öttinger
,
H. C.
, 1998, “
A New Class of Stochastic Simulation Models for Polymer Stress Calculation
,”
J. Chem. Phys.
0021-9606,
109
(
2
), pp.
815
826
.
10.
Quinzani
,
L. M.
,
McKinley
,
G. H.
,
Brown
,
R. A.
, and
Armstrong
,
R. C.
, 1990, “
Modeling the Rheology of Polyisobutylene Solutions
,”
J. Rheol.
0148-6055,
34
, pp.
705
748
.
11.
Quinzani
,
L. M.
,
Armstrong
,
R. C.
, and
Brown
,
R. A.
, 1995, “
Use of Coupled Birefringence and LDV Studies of Flow Through a Planar Contraction to Test Constitutive Equations for Concentrated Polymer Solutions
,”
J. Rheol.
0148-6055,
39
(
6
), pp.
1201
1228
.
12.
Bird
,
R. B.
,
Curtiss
,
C. F.
,
Armstrong
,
R. C.
, and
Hassager
,
O.
, 1987,
Dynamics of Polymeric Liquids
, Volume
2
,
Kinetic Theory
,
2nd ed.
,
Wiley-Interscience
, New York.
13.
Öttinger
,
H. C.
, 2000, “
Thermodynamically Admissible Reptation Models With Anisotropic Tube Cross Sections and Convective Constraint Release
,”
J. Non-Newtonian Fluid Mech.
0377-0257,
89
, pp.
165
185
.
14.
Öttinger
,
H. C.
, 1996,
Stochastic Processes in Polymeric Fluids
,
Springer
, New York.
15.
Feigl
,
K.
, and
Öttinger
,
H. C.
, 2001, “
The Equivalence of the Class of Rivlin-Sawyers Equations and a Class of Stochastic Models for Polymer Stress
,”
J. Math. Phys.
0022-2488,
42
(
2
), pp.
796
817
.
16.
Bernstein
,
B.
,
Malkus
,
D. S.
, and
Olsen
,
E. T.
, 1985, “
A Finite Element for Incompressible Plane Flows of Fluids With Memory
,”
Int. J. Numer. Methods Fluids
0271-2091,
5
, pp.
43
70
.
17.
Bernstein
,
B.
,
Feigl
,
K.
, and
Olsen
,
E. T.
, 1996, “
A First Order Exactly Incompressible Finite Element for Axisymmetric Fluid Flow
,”
SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal.
0036-1429,
33
(
5
), pp.
1736
1758
.
18.
Feigl
,
K.
, and
Öttinger
,
H. C.
, 1996, “
A Numerical Study of the Flow of a Low-Density Polyethylene Melt in a Planar Contraction and Comparison to Experiments
,”
J. Rheol.
0148-6055,
40
(
1
), pp.
21
35
.
19.
Feigl
,
K.
, and
Öttinger
,
H. C.
, 1994, “
The Flow of a LDPE Melt Through an Axisymmetric Contraction: A Numerical Study and Comparison to Experimental Results
,”
J. Rheol.
0148-6055,
38
(
4
), pp.
847
874
.
20.
Bernstein
,
B.
,
Feigl
,
K.
, and
Olsen
,
E. T.
, 1994, “
Steady Flows of Viscoelastic Fluids in Axisymmetric Abrupt Contraction Geometry: A Comparison of Numerical Results
,”
J. Rheol.
0148-6055,
38
(
1
), pp.
53
71
.
21.
Feigl
,
K.
,
Tanner
,
F. X.
,
Edwards
,
B. J.
, and
Collier
,
J. R.
, 2003, “
A Numerical Study of the Measurement of Elongational Viscosity of Polymeric Fluids in a Semihyperbolically Converging Die
,”
J. Non-Newtonian Fluid Mech.
0377-0257,
115
(
2–3
), pp.
191
215
.
You do not currently have access to this content.