Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-29T14:05:58.429Z Has data issue: false hasContentIssue false
  • English
  • Français

The motion of an ellipsoid in tube flow at low Reynolds numbers

Published online by Cambridge University Press:  26 April 2006

Masako Sugihara-Seki
Masako Sugihara-Seki
Affiliation:
Kansai University, Faculty of Engineering, Suita, Osaka 564, Japan e-mail: sekim@gep.kansai-u.ac.jp
Get access Rights & Permissions [Opens in a new window]

Abstract

The motion of a rigid ellipsoidal particle freely suspended in a Poiseuille flow of an incompressible Newtonian fluid through a narrow tube is studied numerically in the zero-Reynolds-number limit. It is assumed that the effect of inertia forces on the motion of the particle and the fluid can be neglected and that no forces or torques act on the particle. The Stokes equation is solved by a finite element method for various positions and orientations of the particle to yield the instantaneous velocity of the particle as well as the flow field around it, and the particle trajectories are determined for different initial configurations. A prolate spheroid is found to either tumble or oscillate in rotation, depending on the particle–tube size ratio, the axis ratio of the particle, and the initial conditions. A large oblate spheroid may approach asymptotically a steady, stable configuration, at which it is located close to the tube centreline, with its major axis slightly tilted from the undisturbed flow direction. The motion of non-axisymmetric ellipsoids is also illustrated and discussed with emphasis on the effect of the particle shape and size.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 324 , 10 October 1996 , pp. 287 - 308
Copyright
© 1996 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bretherton, F. P. 1962 The motion of rigid particles in a shear flow at low Reynolds number. J. Fluid Mech. 14, 284–303.Google Scholar
Bungay, P. M. & Brenner, H. 1973 The motion of a closely fitting sphere in a fluid filled tube. Intl J. Multiphase Flow 1, 25–56.Google Scholar
Chen, T. C. & Skalak, R. 1970 Spheroidal particle flow in a cylindrical tube. Appl. Sci. Res. 22, 403–441.Google Scholar
Chwang, A. L. 1975 Hydromechanics of low-Reynolds-number flow. Part 3. Motion of a spheroidal particle in quadratic flows. J. Fluid Mech. 72, 17–34.Google Scholar
Claeys, I. L. & Brady, J. F. 1993a Suspensions of prolate spheroids in Stokes flow. Part 1. Dynamics of a finite number of particles in an unbounded fluid. J. Fluid Mech. 251, 411–442.Google Scholar
Claeys, I. L. & Brady, J. F. 1993b Suspensions of prolate spheroids in Stokes flow. Part 2. Statistically homogeneous dispersions. J. Fluid Mech. 251, 443–477.Google Scholar
Claeys, I. L. & Brady, J. F. 1993c Suspensions of prolate spheroids in Stokes flow. Part 3. Hydrodynamic transport properties of crystalline dispersions. J. Fluid Mech. 251, 479–500.Google Scholar
Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubbles, Drops, and Particles. Academic.
Goldsmith, H. L. & Mason, S. G. 1967 Rheology, Theory and Applications, vol. IV (ed. F.R. Eirich) pp. 85–250. Academic.
Happel, J. & Brenner, H. 1983 Low Reynolds Number Hydrodynamics. Martinus Nijhoff.
Hinch, E. J. & Leal, L. G. 1972 The effect of Brownian motion on the rheological properties of a suspension of non-spherical particles. J. Fluid Mech. 52, 683–712.Google Scholar
Hinch, E. J. & Leal, L. G. 1979 Rotation of small non-axisymmetric particles in a simple shear flow. J. Fluid Mech. 92, 591–608.Google Scholar
Hsu, R. & Ganatos, P. 1994 Gravitational and zero-drag motion of a spheroid adjacent to an inclined plane at low Reynolds number. J. Fluid Mech. 268, 267–292.Google Scholar
Hsu, R. & Secomb, T. W. 1989 Motion of nonaxisymmetric red blood cells in cylindrical capillaries. J. Biomech. Engng 111, 147–151.Google Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161–179.Google Scholar
Kim, S. & Karrila, S. J. 1991 Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann.
Leal, L. G. & Hinch, E. J. 1971 The effect of weak Brownian rotations on particles in shear flow. J. Fluid Mech. 46, 685–703.Google Scholar
Leichtberg, S., Pfeffer, R. & Weinbaum, S. 1976 Stokes flow past finite coaxial clusters of spheres in a circular cylinder. Intl J. Multiphase Flow 3, 147–169.Google Scholar
Li, X., Zhou, H. & Pozrikidis, C. 1995 A numerical study of the shearing motion of emulsions and foams. J. Fluid Mech. 286, 379–404.Google Scholar
Oberbeck, A. 1876 Ueber stationäre Flüssigkeitsbewegungen mit Berücksichtigung der inneren Reibung. J. Reine Angew. Math. 81, 62–80.Google Scholar
Olson, M. D. & Tuann, S. Y. 1978 Finite Elements in Fluids, vol. 3, pp. 73–87. Wiley.
Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.
Pozrikidis, C. 1994 The motion of particles in the Hele-Shaw cell. J. Fluid Mech. 261, 199–222.Google Scholar
Secomb, T. W. & Hsu, R. 1993 Non-axisymmetric motion of rigid closely fitting particles in fluid-filled tubes. J. Fluid Mech. 257, 403–420.Google Scholar
Secomb, T. W., Skalak, R., Özkaya, N. & Gross, J. F. 1986 Flow of axisymmetric red blood cells in narrow capillaries. J. Fluid Mech. 163, 405–423.Google Scholar
Stover, C. A. & Cohen, C. 1990 The motion of rodlike particles in the pressure driven flow between two flat plates. Rheol. Acta 29, 192–203.Google Scholar
Sugihara-Seki, M. 1993 The motion of an elliptical cylinder in channel flow at low Reynolds numbers. J. Fluid Mech. 257, 575–596.Google Scholar
Sugihara-Seki, M. 1995 Effect of irregularities of vessel cross-section on vascular resistance. Fluid Dyn. Res. 17, 1–11.Google Scholar
Tözeren, H. 1982 Torque on eccentric spheres flowing in tubes. Trans ASME E: J. Appl. Mech. 49, 279–283.Google Scholar
Tözeren, H. & Skalak, R. 1978 The steady flow of closely fitting incompressible elastic spheres in a tube. J. Fluid Mech. 87, 1–16.Google Scholar
Wakiya, S. 1957 Viscous flows past a spheroid. J. Phys. Soc. Japan 12, 1130–1141.Google Scholar
Wang, H. & Skalak, R. 1969 Viscous flow in a cylindrical tube containing a line of spherical particles. J. Fluid Mech. 38, 75–96.Google Scholar
Weinbaum, S., Ganatos, P. & Yan Z.-Y. 1990 Numerical multipole and boundary integral equation techniques in Stokes flow. Ann. Rev. Fluid Mech. 22, 275–316.Google Scholar
Zhou, H. & Pozrikidis, C. 1993a The flow of suspensions in channels: Single files of drops. Phys. Fluids A 5, 311–324.Google Scholar
Zhou, H. & Pozrikidis, C. 1993b The flow of ordered and random suspensions of two-dimensional drops in a channel. J. Fluid Mech. 255, 103–127.Google Scholar
Zhou, H. & Pozrikidis, C. 1995 Adaptive singularity method for Stokes flow past particles. J. Comput. Phys. 117, 79–89.Google Scholar