Interdisciplinary Applied Mathematics

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14.3.1 Hydrodynamic Forces on Spheres


We first discuss some classical semianalytical results for a single sphere, and subsequently we present known results for hydrodynamic interactions between spherical particles, and between particles and solid walls. We assume that    the    flow is    either in    the    Stokes    or in the    low    Reynolds    number


regime.


For a steady motion of an isolated particle, modeled as a sphere, the drag force is given by

Fd = ^CDPfira2V -t/ooKl/ -и.»),


where V is the particle velocity, Uis the undisturbed flow at the particle’s center, CD is the drag coefficient, pf is the fluid density, and a is the particle radius. Semiempirical expressions for the drag coefficient have been given by (Clift et al., 1978) in the form

CD = f(Rep )CDS,













Vi = ut +

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