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The effect of deformable porous surface layers on the motion of a sphere in a narrow cylindrical tube

Published online by Cambridge University Press:  26 April 2006

Wen Wang  and
Kim H. Parker
Wen Wang
Affiliation:
Physiological Flow Studies Group, Centre For Biological and Medical Systems, Imperial College of Science, Technology and Medicine, London SW7 2BY, UK
Kim H. Parker
Affiliation:
Physiological Flow Studies Group, Centre For Biological and Medical Systems, Imperial College of Science, Technology and Medicine, London SW7 2BY, UK
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Abstract

The hydrodynamic influence of deformable porous surface layers on the motion of a rigid sphere falling in a narrow cylindrical tube filled with a stationary Newtonian fluid is studied using lubrication theory. The porous layers on both the surface of the tube and the sphere are modelled as binary mixtures of solid and liquid components. The sphere is placed at an arbitrary position in the tube and is free to rotate. Effects of the clearance between the sphere and the tube, the eccentricity of the position of the sphere and the properties of the surface layers on the velocity and rotation of the sphere are studied. It is found that, when the lengthscale on which the velocity varies within the porous layer is much smaller than the clearance, the effects of the porous layer can be represented by an equivalent slip boundary condition, the slip velocity at the boundary being proportional to the local shear rate. The slip velocities have a strong influence on the motion of the sphere when the clearance is small. For a given clearance and slip parameters, both the falling and rotation velocities of the sphere increase with the sphere eccentricity. The shear stresses on the surfaces of both the tube and the sphere are greatly reduced when slip boundary conditions are applied, as is the pressure gradient in the region between the sphere and the tube wall. This work could have some relevance to the creeping motion of blood cells in the microcirculation where the glycocalyx, a polysaccharide-rich layer, covers the external surfaces of both endothelial and red blood cells.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 283 , 25 January 1995 , pp. 287 - 305
Copyright
© 1995 Cambridge University Press

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