Slow Motion of a Slip Spherical Particle in a Nonconcentric Spherical Cavity
Date Issued
2009
Date
2009
Author(s)
Li, Tai-Cheng
Abstract
A semianalytical study for the creeping flow caused by a spherical fluid or solid particle with a slip surface translating in a viscous fluid within a spherical cavity along the line connecting their centers is presented in the quasisteady limit of small Reynolds number. To solve the Stokes equations for the flow field, a general solution is constructed from the superposition of the fundamental solutions in the two spherical coordinate systems based on the particle and cavity respectively. The boundary conditions on the particle surface and cavity wall are satisfied by a collocation technique. Numerical results for the hydrodynamic drag force exerted on the particle are obtained with good convergence for various values of the ratio of particle-to-cavity radii, the relative location of the particle, the relative viscosity or slip coefficient of the particle, and the slip coefficient of the cavity wall. In the limits of the motions of a spherical particle in a concentric cavity and near a cavity wall with a small curvature, our drag results are in good agreement with the available solutions in the literature. As expected, the boundary-corrected drag force exerted on the particle for all cases is a monotonic increasing function of the ratio of particle-to-cavity radii, and becomes infinite in the touching limit. For a specified ratio of particle-to-cavity radii, the drag force is minimal when the particle is situated at the cavity center and increases monotonically to infinity in the limit when it is located extremely away from the cavity center. The drag force acting on the particle in general increases with an increase in its relative viscosity or with a decrease in its slip coefficient for a given configuration, but there are exceptions when the ratio of particle-to-cavity radii is large.
Subjects
slip
spherical particle
cavity
slow motion
Type
thesis
File(s)![Thumbnail Image]()
Loading...
Name
ntu-98-R96524016-1.pdf
Size
23.53 KB
Format
Adobe PDF
Checksum
(MD5):1e53a833b5708d2e8ce88e4a98e9bb5d