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The viscosity of a dilute suspension of rough spheres

Wilson, HJ; Davis, RH; (2000) The viscosity of a dilute suspension of rough spheres. Journal of Fluid Mechanics , 421 339 - 367. 10.1017/S0022112000001695. Green open access

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Abstract

We consider the flow of a dilute suspension of equisized solid spheres in a viscous fluid. The viscosity of such a suspension is dependent on the volume fraction, c, of solid particles. If the particles are perfectly smooth, then solid spheres will not come into contact, because lubrication forces resist their approach. In this paper, however, we consider particles with microscopic surface asperities such that they are able to make contact. For straining motions we calculate the O(c²) coefficient of the resultant viscosity, due to pairwise interactions. For shearing motions (for which the viscosity is undetermined because of closed orbits on which the probability distribution is unknown) we calculate the c² contribution to the normal stresses N1 and N2. The viscosity in strain is shown to be slightly lower than that for perfectly smooth spheres, though the increase in the O(c) term caused by the increased effective radius due to surface asperities will counteract this decrease. The viscosity decreases with increasing contact friction coefficient. The normal stresses N1 and N2 are zero if the surface roughness height is less than a critical value of 0.000211 times the particle radius, and then become negative as the roughness height is increased above this value. N1 is larger in magnitude than N2.

Type: Article
Title: The viscosity of a dilute suspension of rough spheres
Open access status: An open access version is available from UCL Discovery
DOI: 10.1017/S0022112000001695
Publisher version: http://dx.doi.org/10.1017/S0022112000001695
Language: English
Additional information: © 2000 Cambridge University Press
Keywords: Suspension, rough contact, viscosity, rheology
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/113351
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