Viscoelastic effects on drop deformation in a converging pipe flow

Journal of Rheology

Volumn 52, Issue 2, 2008, Pages 469-487

  Zhou, Diwen ^a   Yue, Pengtao ^a   Feng, James J ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Adaptive meshing; Cahn Hilliard model; Capillary number; Finite elements; Interfacial tension; Viscosity ratio

Indexed keywords

CAPILLARY FLOW; DROPS; FINITE ELEMENT METHOD; PARAMETER ESTIMATION; PIPE FLOW;

CAPILLARY NUMBER; GIESEKUS FLUID; TRANSIENT DEFORMATION;

VISCOELASTICITY;

EID: 40549117241     PISSN: 01486055     EISSN: None     Source Type: Journal    
DOI: 10.1122/1.2837525     Document Type: Article

References (45)

1. Anderson, D. M., G. B. McFadden, and A. A. Wheeler, " Diffuse-interface methods in fluid mechanics.," Annu. Rev. Fluid Mech. ARVFA3 0066-4189 10.1146/annurev.fluid.30.1.139 30, 139-165 (1998).
2. Bird, R. B., R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, Vol. 1. Fluid Mechanics (Wiley, New York, 1987a).
3. Bird, R. B., C. F. Curtiss, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, Vol. 2. Kinetic Theory (Wiley, New York, 1987b).
4. Bourry, D., R. E. Khayat, L. A. Utracki, F. Goudbille, J. Picot, and A. Luciani, " Extensional flow of polymeric dispersions.," Polym. Eng. Sci. PYESAZ 0032-3888 39, 1072-1086 (1999).
5. Chin, H. B., and C. D. Han, " Studies on droplet deformation and breakup. I. Droplet deformation in extensional flow.," J. Rheol. JORHD2 0148-6055 10.1122/1.549510 23, 557-590 (1979).
6. Cogswell, F. N., " Measuring the extensional rheology of polymer melts.," J. Rheol. JORHD2 0148-6055 10.1122/1.549257 16, 383-403 (1972).
7. Delaby, I., B. Ernst, Y. Germain, and R. Muller, " Droplet deformation in polymer blends during uniaxial elongational flow: Influence of viscosity ratio for large capillary numbers.," J. Rheol. JORHD2 0148-6055 10.1122/1.550568 38, 1705-1720 (1994).
8. Delaby, I., R. Muller, and B. Ernst, " Drop deformation during elongational flow in blends of viscoelastic fluids. Small deformation theory and comparison with experimental results.," Rheol. Acta RHEAAK 0035-4511 10.1007/BF00712313 34, 525-533 (1995).
9. Elmendorp, J. J., and R. J. Maalcke, " A study on polymer blending microrheology: Part I.," Polym. Eng. Sci. PYESAZ 0032-3888 10.1002/pen.760251608 25, 1041-1047 (1985).
10. Feng, J. J., C. Liu, J. Shen, and P. Yue, " An energetic variational formulation with phase field methods for interfacial dynamics of complex fluids: Advantages and challenges.," in Modeling of Soft Matter, edited by, M.-C. T. Calderer, and, E. Terentjev, (Springer, New York, 2005), pp. 1-26.
11. Ghodgaonkar, P. G., and U. Sundararaj, " Prediction of dispersed phase drop diameter in polymer blends: The effect of elasticity.," Polym. Eng. Sci. PYESAZ 0032-3888 10.1002/pen.10562 36, 1656-1665 (1996).
12. Greco, F., " Drop deformation for non-Newtonian fluids in slow flows.," J. Non-Newtonian Fluid Mech. JNFMDI 0377-0257 10.1016/S0377- 0257(02)00144-1 107, 111-131 (2002).
13. Grillet, A. M., A. G. Lee, and E. S. G. Shaqfeh, " Observations of ribbing instabilities in elastic fluid flows with gravity stabilization.," J. Fluid Mech. JFLSA7 0022-1120 10.1017/S002211209900628X 399, 49-83 (1999).
14. Guido, S., M. Simeone, and F. Greco, " Deformation of a Newtonian drop in a viscoelastic matrix under steady shear flow. Experimental validation of slow flow theory.," J. Non-Newtonian Fluid Mech. JNFMDI 0377-0257 10.1016/S0377-0257(03)00118-6 114, 65-82 (2003).
