Global models for moving contact lines

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 63, Issue 1, 2001, Pages

  Diez, Javier A ^a   Kondic, L ^a,b   Bertozzi, Andrea ^a  

^a DUKE UNIVERSITY   (United States)

^b NEW JERSEY INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 18644386665     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.63.011208     Document Type: Article

References (51)

1. E.B. Dussan V., Annu. Rev. Fluid Mech. 11, 317 (1979).
2. P.G. de Gennes, Rev. Mod. Phys. 57, 827 (1985).
3. A. Oron, S.H. Davis, and S. Bankoff, Rev. Mod. Phys. 69, 931 (1997).
4. S.M. Troian, E. Herbolzheimer, S.A. Safran, and J.F. Joanny, Europhys. Lett. 10, 25 (1989).
5. A.L. Bertozzi and M.P. Brenner, Phys. Fluids 9, 530 (1997).
6. P. Constantin, T.F. Duppont, R.E. Goldstein, L.P. Kadanoff, M.J. Shelley, and S.M. Zhou, Phys. Rev. E 47, 4169 (1993).
7. J.R. King, Ph.D. thesis, Oxford University, 1987 (unpublished).
8. F. Bernis, in Nonlinear Diffusion Equations and their Equilibrium States, edited by N.G. Lloyd, W.-M. Ni, and L.A. Peletier (Springer-Verlag, Basel, 1992), Vol. 3, p. 77.
9. C.M. Elliott and H. Garcke, SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 27, 404 (1996).
10. M.A. Lewis, Theor. Popul. Biol. 45, 277 (1994).
11. G. Grün, Z. Anal Anwendungen 14, 541 (1995).
12. S. Boatto, L.P. Kadanoff, and P. Olla, Phys. Rev. E 48, 4423 (1993).
13. V. Ludviksson and E.N. Lightfoot, AIChE J. 14, 674 (1968).
14. R.J. Hansen and T.Y. Toong, J. Colloid Interface Sci. 36, 410 (1971).
15. M.H. Eres, L.W. Schwartz, and R.V. Roy, Phys. Fluids 12, 1278 (2000).
16. J. Lowengrub and L. Truskinovsky, Proc. R. Soc. London, Ser. A 454, 2617 (1998).
17. P.H. Leo, J.S. Lowengrub, and J.H. Jou, Acta Mater. 46, 2113 (1998).
18. E.B. Dussan V., J. Fluid Mech. 77, 665 (1976).
19. H.P. Greenspan, J. Fluid Mech. 84, 125 (1978).
20. H.P. Greenspan and B.M. McCay, Stud. Appl. Math. 64, 95 (1981).
21. L.M. Hocking and A.D. Rivers, J. Fluid Mech. 121, 425 (1982).
22. P.J. Haley and M.J. Miksis, J. Fluid Mech. 223, 57 (1991).
23. J.A. Moriarty and L.W. Schwartz, J. Eng. Math. 26, 81 (1992).
24. A.L. Bertozzi, Notices Am. Math. Soc. 45, 689 (1998).
25. L. Zhornitskaya and A.L. Bertozzi, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 37, 523 (2000).
26. J.W. Barrett, J.F. Blowey, and H. Garcke, Numer. Math. 80, 525 (1998).
27. G. Grün and Rumpf (unpublished).
28. An example of a weak form of Eq. (2) satisfies (Formula presented) for any sufficiently smooth test function (Formula presented) where the integrals are over all time and space. This expression is obtained by multiplying Eq. (2) by (Formula presented) and integrating twice by parts with no-flow boundary conditions, (Formula presented) (other similar definitions may be found in the literature). Such formulations allow for solutions of the equation with discontinuous derivatives (as in the case of a moving contact line) where the solution goes to zero.
29. R.E. Goldstein, A.I. Pesci, and M.J. Shelley, Phys. Rev. Lett. 70, 3043 (1993).
30. R.E. Goldstein, A.I. Pesci, and M.J. Shelley, Phys. Rev. Lett. 75, 3665 (1995).
31. F. Bernis and A. Friedman, J. Diff. Eqns. 83, 179 (1990).
32. A.L. Bertozzi, M.P. Brenner, T.F. Dupont, and L.P. Kadanoff, in Trends and Perspectives in Applied Mathematics, edited by L. Sirovich, Applied Mathematical Sciences Vol. 100 (Springer-Verlag, New York, 1994), p. 155.
33. E. Beretta, M. Berstch, and R. Dal Passo, Arch. Ration. Mech. Anal. 129, 175 (1995).
34. A.L. Bertozzi and M. Pugh, Commun. Pure Appl. Math. 49, 85 (1996).
35. T.F. Dupont, R.E. Goldstein, L.P. Kadanoff, and S. Zhou, Phys. Rev. E 47, 4182 (1993).
36. A.L. Bertozzi, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 56, 681 (1996).
37. R. Almgren, A.L. Bertozzi, and M.P. Brenner, Phys. Fluids 8, 1356 (1996).
38. L. Zhornitskaya, Ph.D. thesis, Duke University, 1999 (unpublished).
39. F. Bernis, L.A. Peletier, and S.M. Williams, Nonlinear Analysis, Theory, Methods and Applications 18, 217 (1992).
40. R. Ferreira and F. Bernis, Eur. J. Appl. Math. 8, 507 (1997).
41. G.I. Barenblatt, Scaling, Self-Similarity, and Intermediate Asymptotics (Cambridge University Press, New York, 1996).
42. M. Brenner and A.L. Bertozzi, Phys. Rev. Lett. 71, 593 (1993).
43. R. Gratton, J. Diez, L. Thomas, B. Marino, and S. Betelú, Phys. Rev. E 53, 3563 (1996).
44. P. Ehrhard and S. Davis, J. Fluid Mech. 257, 463 (1993).
45. V.V. Kalinin and V.M. Starov, Colloid J. Russian Acad. Sci. 50, 19 (1988).
46. W.D. Bascom, R.L. Cottington, and C.R. Singleterry, Adv. Chem. Am. Chem. Soc. 43, 389 (1964).
47. H.E. Huppert, J. Fluid Mech. 121, 43 (1982).
48. J. Gratton and F. Minotti, J. Fluid Mech. 210, 155 (1990).
49. B.M. Marino, L.P. Thomas, J.A. Diez, and R. Gratton, J. Colloid Interface Sci. 177, 14 (1996).
50. Calculations with such small (Formula presented)’s are not computationally too expensive since, for instance, the average time step (Formula presented) for (Formula presented) is approximately only (Formula presented) smaller than for (Formula presented)
51. A.M. Cazabat and M.A. Cohen Stuart, J. Phys. Chem. 90, 5845 (1986).