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Analysis of general creeping motion of a sphere inside a cylinder

Published online by Cambridge University Press:  07 December 2009

SUKALYAN BHATTACHARYA ,
COLUMBIA MISHRA  and
SONAL BHATTACHARYA
SUKALYAN BHATTACHARYA*
Affiliation:
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, USA
COLUMBIA MISHRA
Affiliation:
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, USA
SONAL BHATTACHARYA
Affiliation:
Department of Electrical & Computer Engineering, Texas Tech University, Lubbock, TX 79409, USA
*
†Email address for correspondence: [email protected]
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Abstract

In this paper, we develop an efficient procedure to solve for the Stokesian fields around a spherical particle in viscous fluid bounded by a cylindrical confinement. We use our method to comprehensively simulate the general creeping flow involving the particle-conduit system. The calculations are based on the expansion of a vector field in terms of basis functions with separable form. The separable form can be applied to obtain general reflection relations for a vector field at simple surfaces. Such reflection relations enable us to solve the flow equation with specified conditions at different disconnected bodies like the sphere and the cylinder. The main focus of this article is to provide a complete description of the dynamics of a spherical particle in a cylindrical vessel. For this purpose, we consider the motion of a sphere in both quiescent fluid and pressure-driven parabolic flow. Firstly, we determine the force and torque on a translating-rotating particle in quiescent fluid in terms of general friction coefficients. Then we assume an impending parabolic flow, and calculate the force and torque on a fixed sphere as well as the linear and angular velocities of a freely moving particle. The results are presented for different radial positions of the particle and different ratios between the sphere and the cylinder radius. Because of the generality of the procedure, there is no restriction in relative dimensions, particle positions and directions of motion. For the limiting cases of geometric parameters, our results agree with the ones obtained by past researchers using different asymptotic methods.

JFM classification

Low-Reynolds-number flows: Stokesian dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 642 , 10 January 2010 , pp. 295 - 328
Copyright
Copyright © Cambridge University Press 2009

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References

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