Simulations of sedimentation of a sphere in a viscoelastic fluid using molecular based constitutive models

Journal of Non-Newtonian Fluid Mechanics

Volumn 82, Issue 2-3, 1999, Pages 429-452

  Yang, Bin ^a   Khomami, Bamin ^a  

^a WASHINGTON UNIVERSITY IN ST LOUIS   (United States)

Author keywords

Constitutive equations; Numerical solution; Sedimentation of sphere; Viscoelastic flow

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; DRAG; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; ORGANIC POLYMERS; SEDIMENTATION; SOLUTIONS; SPHERES; VISCOELASTICITY;

BOGER FLUID; POLYISOBUTYLENE; VISCOELASTIC FLOW;

COMPUTER SIMULATION;

SEDIMENTATION; SPHERE; VISCOELASTIC FLOW;

EID: 0033133890     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0257(98)00174-8     Document Type: Article

References (29)

1. Crochet M.J. Numerical simulation of viscoelastic flow: a review. Rubber Chem. Technol. 62:1989;426-455.
2. Khomami B., Talwar K.K., Ganpule H.K. A comparative study of higher- and lower-order finite element techniques for computation of viscoelastic flows. J. Rheol. 38:1994;255-289.
3. Brown R.A., Szady M.J., Northey P.J., Armstrong R.C. On the numerical stability of mixed finite-element method for viscoelastic flows governed by differential constitutive equations. Theor. Comput. Fluid Dyna. 51:1993;77-106.
4. R.A. Brown and G.H. McKiley, Report on the VIII int. workshop on numerical methods in non-Newtonian flows, J. Non-Newtonian Fluid Mech. 52, 407-413.
5. Caswell B. Report on IXth international workshop on numerical methods in non-Newtonian flows. J. Non-Newtonian Fluid Mech. 62:1996;99-110.
6. Quinzani L.M., Armstrong R.C., Brown R.A. Birefringence and laser-doppler velocimetry (LDV) studies of viscoelastic flow through a planar contraction. J. Non-Newtonian Fluid Mech. 25:1994;1-36.
7. Rajagopalan D., Byars J.A., Armstrong R.C., Brown R.A., Lee J.S., Fuller G.G. Comparison of numerical simulations and birefringence measurements in viscoelastic flow between eccentric rotating cylinders. J. Rheol. 36:1992;1349-1375.
8. J.P.W. Baaijens, Evaluation of Constitutive Equations for Polymer Melts and Solutions in Complex Flows, Ph.D. Thesis, Eindhoven University of Technology (1994).
9. Baaijens F.P.T., Baaijens H.P.W., Peters G.W.M., Meijer H.E.H. An experimental and numerical investigation of a viscoelastic flow around a cylinder. J. Rheol. 38:1994;351-376.
10. Baaijens H.P.W., Peters G.W.M., Baaijens F.P.T., Meijer H.E.H. Viscoelastic flow past a confined cylinder of a polyisobutylene solution. J. Rheol. 39:1995;1243-1277.
11. Li J.-M., Burghardt W.R., Yang B., Khomami B. Flow birefringence and computational studies of a shear thinning polymer solution in axisymmetric stagnation flow. J. Non-Newtonian Fluid Mech. 74:1998;151-193.
12. C. Macosko, Rheology, VCH Publishers, New York, 1994, p. 37.
13. Doyle P.S., Shaqfeh E.S.G., McKinley G.H., Spiegelberg S.H. Relaxation of dilute polymer solutions following extensional flows. J. Non-Newtonian fluid Mech. 76:1998;79-110.
14. Arigo M.T., Rajagopalan D.R., Shapely N.T., McKinley G.H. The sedimentation of a sphere through an elastic fluid: part I - steady motion. J. Non-Newtonian Fluid Mech. 60:1995;225-257.
15. Hinch E.J. Uncoiling a polymer molecule in a strong extensional flow. J. Non-Newtonian Fluid Mech. 54:1994;209-230.
16. Rallison J.M. Dissipative stresses in dilute polymer solutions. J. Non-Newtonian Fluid Mech. 68:1997;61-83.
17. M.R.J. Verhoef, B.H.A.A. vanden Brule M.A. Hulsen, On the modeling of a PIB/PB boger fluid in extensional flow, J. Non-Newtonian Fluid Mech., in press.
18. R.B. Bird, R.C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, Fluid Mech., vol. 1, Wiley, New York, pp. 1987.
19. Chilcott M.D., Rallison J.M. Creeping flow of dilute polymer solutions past cylinders and spheres. J. Non-Newtonian Fluid Mech. 29:1988;381.
20. R.B. Bird, C.F. Curtiss, R.C. Armstrong, O. Hassager, Dynamics of polymeric liquids, Kinetic Theory, vol. 2, Wiley, New York, p. 1987.
21. B. Yang B. Khomami, Modeling of viscoelastic flow past spheres and in contraction flows with Hp-adaptive finitge element techniques, in: A. Ait-Kadi, J.M. Dealy, D.F. James, M.C. Williams (Eds.), Proc. XIIth Int. Congr. on Rheology, August 1996, Quebec, Canada, pp. 409-410.
22. Talwar K.K., Ganpule H.K., Khomami B. A note on selection of spaces in computation of viscoelastic flows using the Hp-finite element method. J. Non-Newtonian Fluid Mech. 52:1994;293-307.
23. Talwar K.K., Khomami B. Higher order finite element techniques for viscoelastic flow problems with change of type and singularities. J. Non-Newtonian Fluid Mech. 59:1995;49-72.
24. Guenette R., Fortin M. A new mixed finite element method for computing viscoelastic flows. J. Non-Newtonian Fluid Mech. 60:1995;27.
25. L.M. Quinzani, G.H. McKinley, R.A. Brown, R.C. Armstrong, Modeling the rheology of polyisobutylene solutions, J. Rheol. 34 (1990) 705-748.
26. Spiegelberg S.H., Ables D.C., McKinley G.H. The role of end-effects on measurements of extensional viscosity in viscoelastic polymer solutions with a filament stretching rheometer. J. Non-Newtonian Fluid Mech. 64:1996;229-267.
27. V.G. Levich, Physiochemical Hydrodynamics, Prentice-Hall, Englewood Cliffs, NJ, 1962.
28. Chmielewski C., Nichols K.L., Jayaraman K. A comparison of the drag coefficients of sphere translating in corn-syrup-based and polybutene-based Boger fluids. J. Non-Newtonian Fluid Mech. 35:1990;37.
29. Perkins T.T., Smith D.E., Chu S. Single polymer dynamics in an elongational flow. Science. 276:1997;2016-2021.