Nonlinear dynamics of a two-dimensional viscous drop under shear flow

Physics of Fluids

Volumn 18, Issue 7, 2006, Pages

  Zhang, J ^a   Miksis, M J ^a   Bankoff, S G ^a  

^a Northwestern University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CHANNEL FLOW; REYNOLDS NUMBER; SHEAR FLOW; VISCOSITY; VISCOUS FLOW; WALL FLOW;

CAPILLARY NUMBER; PARALLEL-WALLED CHANNEL; STEADY STATE SOLUTIONS; VISCOUS DROP;

DROP FORMATION;

BOUNDARY CONDITIONS; CHANNEL FLOW; DROP FORMATION; REYNOLDS NUMBER; SHEAR FLOW; VISCOSITY; VISCOUS FLOW; WALL FLOW;

EID: 33746747500     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2221715     Document Type: Article

References (20)

1. J. Q. Feng and O. A. Basaran, "Shear flow over a translationally symmetric cylindrical bubble pinned on a slot in a plane wall," J. Fluid Mech. JFLSA70022-112010.1017/S0022112094002399 275, 351 (1994).
2. P. Dimitrakopoulos and J. J. L. Higdon, "Displacement of fluid droplets from solid surfaces in low-Reynolds-number shear flows," J. Fluid Mech. JFLSA70022-112010.1017/S0022112096004788 336, 351 (1997).
3. P. Dimitrakopoulos and J. J. L. Higdon, "On the displacement of three-dimensional droplets from solid surfaces in low-Reynolds-number shear flows," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112098002985 377, 189 (1998).
4. P. Dimitrakopoulos and J. J. L. Higdon, "On the gravitational displacement of three-dimensional droplets from inclined solid surfaces," J. Fluid Mech. JFLSA70022-112010.1017/S0022112099005844 395, 181 (1999).
5. P. Dimitrakopoulos and J. J. L. Higdon, "On the displacement of three-dimensional droplets adhering to a plane wall in viscous pressure driven flows," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112001003883 435, 327 (2001).
6. E. B. Dussan, "Spreading of liquids on solid-surfaces-static and dynamic contact lines," Annu. Rev. Fluid Mech. ARVFA30066-418910.1146/annurev.fl.11.010179.002103 11, 371 (1979).
7. S. F. Kistler, "Hydrodynamics of wetting," in Wettability, Surfactant Science Series, edited by J. C. Berg (Marcel Dekker, New York, 1993), Vol. 49, pp. 311-429.
8. M. J. Miksis, "Contact lines," in A Celebration of Mathematical Modeling, edited by D. Givoli, M. J. Grote, and G. C. Papanicolaou (Kluwer Academic, Dordrecht, 2004), pp. 161-180.
9. J. Lowndes, "The numerical simulation of the steady movement of a fluid meniscus in a capillary tube," J. Fluid Mech. JFLSA70022-1120 101, 631 (1980).
10. P. Bach and O. Hassager, "An algorithm for the use of the Lagrangian specification in Newtonian fluid mechanics and applications to free surface flow," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112085000635 152, 173 (1984).
11. S. N. Reznik and A. L. Yarin, "Spreading of a viscous drop due to gravity and capillarity on a horizontal or an inclined dry wall," Phys. Fluids PHFLE61070-663110.1063/1.1426388 14, 118 (2002).
12. R. G. Cox, "The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow," J. Fluid Mech. JFLSA70022-112010.1017/S0022112086000332 168, 169 (1986).
13. A. D. Schleizer and R. T. Bonnecaze, "Displacement of a two-dimensional immiscible droplet adhering to a wall in shear and pressure-driven flows," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112098003462 383, 29 (1999).
14. Q. Kang, D. Zhang, and S. Chen, "Displacement of a two-dimensional immiscible droplet in a channel," Phys. Fluids PHFLE61070-663110.1063/1.1499125 14, 3203 (2002).
15. S. O. Unverdi and G. Tryggvason, "A front tracking method for viscous, incompressible, multifluid flows," J. Comput. Phys. JCTPAH0021-999110.1016/0021-9991(92)90307-K 100, 25 (1992).
16. G. Tryggvason, B. Bunner, A. Esmaeeli, D. Juric, N. Al-Rawahi, W. Tauber, J. Han, S. Nas, and Y.-J. Jan, "A front-tracking method for the computations of multiphase flow," J. Comput. Phys. JCTPAH0021-999110.1006/jcph.2001.6726 169, 708 (2001).
17. J. Zhang,"The dynamics of a viscous drop with a moving contact line," Ph.D. thesis, Northwestern University (2002).
18. E. B. Dussan V., "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. JFLSA70022-1120 174, 381 (1987).
19. P. J. Haley and M. J. Miksis, "The effect of the contact line on droplet spreading," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112091001337 223, 57 (1991).
20. L. M. Hocking and S. H. Davis, "Inertial effects in time-dependent motion of thin films and drops," J. Fluid Mech. JFLSA70022-1120 467, 1 (2002).