Small inertial effects on a spherical bubble, drop or particle moving near a wall in a time-dependent linear flow

Journal of Fluid Mechanics

Volumn 485, Issue , 2003, Pages 115-142

  Magnaudet, Jacques ^a  

^a IMFT   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BUBBLES (IN FLUIDS); DIFFUSION IN LIQUIDS; DRAG; HYDRODYNAMICS; LIFT; SHEAR STRESS; SPHERES; VISCOSITY OF LIQUIDS;

LIQUID DROPS;

FLOW OF FLUIDS;

BUBBLE; DROPLET; HYDRODYNAMICS; INERTIA; PARTICLE; TIMER;

EID: 0038503462     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112003004464     Document Type: Article

References (48)

1. ANNAMALAI, P. & COLE, R. 1986 Particle migration in rotating liquids. Phys. Fluids 29, 647-649.
2. ASMOLOV, E. S. & McLAUGHLIN, J. B. 1999 The inertial lift on an oscillating sphere in a linear shear flow. Intl. J. Multiphase Flow 25, 739-751.
3. AUTON, T. R. 1987 The lift force on a spherical body in a rotational flow. J. Fluid Mech. 183, 199-218.
4. AUTON, T. R, HUNT, J. C. R. & PRUD'HOMME, M. 1988 The force exerted on a body moving in an inviscid unsteady non-uniform rotational flow. J. Fluid Mech. 197, 241-257.
5. BEDEAUX, D. & RUBI, J. M. 1987 Drag on a sphere moving slowly through a fluid in elongational flow. Physica A 144, 285-298.
6. BRETHERTON, F. P. 1962 The motion of rigid particles in a shear flow at low Reynolds number. J. Fluid Mech. 14, 284-304.
7. BUSH, J. W. M., STONE, H. A. & TANZOSH, J. P. 1994 Particle motion in rotating viscous fluids: Historical survey and recent developments. Current Topics in The Physics of Fluids, vol. 1, pp. 337-355. Research Trends, Trivandrum, India.
8. CHAN, P. C. H. & LEAL, L. G. 1979 The motion of a deformable drop in a second-order fluid. J. Fluid Mech. 92, 131-170.
9. CHERUKAT, P. & McLAUGHLIN, J. B. 1990 Wall-induced lift on a sphere. Intl. J. Multiphase Flow 16, 899-907.
10. CHERUKAT, P. & McLAUGHLIN, J. B. 1994 The inertial lift on a rigid sphere in a linear shear flow field near a flat wall. J. Fluid Mech. 263, 1-18.
11. CHILDRESS, S. 1964 The slow motion of a sphere in a rotating, viscous fluid. J. Fluid Mech. 20, 305-314.
12. COX, R. G. & BRENNER, H. 1968 The lateral migration of solid particles in Poiseuille flow: 1. Theory. Chem. Engng Sci. 23, 147-173.
13. COX, R. G. & HSU, S. K. 1977 The lateral migration of solid particles in a laminar flow near a plate. Intl. J. Multiphase Flow 3, 201-222.
14. DREW, D. 1978 The force on a small sphere in slow viscous flow. J. Fluid Mech. 88, 393-400.
15. GATIGNOL, R. 1983 The Faxén formulae for a rigid particle in an unsteady non-uniform Stokes flow. J. Méc. Théor. Appl. 1, 143-160.
16. GOTOH, T. 1990 Brownian motion in a rotating flow. J. Statist. Phys. 59, 371-402.
17. HALOW, J. S. & WILLS, G. B. 1970 Radial migration of spherical particles in Couette systems. AIChE J. 16, 281-286.
18. HAPPEL, J. & BRENNER, H. 1973 Low Reynolds Number Hydrodynamics. Martinus Nijhoff.
19. HARPER, E. Y. & CHANG, I. D. 1968 Maximum dissipation resulting from lift in a slow viscous shear flow. J. Fluid Mech. 33, 209-225.
20. HERRON, I. H., DAVIES, S. H. & BRETHERTON, F. P. 1975 On the sedimentation of a sphere in a centrifuge. J. Fluid Mech. 68, 209-234.
21. HO, B. P. & LEAL, L. G. 1974 Inertial migration of rigid spheres in two-dimensional unidirectional flows. J. Fluid Mech. 65, 365-400.
22. HOGG, A. J. 1994 The inertial migration of non-neutrally buoyant spherical particles in two-dimensional shear flows. J. Fluid Mech. 272, 285-318.
23. KRISHNAN, G. P. & LEIGHTON, D. T. 1995 Inertial lift on a moving sphere in contact with a plane wall in a shear flow. Phys. Fluids 7, 2538-2545.
