Shear flow past two-dimensional droplets pinned or moving on an adhering channel wall at moderate Reynolds numbers: A numerical study

Journal of Fluid Mechanics

Volumn 561, Issue , 2006, Pages 439-463

  Spelt, Peter D M ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CHANNEL FLOW; COMPUTER SIMULATION; CONTACT ANGLE; HYSTERESIS; NAVIER STOKES EQUATIONS; REYNOLDS NUMBER; WALL FLOW;

CHANNEL WALL; DROPLETS; LEVEL-SET METHOD; WEBER NUMBER;

SHEAR FLOW;

BOUNDARY CONDITIONS; CHANNEL FLOW; COMPUTER SIMULATION; CONTACT ANGLE; HYSTERESIS; NAVIER STOKES EQUATIONS; REYNOLDS NUMBER; SHEAR FLOW; WALL FLOW;

BOUNDARY CONDITION; CHANNEL FLOW; COMPUTER SIMULATION; REYNOLDS NUMBER; SHEAR FLOW; DROPLET; SIMULATION;

CHANNEL WALL; DROPLETS; LEVEL-SET METHOD; WEBER NUMBER;

EID: 33747065221     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112006000954     Document Type: Article

References (40)

1. Briant, A. J., Wagner, A. J. & Yeomans, J. M. 2004 Lattice Boltzmann simulations of contact line motion. I. Liquid-gas systems. Phys. Rev. E 69, 031602.
2. Briant, A. J. & Yeomans, J. M. 2004 Lattice Boltzmann simulations of contact line motion. II. Binary fluids. Phys. Rev. E 69, 031603.
3. Cao, J., Donell, B., Deaver, D. R., Lawrence, M. B. & Dong, C. 1998 In vitro side-view imaging technique and analysis of human t-leukemic cell adhesion to ICAM-1 in shear flow. Microvacs. Res. 55, 124.
4. Chang, Y. C., Hou, T. Y., Merriman, B. & Osher, S. 1996 A level formulation of Eulerian interface capturing methods for incompressible fluid flows. J. Comput. Phys. 124, 449-464.
5. Charcosset, C., Limayern, I. & Fessi H. 2004 The membrane emulsification process: A review. J. Chem. Technol. Biotechnol. 79, 209.
6. Chatterjee, J. 2001 A criterion for buoyancy induced drop detachment based on an analytical approximation of the drop shape. Colloid Surf. A: Physiochem. Engng Asp. 178, 249.
7. Cox, R. G. 1986 The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow. J. Fluid Mech. 168, 169.
8. Davis, S. H. 2000 Interfacial fluid dynamics. In Perspectives in Fluid Dynamics (ed. G. K. Batchelor, H. K. Moffatt & M. G. Worster), chap. 1. Cambridge University Press.
9. Dimitrakopoulos, P. & Higdon, J. J. L. 1997 Displacement of fluid droplets from solid surfaces in low-Reynolds-number shear flows. J. Fluid Mech. 336, 351-378.
10. Dimitrakopoulos, P. & Higdon, J. J. L. 1998 On the displacement of three-dimensional fluid droplets from solid surfaces in low-Reynolds-number shear flows. J. Fluid Mech. 377, 189-222.
11. Dimitrakopoulos, P. & Higdon, J. J. L. 1999 On the gravitational displacement of three-dimensional fluid droplets from inclined solid surfaces in low-Reynolds-number shear flows. J. Fluid Mech. 395, 181-209.
12. Dimitrakopoulos, P. & Higdon, J. J. L. 2001 On the displacement of three-dimensional fluid droplets adhering to a plane wall in viscous pressure-driven flows. J. Fluid Mech. 435, 327-350.
13. Duhar, G. & Colin, C. 2004 A predictive model for the detachment of bubbles injected in a viscous shear flow with small inertial effetcs. Phys. Fluids 16, L31-L34.
14. Dussan V., E. B. 1979 On the spreading of liquids on solid surfaces: static and dynamic contact lines. Annu. Rev. Fluid Mech. 11, 371-400.
15. Dussan V., E. B. 1987 On the ability of drops to stick to surfaces of solids. Part 3. The influences of the motion of the surrounding fluid on dislodging drops. J. Fluid Mech. 174, 381-397.
