Motion of a particle between two parallel plane walls in low-Reynolds-number Poiseuille flow

Physics of Fluids

Volumn 15, Issue 6, 2003, Pages 1711-1733

  Staben, Michelle E ^a   Zinchenko, Alexander Z ^a   Davis, Robert H ^a  

^a University of Colorado at Boulder   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; PARTICLE SIZE ANALYSIS; REYNOLDS NUMBER; TENSORS; VELOCITY MEASUREMENT;

POISEUILLE FLOW;

FLOW OF FLUIDS;

ALGORITHM; CHANNEL FLOW; FLOW VELOCITY; MATHEMATICAL METHOD; PARALLEL PLATES; PARTICLE MOTION; POISEUILLE FLOW;

EID: 0037830988     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1568341     Document Type: Article

References (28)

1. H. A. Lorentz, "A general theorem concerning the motion of a viscous fluid and a few consequences derived from it," Zittingsverlag Konikl. Akad. Wetensch. Amsterdam 5, 168 (1896) [also in Abhandlungen über Theoretische Physik (Leipzig, Berlin, 1907), Vol. 1, p. 23; and Collected Papers (Martinus Nijhoff, The Hague, 1937), Vol. 4, p. 7].
2. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics. 4th ed. (Martinus Nijhoff, Dordrecht, 1986).
3. W. R. Dean and M. E. O'Neill, "A slow motion of viscous liquid caused by the rotation of a solid sphere," Mathematika 10, 13 (1963).
4. M. E. O'Neill, "A slow motion of viscous liquid caused by a slowly moving solid sphere," Mathematika 11, 67 (1964).
5. M. E. O'Neill, "A slow motion of viscous liquid caused by a slowly moving solid sphere: An addendum," Mathematika 14, 170 (1967 ).
6. A. J. Goldman, R. G. Cox, and H. Brenner, "Slow viscous motion of a sphere parallel to a plane wall. I. Motion through a quiescent fluid," Chem. Eng. Sci. 22, 637 (1967).
7. A. J. Goldman, R. G. Cox, and H. Brenner, "Slow viscous motion of a sphere parallel to a plane wall. II. Couette flow," Chem. Eng. Sci. 22, 653 (1967).
8. C. Pozrikidis, "The motion of particles in the Hele-Shaw cell," J. Fluid Mech. 261, 199 (1994).
9. B. P. Ho and L. G. Leal, "Inertial migration of rigid spheres in 2-dimensional unidirectional flows," J. Fluid Mech. 65, 365 (1974).
10. P. Ganatos, R. Pfeffer, and S. Weinbaum, "A strong interaction theory for the creeping motion of a sphere between plane parallel boundaries. 2. Parallel motion," J. Fluid Mech. 99, 755 (1980).
11. P. Ganatos, S. Weinbaum, and R. Pfeffer, "A strong interaction theory for the creeping motion of a sphere between plane parallel boundaries. 1, Perpendicular motion," J. Fluid Mech. 99, 739 (1980).
12. P. Ganatos, S. Weinbaum, and R. Pfeffer, "Gravitational and zero-drag motion of a sphere of arbitrary size in an inclined channel at low Reynolds-number," J. Fluid Mech. 124, 27 (1982).
13. Z. Yu, "The creeping motion of a body between two parallel planes with applications to osmosis in biological membranes," Ph.D. thesis, City University of New York, City College, 1994.
14. S. Kim and S. J. Karrila, Microhydrodynamics: Principles and Selected Applications (Butterworths-Heinemann, Boston, 1991).
15. C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow (Cambridge University Press, Cambridge, MA, 1992).
16. R. Hsu and P. Ganatos, "The motion of a rigid body in viscous-fluid bounded by a plane wall," J. Fluid Mech. 207, 29 (1989).
17. J. R. Blake, "A note on the image system for a Stokeslet in a no-slip boundary," Proc. Cambridge Philos. Soc. 70, 303 (1971).
18. N. Liron and S. Mochon, "Stokes flow for a Stokes-let between 2 parallel flat plates," J. Eng. Math. 10, 287 (1976).
19. S. Weinbaum, P. Ganatos, and Z. Y. Yan, "Numerical multipole and boundary integral-equation techniques in Stokes-flow," Annu. Rev. Fluid Mech. 22, 275 (1990).
20. A. Z. Zinchenko, M. A. Rother, and R. H. Davis, "A novel boundary-integral algorithm for viscous interaction of deformable drops," Phys. Fluids 9, 1493 (1997).
21. C. Coulliette and C. Pozrikidis, "Motion of an array of drops through a cylindrical tube," J. Fluid Mech. 358, 1 (1998).
22. J. M. Rallison, "A numerical study of the deformation and burst of a viscous drop in general shear flows," J. Fluid Mech. 109, 465 (1981).
23. R. Fletcher, "Conjugate gradient methods for indefinite systems," in Lecture Notes in Mathematics (Springer-Verlag, Berlin, 1976), Vol. 506.
24. A. Z. Zinchenko, M. A. Rother, and R. H. Davis, "Cusping, capture, and breakup of interacting drops by a curvatureless boundary-integral algorithm," J. Fluid Mech. 391, 249 (1999).
25. M. Loewenberg and E. J. Hinch, "Numerical simulation of a concentrated emulsion in shear flow," J. Fluid Mech. 321, 395 (1996 ).
26. H. Brenner and L. J. Gaydos, "Constrained Brownian-movement of spherical-particles in cylindrical pores of comparable radius-models of diffusive and convective transport of solute molecules in membranes and porous-media," J. Colloid Interface Sci. 58, 312 (1977).
27. M. Sugiharaseki, "The motion of an elliptic cylinder in channel flow at low Reynolds-numbers," J. Fluid Mech. 257, 575 (1993).
28. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1965).