24. LEAL, L. G. 1980 Particle motions in a viscous fluid. Annu. Rev. Fluid Mech. 12, 435-476.
25. LEGENDRE, D. & MAGNAUDET, J. 1997 A note on the lift force on a bubble or a drop in a low-Reynolds-number shear flow. Phys. Fluids 9, 3572 3574.
26. LOVALENTI, P. M. & BRADY, J. F. 1993a The hydrodynamic force on a rigid particle undergoing arbitrary time-dependent motion at small Reynolds number. J. Fluid Mech. 256, 561-605.
27. LOVALENTI, P. M. & BRADY, J. F. 1993b The force on a bubble, drop, or particle in arbitrary time-dependent motion at small Reynolds number. Phys. Fluids A 5, 2104-2116.
28. McLAUGHLIN, J. B. 1993 The lift on a small sphere in wall-bounded linear shear flows. J. Fluid Mech. 246, 249-265.
29. MAGNAUDET, J., RIVERO, M. & FABRE, J. 1995 Accelerated flows past a rigid sphere or a spherical bubble. Part 1. Pure straining flow. J. Fluid Mech. 284, 97-135.
30. MAGNAUDET, J., TAKAGI, S. & LEGENDRE, D. 2003 Drag, deformation and lateral migration of a buoyant drop moving near a wall. J. Fluid Mech. 476, 115-157.
31. MAXEY, M. R. & RILEY, J. J. 1983 Equation of motion for a small rigid sphere in a non-uniform flow. Phys. Fluids 26, 883 889.
32. MILNE-THOMSON, L. M. 1968 Theoretical Hydrodynamics. Macmillan.
33. MIYAZAKI, K. 1995 Dependence of the friction tensor on the rotation of a frame of reference. Physica A 222, 248 260.
34. MIYAZAKI, K., BEDEAUX, D. & BONET AVALOS, J. 1995 Drag on a sphere in slow shear flow. J. Fluid Mech. 296, 373 390.
35. MOUGIN, G. & MAGNAUDET, J. 2002 The generalized Kirchhoff equations and their application to the interaction between a rigid body and an arbitrary time-dependent viscous flow. Intl. J. Multiphase Flow 28, 1837 1851.
36. PEREZ-MADRID, A., RUBI, J. M. & BEDEAUX, D. 1990 Motion of a sphere through a fluid in stationary homogeneous flow. Physica A 163, 778 790.
37. ROBERTS, G. O., KORNFELD, D. M. & FOWLIS, W. W. 1991 Particle orbits in a rotating liquid. J. Fluid Mech. 229, 555 567.
38. SAFFMAN, P. G. 1965 The lift force on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385-400.
39. SCHONBERG, J. A. & HINCH, E. J. 1989 Inertial migration of a sphere in Poiseuille flow. J. Fluid Mech. 203, 517-524.
40. SEGRÉ, G. & SILBERBERG, A. 1962a Behaviour of macroscopic rigid spheres in Poiseuille flow. Part 1. Determination of local concentration by statistical analysis of particle passages through crossed light beams. J. Fluid Mech. 14, 115 135.
41. SEGRÉ, G. & SILBERBERG, A. 1962b Behaviour of macroscopic rigid spheres in Poiseuille flow. Part 2. Experimental results and interpretation. J. Fluid Mech. 14, 136-157.
42. STONE, H. A. 2000 Philip Saffman and viscous flow theory. J. Fluid Mech. 409, 165-183.
43. TAKEMURA, F., TAKAGI, S., MAGNAUDET, J. & MATSUMOTO, Y. 2002 Drag and lift forces on a bubble rising near a vertical wall in a viscous liquid. J. Fluid Mech. 461, 277-300.
44. TAYLOR, G. I. 1928 The forces on a body placed in a curved or converging stream of fluid. Proc. R. Soc. Lond. A 120, 260-283.
45. VASSEUR, P. & COX, R. G. 1976 The lateral migration of a spherical particle in two-dimensional shear flows. J. Fluid Mech. 78, 385 413.
46. VASSEUR, P. & COX, R. G. 1977 The lateral migration of spherical particles sedimenting in a stagnant bounded fluid. J. Fluid Mech. 80, 561 591.
47. WEISERBORN, A. J. 1985 Drag on a sphere moving slowly in a rotating viscous fluid. J. Fluid Mech. 153, 215-227.
48. YANG S. & LEAL, L. G. 1991 A note on memory-integral contributions to the force on an accelerating spherical drop at low Reynolds number. Phys. Fluids A 3, 1822-1823.