Global models for moving contact lines

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 63, Issue 1 I, 2001, Pages 0112081-01120813

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

^a DUKE UNIVERSITY   (United States)

^b UNIVERSIDAD NACIONAL DEL CENTRO DE LA PROVINCIA DE BUENOS AIRES   (Argentina)

^c NEW JERSEY INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; DIFFUSION IN LIQUIDS; GRAVITATION; LUBRICATION; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; SURFACE TENSION; THIN FILMS;

PRECURSOR FILM MODELS;

COMPUTATIONAL FLUID DYNAMICS;

EID: 17744373671     PISSN: 15393755     EISSN: 15502376     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.O. 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 J.R. King, Ph.D. thesis, Oxford University, 1987 (unpublished).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. Serais, in Nonlinear Diffusion Equations and their Equilibrium States, edited by N.G. Lloyd, W.-M. Ni, and L.A. Peleder (Springer-Verlag, Basel, 1992), Vol. 3, p. 77.
9. [9j 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 Sei. 36, 410 (1971).
15. M.H. Eres, L.W. Schwanz, and R.V. Roy, Phys. Fluids 12, 1278 (2000).
16. J. Lowengruh 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, I. 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. Berlozzi, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 37, 523 (2000).
26. J.W. Barren, J.F. Blowey, and H. Garcke, Numer. Math. 80, 525 (1998).
27. G. Grün and Rurnpf (unpublished).
28. c=0 (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, Vl.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, S1AM (Soc. Ind. Appl. Math.) J. Appi. 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. Peleiier, and S.M. Williams, Nonlinear Analysis, Theory, Methods and Applications 18, 217 (1992).
40. R. Ferreira and F. Bernis, Eur. J. Appi. Math. 8, 507 (1997).
41. G.I. Barenblati, Scaling, Self-Similarity, and Intermediate Axymptotics (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. Tnornas, 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 End V.M. Siarov, Colloid J. Russian Acad. Sci. 50, 19 (1988).
46. W.D. Bascom, R.L. Coitington, and C.R. Singleterry, Adv. Chem. Am. Chem. Soc. 43, 389 (1964).
47. U.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 Sei. 177, 14 (1996).
50. -2.
51. A.M. Cazabat and M.A. Cohen Stuart, J. Phys. Chem. 90, 5845 (1986).