3D phase-field simulations of interfacial dynamics in Newtonian and viscoelastic fluids

Journal of Computational Physics

Volumn 229, Issue 2, 2010, Pages 498-511

  Zhou, Chunfeng ^a,d   Yue, Pengtao ^b   Feng, James J ^a   Ollivier Gooch, Carl F ^a   Hu, Howard H ^c  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

^c UNIVERSITY OF PENNSYLVANIA   (United States)

^d University of Minnesota   (United States)

Author keywords

Adaptive meshing; Contact angle; Contact line motion; Diffuse interface model; Drop dynamics; Finite elements; Wetting condition

Indexed keywords

ALGEBRA; DROPS; FINITE ELEMENT METHOD; ITERATIVE METHODS; NAVIER STOKES EQUATIONS; NON NEWTONIAN FLOW; NON NEWTONIAN LIQUIDS; PHASE INTERFACES; THREE DIMENSIONAL COMPUTER GRAPHICS; VISCOELASTICITY;

ADAPTIVE MESHING; CONTACT LINE MOTION; DIFFUSE-INTERFACE MODELS; DROP DYNAMICS; FINITE ELEMENT; INTERFACIAL DYNAMICS; NEWTONIAN FLUIDS; VIS-COELASTIC FLUIDS; VISCO-ELASTIC FLUID; WETTING CONDITIONS;

WETTING;

EID: 77951945499     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.09.039     Document Type: Article

References (54)

