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Hydrodynamic interaction of rough spheres

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The approach of two spheres along their line of centres is analyzed assuming that each sphere is covered by a porous layer. The slip of the fluid at the surface of the porous layers then permits the spheres to touch without a singularity in the associated force. In a corresponding analysis for flat surfaces, an analytical formula for the force is obtained. This force is also finite for vanishing gap width. It is shown how the properties of the porous layers can be related to the statistics of spatial distributions of surface asperities. Finally, it is emphasised that a finite force is associated with a finite asperity height.

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Jenkins, J., Koenders, M. Hydrodynamic interaction of rough spheres. Granular Matter 7, 13–18 (2005).

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