16. Eggers, J. 2004 Hydrodynamic theory of forced dewetting. Phys. Rev. Lett. 93, 094502.
17. Eggers, J. & Stone, H. A. 2004 Characteristic lengths at moving contact lines for a perfectly wetting fluid: The influence of speed on the dynamic contact angle. J. Fluid Mech. 505, 309-321.
18. Feng, J. Q. & Basaran, O. A. 1994 Shear flow over a translationally symmetric cylindrical bubble pinned on a slot in a plane wall. J. Fluid Mech. 275, 351.
19. de Gennes, P. G. 1985 Wetting: Statics and dynamics. Rev. Mod. Phys. 57, 827.
20. Hewitt, G. F. 1978 Measurement of Two Phase Flow Parameters. Academic.
21. Hocking, L. M. & Davis, S. H. 2002 Inertial effects in time-dependent motion of thin films J. Fluid Mech. 467, 1-17.
22. Hodges, S. R. & Jensen, O. E. 2002 Spreading and peeling dynamics in a model of cell adhesion. J. Fluid Mech. 460, 381-409.
23. Huh, C. & Scriven, L. E. 1971 Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid Interf. Sci. 35, 85-101.
24. Jacqmin, D. 2000 Contact-line dynamics of a diffuse fluid interface J. Fluid Mech. 402, 57.
25. Jacqmin, D. 2004 Onset of wetting failure in liquid-liquid systems J. Fluid Mech. 517, 209.
26. Leal, L. G. 1992 Laminar Flow and Convective Transport Processes. Butterworth-Heinemann.
27. Li, X. & Pozrikidis, C. 1996 Shear flow over a liquid drop adhering to a solid surface. J. Fluid Mech. 307, 167-190.
28. Magnaudet, J., Bonometti, T. & Benkenida, A. 2006 The modelling of viscous stresses for computing incompressible two-phase flows on fixed grids. Preprint.
29. Mazouchi, A., Gramlich, C. M. & Homsy, G. M. 2004 Time-dependent free surface Stokes flow with a moving contact line. I. Flow over plane surfaces. Phys. Fluids 16, 1647-1659.
30. Minnaert, M. 1974 De Natuurkunde van't Vrije Veld: Rust en Beweging. (in Dutch). Thieme.
31. Russo, G. & Smereka, P. 2000 A remark on computing distance functions. J. Comput. Phys. 163, 51-67.
32. Schleizer, A. D. & Bonnecaze, R. T. 1999 Displacement of a two-dimensional immiscible droplet adhering to a wall in shear and pressure-driven flows. J. Fluid Mech. 383, 29-54.
33. Shikhmurzaev, Y. D. 1997 Moving contact lines in liquid/liquid/solid systems. J. Fluid Mech. 334, 211.
34. Spelt, P. D. M. 2005 A level-set approach for simulations of flows with multiple moving contact lines with hysteresis. J. Comput. Phys. 207, 389-404.
35. Sussman, M. & Uto, S. 1998 A computational study of the spreading of oil underneath a sheet of ice. CAM Rep. 98-32.
36. Sussman, M., Smereka, P. & Osher, S. 1994 A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114, 146-159.
37. Sussman, M., Almgren, A. S., Bell, J. B., Colella, P., Howell, L. H. & Welcome, M. L. 1999 An adaptive level set approach for incompressible two-phase flows. J. Comput. Phys. 148, 81-124.
38. Tuck, E. O. & Schwartz, L. W. 1990 A numerical and asymptotic study of some third-order ordinary differential equations relevant to draining and coating flows. SIAM Rev. 32, 453-460.
39. Wakiya, S. 1975 Application of bipolar coordinates to the two-dimensional creeping motion of a liquid. I. Flow over a projection or a depression on a wall. J. Phys. Soc. Japan 39, 1113-1120.
40. Yon, S. & Pozrikidis, C. 1999 Deformation of a liquid drop adhering to a plane wall: Significance of the drop viscosity and the effect of an insoluble surfactant. Phys. Fluids 11, 1297-1308.