Low-Reynolds-number motion of a deformable drop between two parallel plane walls

International Journal of Multiphase Flow

Volumn 33, Issue 2, 2007, Pages 182-206

  Griggs, Andrew J ^a   Zinchenko, Alexander Z ^a   Davis, Robert H ^a  

^a UCB 450   (United States)

Author keywords

Boundary integral; Bubbles; Channel; Drops; Stokes flow

Indexed keywords

ALGORITHMS; BUBBLES (IN FLUIDS); BUOYANCY; COMPUTER SIMULATION; DROP BREAKUP; GREEN'S FUNCTION; REYNOLDS NUMBER; VISCOSITY;

BOUNDARY INTEGRAL ALGORITHMS; CHANNELS; DROPS; STOKES FLOW;

FLOW OF FLUIDS;

ALGORITHMS; BUBBLES (IN FLUIDS); BUOYANCY; COMPUTER SIMULATION; DROP BREAKUP; FLOW OF FLUIDS; GREEN'S FUNCTION; REYNOLDS NUMBER; VISCOSITY;

EID: 33846318555     PISSN: 03019322     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijmultiphaseflow.2006.06.012     Document Type: Article

References (27)

1. Abramowitz M., and Stegun I.A. Handbook of Mathematical Functions with Formulas, Graphs, & Mathematical Tables (1972), Dover, New York
2. Bhattacharya S., and Blawzdziewicz J. Image system for Stokes-flow singularity between two parallel planar walls. J. Math. Phys. 43 (2002) 5720
3. Blake J.R. A note on the image system for a stokeslet in a no-slip boundary. Proc. Cam. Philos. Soc.-Math. Phys. Sci. 70 (1971) 303
4. Chen K.H., and Keh P.Y. Slow motion of a droplet between two parallel walls. Chem. Eng. Sci. 56 (2001) 6863-6871
5. Coulliette C., and Pozrikidis C. Motion of an array of drops through a cylindrical tube. J. Fluid Mech. 358 (1998) 1-28
6. Cristini V., Blawzdziewicz J., and Loewenberg M. Drop breakup in three-dimensional viscous flows. Phys. Fluids 10 (1998) 1781-1783
7. Cristini V., Blawzdziewicz J., and Loewenberg M. An adaptive mesh algorithm for evolving surfaces: simulations of drop breakup and coalescence. J. Comput. Phys. 168 (2001) 445-463
8. DeBisschop K.M., Miksis M.J., and Eckmann D.M. Bubble rising in an inclined channel. Phys. Fluids 14 (2002) 93-106
9. Ganatos P., Pfeffer R., and Weinbaum S. A strong interaction theory for the creeping motion of a sphere between plane parallel boundaries. Part 2 Parallel motion. J. Fluid Mech. 99 (1980) 755-783
10. Hodges S.R., Jensen O.E., and Rallison J.M. The motion of a viscous drop through a cylindrical tube. J. Fluid Mech. 501 (2004) 279-301
11. Kim S., and Karrila S.J. Microhydrodynamics: Principles and Selected Applications (1991), Butterworths-Heinemann, Boston, MA
12. Liron N., and Mochon S. Stokes flow for a stokes-let between two parallel flat plates. J. Eng. Math. 10 (1976) 287
13. Martinez M.J., and Udell K.S. Axisymmetric creeping motion of drops through circular tubes. J. Fluid Mech. 210 (1990) 565-591
14. Mortazavi S., and Tryggvasson G. A numerical study of the motion of drops in Poiseuille flow. Part 1. Lateral migration of one drop. J. Fluid Mech. 411 (2000) 325-350
15. Olbricht W., and Kung D. The deformation & breakup of liquid drops in low Reynolds number flow through a capillary. Phys. Fluids A 4 (1992) 1347-1354
16. Pozrikidis C. Boundary Integral & Singularity Methods for Linearized Viscous Flow (1992), Cambridge University Press, Cambridge, MA
17. Rallison J.M., and Acrivos A. A numerical study of the deformation and burst of a viscous drop in an extensional flow. J. Fluid Mech. 89 (1978) 191-200
18. Rallison J.M. A numerical study of the deformation & burst of a viscous drop in general shear flows. J. Fluid Mech. 109 (1981) 465-482
19. Shapira M., and Haber S. Low Reynolds number motion of a droplet between two parallel plates. Int. J. Multiphase Flow 14 (1988) 483-506
20. Smart J.R., and Leighton D.T. Measurement of the drift of a droplet due to the presence of a plane. Phys. Fluids A 3 (1991) 21-28
21. Staben M.E., Zinchenko A.Z., and Davis R.H. Motion of a particle between two parallel plane walls in low-Reynolds number Poiseuille flow. Phys. Fluids 15 (2003) 1711-1733 (Erratum: Phys. Fluids 16, 4204)
22. Tsai T., and Miksis M. Dynamics of a drop in a constricted capillary tube. J. Fluid Mech. 274 (1994) 197-217
23. Uijttewaal W.S.J., Nijihof E.J., and Heethaar R.M. Droplet migration, deformation, and orientation in the presence of a plane wall: a numerical study compared with analytical theories. Phys. Fluids A 4 (1993) 819-825
24. Zinchenko A.Z., Rother M.A., and Davis R.H. A novel boundary-integral algorithm for viscous interaction of deformable drops. Phys. Fluids 9 (1997) 1493-1511
25. Zinchenko A.Z., Rother M.A., and Davis R.H. Cusping, capture, & breakup of interacting drops by a curvatureless boundary-integral algorithm. J. Fluid Mech. 391 (1999) 249-291
26. Zinchenko A.Z., and Davis R.H. An efficient algorithm for hydrodynamical interaction of many deformable drops. J. Comp. Phys. 157 (2000) 539-587
27. Zinchenko A.Z., and Davis R.H. A multipole-accelerated algorithm for close interaction of slightly deformable drops. J. Comp. Phys. 207 (2005) 695-735