15. Hooper, R., M. Toose, C. W. Macosko, and J. J. Derby, " A comparison of boundary element and finite element methods for modeling axisymmetric polymeric drop deformation.," Int. J. Numer. Methods Fluids IJNFDW 0271-2091 10.1002/fld.190 37, 837-864 (2001a).
16. Hooper, R. W., V. F. de Almeida, C. W. Macosko, and J. J. Derby, " Transient polymeric drop extension and retraction in uniaxial extensional flows.," J. Non-Newtonian Fluid Mech. JNFMDI 0377-0257 10.1016/S0377- 0257(01)00112-4 98, 141-168 (2001b).
17. Jacqmin, D., " Calculation of two-phase Navier-Stokes flows using phase-field modeling.," J. Comput. Phys. JCTPAH 0021-9991 10.1006/jcph.1999.6332 155, 96-127 (1999).
18. Khan, S. A., and R. G. Larson, " Comparison of simple constitutive equations for polymer melts in shear and biaxial and uniaxial extensions.," Eng. Anal. Boundary Elem. EABAEL 0955-7997 31, 207-234 (1987).
19. Khayat, R. E., " Boundary element analysis of planar drop deformation in confined flow. Part II. Viscoelastic fluids.," Eng. Anal. Boundary Elem. EABAEL 0955-7997 22, 291-306 (1998).
20. Khismatullin, D., Y. Renardy, and M. Renardy, " Development and implementation of VOF-PROST for 3D viscoelastic liquid-liquid simulations.," J. Non-Newtonian Fluid Mech. JNFMDI 0377-0257 140, 120-131 (2006).
21. Kim, S. J., and C. D. Han, " Finite element analysis of axisymmetric creeping motion of a deformable non-Newtonian drop in the entrance region of a cylindrical tube.," J. Rheol. JORHD2 0148-6055 10.1122/1.1402659 45, 1279-1303 (2001).
22. Liu, C., and J. Shen, " A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method.," Physica D PDNPDT 0167-2789 10.1016/S0167-2789(03)00030-7 179, 211-228 (2003).
23. Lowengrub, J., and L. Truskinovsky, " Quasi-incompressible Cahn-Hilliard fluids and topological transitions.," Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 10.1098/rspa.1998.0273 454, 2617-2654 (1998).
24. Mighri, F., A. Ajji, and P. J. Carreau, " Influence of elastic properties on drop deformation in elongational flow.," J. Rheol. JORHD2 0148-6055 10.1122/1.550853 41, 1183-1201 (1997).
25. Mighri, F., P. J. Carreau, and A. Ajji, " Influence of elastic properties on drop deformation and breakup in shear flow.," J. Rheol. JORHD2 0148-6055 10.1122/1.550897 42, 1477-1490 (1998).
26. Olbricht, W. L., and L. G. Leal, " The creeping motion of immiscible drops through a converging/diverging tube.," J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112083003390 134, 329-355 (1983).
27. Rallison, J. M., " The deformation of small viscous drops and bubbles in shear flows.," Annu. Rev. Fluid Mech. ARVFA3 0066-4189 10.1146/annurev.fluid.16.1.45 16, 45-66 (1984).
28. Ramaswamy, S., and L. G. Leal, " The deformation of a Newtonian drop in the uniaxial extensional flow of a viscoelastic liquid.," J. Non-Newtonian Fluid Mech. JNFMDI 0377-0257 10.1016/S0377-0257(99)00010-5 88, 149-172 (1999a).
29. Ramaswamy, S., and L. G. Leal, " The deformation of a viscoelastic drop subjected to steady uniaxial extensional flow of a Newtonian fluid.," J. Non-Newtonian Fluid Mech. JNFMDI 0377-0257 10.1016/S0377-0257(98)00212-2 85, 127-163 (1999b).