1. M. Joanicot, A. Ajdari, Droplet control for microfluidics, Science 309 (2005) 887-888.
2. J.A. Sethian, P. Smereka, Level set methods for fluid interfaces, Ann. Rev. Fluid Mech. 35 (2003) 341-372.
3. X.Y. Xie, L.C. Musson, M. Pasquali, An isochoric domain deformation method for computing steady free surface flows with conserved volumes, J. Comput. Phys. 226 (2007) 398-413.
4. N. Aggarwal, K. Sarkar, Deformation and breakup of a viscoelastic drop in a Newtonian matrix under steady shear, J. Fluid Mech. 584 (2007) 1-21.
5. P. Yue, J.J. Feng, C.A. Bertelo, H.H. Hu, An arbitrary Lagrangian-Eulerian method for simulating bubble growth in polymer foaming, J. Comput. Phys. 226 (2007) 2229-2249.
6. P. Yue, J.J. Feng, C. Liu, J. Shen, Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids, J. Non-Newtonian Fluid Mech. 129 (2005) 163-176.
7. P. Yue, J.J. Feng, C. Liu, J. Shen, A diffuse-interface method for simulating two-phase flows of complex fluids, J. Fluid Mech. 515 (2004) 293-317.
8. J.J. Feng, C. Liu, J. Shen, P. Yue, An energetic variational formulation with phase field methods for interfacial dynamics of complex fluids: advantages and challenges, in: M.-C.T. Calderer, E.M. Terentjev (Eds.), Modeling of Soft Matter, Springer, New York, 2005, pp. 1-26.
9. P. Lin, C. Liu, Simulations of singularity dynamics in liquid crystal flows: a C-0 finite element approach, J. Comput. Phys. 215 (2006) 348-362.
10. P. Lin, C. Liu, H. Zhang, An energy law preserving C-0 finite element scheme for simulating the kinematic effects in liquid crystal dynamics, J. Comput. Phys. 227 (2007) 1411-1427.
11. P. Yue, J.J. Feng, C. Liu, J. Shen, Interfacial force and Marangoni flow on a nematic drop retracting in an isotropic fluid, J. Colloid Interf. Sci. 290 (2005) 281-288.
12. C. Zhou, P. Yue, J.J. Feng, Formation of simple and compound drops in microfluidic devices, Phys. Fluid 18 (2006) 092105.
13. L.M. Pismen, Nonlocal diffuse interface theory of thin films and the moving contact line, Phys. Rev. E 64 (2001) 021603.
14. P. Yue, C. Zhou, J.J. Feng, Sharp interface limit of the Cahn-Hilliard model for moving contact lines, J. Fluid Mech., in press.
15. J. Lowengrub, L. Truskinovsky, Quasi-incompressible Cahn-Hilliard fluids and topological transitions, Proc. Roy. Soc. Lond. A 454 (1998) 2617-2654.
16. D. Jacqmin, Calculation of two-phase Navier-Stokes flows using phase-field modelling, J. Comput. Phys. 155 (1999) 96-127.
17. B.J. Keestra, P.C.J. van Puyvelde, P.D. Anderson, H.E.H. Meijer, Diffuse interface modeling of the morphology and rheology of immiscible polymer blends, Phys. Fluid 15 (2003) 2567-2575.
18. V.E. Badalassi, H.D. Ceniceros, S. Banerjee, Computation of multiphase systems with phase field model, J. Comput. Phys. 190 (2003) 371-397.
19. G. Caginalp, X. Chen, Convergence of the phase field model to its sharp interface limits, Eur. J. Appl. Math. 9 (1998) 417-445.
20. P. Yue, C. Zhou, J.J. Feng, C.F. Ollivier-Gooch, H.H. Hu, Phase-field simulations of interfacial dynamics in viscoelastic fluids using finite elements with adaptive meshing, J. Comput. Phys. 219 (2006) 47-67.
21. P. Yue, C. Zhou, J.J. Feng, A computational study of the coalescence between a drop and an interface in Newtonian and viscoelastic fluids, Phys. Fluid 18 (2006) 102102.
22. C. Zhou, P. Yue, J.J. Feng, Simulation of neutrophil deformation and transport in capillaries using simple and compound drop models, Ann. Biomed. Eng. 35 (2007) 766-780.
23. C. Zhou, P. Yue, J.J. Feng, The rise of Newtonian drops in a nematic liquid crystal, J. Fluid Mech. 593 (2007) 385-404.
24. C. Zhou, P. Yue, J.J. Feng, Dynamic simulation of droplet interaction and self-assembly in a nematic liquid crystal, Langmuir 24 (2008) 3099-3110.
25. D. Jacqmin, Onset of wetting failure in liquid-liquid systems, J. Fluid Mech. 517 (2004) 209-228.
26. D.D. Joseph, Lubricated pipelining, Powder Technol. 94 (1997) 211-215.
27. P. Yue, C. Zhou, J. Dooley, J.J. Feng, Elastic encapsulation in bicomponent stratified flow of viscoelastic fluids, J. Rheol. 52 (2008) 1027-1042.
28. D.M. Anderson, G.B. McFadden, A.A. Wheeler, Diffuse-interface methods in fluid mechanics, Ann. Rev. Fluid Mech. 30 (1998) 139-165.
29. C. Zhou, P. Yue, J.J. Feng, C. Liu, J. Shen, Heart-shaped bubbles rising in anisotropic liquids, Phys. Fluid 19 (2007) 041703.
30. C. Zhou, P. Yue, J.J. Feng, Dynamic simulation of capillary breakup of nematic fibers: molecular orientation and interfacial rupture, J. Comput. Theor. Nanosci., in press
31. R.B. Bird, C.F. Curtiss, R.C. Armstrong, O. Hassager, Dynamics of polymeric liquids, Kinetic Theory, vol. 2, Wiley, New York, 1987.
32. J.W. Cahn, J.E. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys. 28 (1958) 258-267.
33. D. Jacqmin, Contact-line dynamics of a diffuse fluid interface, J. Fluid Mech. 402 (2000) 57-88.
34. J.W. Cahn, Critical-point wetting, J. Chem. Phys. 66 (1977) 3667-3672.
35. J. Shen, Efficient spectral-Galerkin method. II. Direct solvers of second and fourth order equations by using Chebyshev polynomials, SIAM J. Sci. Comput. 16 (1995) 74-87.
36. H.H. Hu, N.A. Patankar, M.Y. Zhu, Direct numerical simulations of fluid-solid systems using the arbitrary Lagrangian-Eulerian technique, J. Comput. Phys. 169 (2001) 427-462.
37. H. Gan, J.J. Feng, H.H. Hu, Simulation of the sedimentation of melting solid particles, Int. J. Multiphase Flow 29 (2003) 751-769.
38. L.A. Freitag, C.F. Ollivier-Gooch, Tetrahedral mesh improvement using swapping and smoothing, Int. J. Numer. Methods Eng. 40 (1997) 3979-4002.
39. C.F. Ollivier-Gooch, C. Boivin, Guaranteed-quality simplical mesh generation with cell size and grading control, Eng. Comput. 17 (2001) 269-286.
40. C. Boivin, C.F. Ollivier-Gooch, Guaranteed-quality triangular mesh generation for domains with curved boundaries, Int. J. Numer. Methods Eng. 55 (2002) 1185-1213.
41. J.R. Shewchuk, Delaunay Refinement Mesh Generation, Ph.D. Thesis, Carnegie Mellon University, 1997.
42. D.F. Watson, Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes, Comput. J. 24 (1981) 167-172.
43. H. Mo, C. Zhou, W. Yu, A new method to determine interfacial tension from the retraction of ellipsoidal drops, J. Non-Newtonian Fluid Mech. 91 (2000) 221-232.
44. Y. Son, K.B. Migler, Interfacial tension measurement between immiscible polymers: improved deformed drop retraction method, Polymer 43 (2002) 3001-3006.
45. S. Velankar, H. Zhou, H.K. Jeon, C.W. Macosko, CFD evaluation of drop retraction methods for the measurement of interfacial tension of surfactantladen drops, J. Colloid Interf. Sci. 272 (2004) 172-185.
46. V.E. Ziegler, B.A. Wolf, Interfacial tensions from drop retraction versus pendant drop data and polydispersity effects, Langmuir 20 (2004) 8688-8692.
47. S. Guido, M. Villone, Measurement of interfacial tension by drop retraction analysis, J. Colloid Interf. Sci. 209 (1999) 247-250.
48. R.W. Hooper, V.F. de Almeida, C.W. Macosko, J.J. Derby, Transient polymeric drop extension and retraction in uniaxial extensional flows, J. Non-Newtonian Fluid Mech. 98 (2001) 141-168.
49. M. Renardy, Y. Renardy, J. Li, Numerical simulation of moving contact line problems using a volume-of-fluid method, J. Comput. Phys. 171 (2001) 243-263.
50. A. Mazouchi, C.M. Gramlich, G.M. Homsy, Time-dependent free surface Stokes flow with a moving contact line. I. Flow over plane surfaces, Phys. Fluid 16 (2004) 1647-1659.
51. W. Villanueva, G. Amberg, Some generic capillary-driven flows, Int. J. Multiphase Flow 32 (2006) 1072-1086.
52. V.V. Khatavkar, P.D. Anderson, H.E.H. Meijer, Capillary spreading of a droplet in the partially wetting regime using a diffuse-interface model, J. Fluid Mech. 572 (2007) 367-387.
53. H. Ding, P.D.M. Spelt, Inertial effects in droplet spreading: a comparison between diffuse-interface and level-set simulations, J. Fluid Mech. 576 (2007) 287-296.
54. A. Zosel, Studies of the wetting kinetics of liquid drops on solid surfaces, Colloid Polym. Sci. 271 (1993) 680-687.