Open Access

ARTICLE

Axisymmetric Slow Motion of a Prolate Particle in a Circular Capillary with Slip Surfaces

Hong Y. Yeh, Huan J. Keh^{1, *}

1 Department of Chemical Engineering, National Taiwan University, Taipei, 10617, Taiwan, ROC. *Corresponding author: E-mail: huan@ntu.edu.tw.

Computer Modeling in Engineering & Sciences 2017, 113(3), 343-366. https://doi.org/10.3970/cmes.2017.113.361

Abstract

The problem of the steady migration of an axially symmetric prolate particle along its axis of revolution coinciding with the centerline of a circular capillary is investigated semi-analytically in the limit of low Reynolds number, where the viscous fluid may slip at the solid surfaces. A method of distribution of spherical singularities along the axis inside the particle is employed to establish the general solution of the fluid velocity satisfying the boundary conditions at the capillary wall and infinity. The slip condition at the particle surface is then satisfied by using a boundary collocation method to determine the unknown constants in this solution. The hydrodynamic drag force acting on the particle is obtained with good convergence for the cases of a prolate spheroid and a prolate Cassini oval with various values of the slip parameter of the particle, slip parameter of the capillary wall, aspect ratio or shape parameter of the particle, and spacing parameter between the particle and the wall. For the axially symmetric migrations of a spheroid and a Cassini oval in a capillary with no-slip surfaces and of a sphere in a capillary with slip surfaces, our results agree excellently with the numerical solutions obtained earlier. The capillary wall affects the particle migration significantly when the solid surfaces get close to each other. For a specified particle-in-capillary configuration, the normalized drag force exerted on the particle in general decreases with increasing slippage at the solid surfaces, except when the fluid slips little at the capillary wall and the particle-wall spacing parameter is relatively large. For fixed spacing parameter and slip parameters, the drag force increases with an increase in the axial-to-radial aspect ratio (or surface area effective for viscous interaction with the capillary wall) of the particle, but this tendency can be reversed when the particle is highly slippery.

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