30. Sethian, J. A., and P. Smereka, " Level set methods for fluid interfaces.," Annu. Rev. Fluid Mech. ARVFA3 0066-4189 10.1146/annurev. fluid.35.101101.161105 35, 341-372 (2003).
31. Sibillo, V., M. Simeone, and S. Guido, " Break-up of a Newtonian drop in a viscoelastic matrix under simple shear flow.," Rheol. Acta RHEAAK 0035-4511 10.1007/s00397-004-0374-7 43, 449-456 (2004).
32. Sibillo, V., M. Simeone, S. Guido, F. Greco, and P. Maffettone, " Start-up and retraction dynamics of a Newtonian drop in a viscoelastic matrix under simple shear flow.," J. Non-Newtonian Fluid Mech. JNFMDI 0377-0257 10.1016/j.jnnfm.2005.10.011 134, 27-32 (2006).
33. Stone, H. A., " Dynamics of drop deformation and breakup in viscous fluids.," Annu. Rev. Fluid Mech. ARVFA3 0066-4189 10.1146/annurev.fl.26. 010194.000433 26, 65-102 (1994).
34. Stone, H. A., B. J. Bentley, and L. G. Leal, " An experimental study of transient effects in the breakup of viscous drop.," J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112086001118 173, 131-158 (1986).
35. Tirtaatmadja, V., and T. Sridhar, " Comparison of constitutive equations for polymer solutions in uniaxial extension.," J. Rheol. JORHD2 0148-6055 10.1122/1.550632 39, 1133-1160 (1995).
36. Tretheway, D. C., and L. G. Leal, " Deformation and relaxation of Newtonian drops in planar extensional flows of a Boger fluid.," J. Non-Newtonian Fluid Mech. JNFMDI 0377-0257 10.1016/S0377-0257(01)00123-9 99, 81-108 (2001).
37. Tucker, C. L., and P. Moldenaers, " Microstructural evolution in polymer blends.," Annu. Rev. Fluid Mech. ARVFA3 0066-4189 10.1146/annurev.fluid.34.082301.144051 34, 177-210 (2002).
38. van der Reijden-Stolk, C., and A. Sara, " A study on polymer blending microrheology. Part 3. Deformation of Newtonian drops submerged in another Newtonian fluid flowing through a converging cone.," Polym. Eng. Sci. PYESAZ 0032-3888 10.1002/pen.760261802 26, 1229-1239 (1986).
39. Yue, P., J. J. Feng, C. Liu, and J. Shen, " Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids.," J. Non-Newtonian Fluid Mech. JNFMDI 0377-0257 10.1016/j.jnnfm.2005.07.002 129, 163-176 (2005a).
40. Yue, P., J. J. Feng, C. Liu, and J. Shen, " Transient drop deformation upon startup of shear in viscoelastic fluids.," Phys. Fluids PHFLE6 1070-6631 10.1063/1.2139630 17, 123101 (2005b).
41. Yue, P., J. J. Feng, C. Liu, and J. Shen, " Viscoelastic effects on drop deformation in steady shear.," J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112005006166 540, 427-437 (2005c).
42. Yue, P., C. Zhou, and J. J. Feng, " A computational study of the coalescence between a drop and an interface in Newtonian and viscoelastic fluids.," Phys. Fluids PHFLE6 1070-6631 10.1063/1.2364144 18, 102102 (2006a).
43. Yue, P., C. Zhou, and J. J. Feng, " Spontaneous shrinkage of drops and mass conservation in phase-field simulations.," J. Comput. Phys. JCTPAH 0021-9991 10.1016/j.jcp.2006.11.020 223, 1-9 (2007).
44. Yue, P., C. Zhou, J. J. Feng, C. F. Ollivier-Gooch, and H. H. Hu, " Phase-field simulations of interfacial dynamics in viscoelastic fluids using finite elements with adaptive meshing.," J. Comput. Phys. JCTPAH 0021-9991 10.1016/j.jcp.2006.03.016 219, 47-67 (2006b).
45. Zhou, C., P. Yue, and J. J. Feng, " Simulation of neutrophil deformation and transport in capillaries using simple and compound drop models.," Ann. Biomed. Eng. ABMECF 0090-6964 10.1007/s10439-007-9286-x 35, 766-780 (2007).