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Time-dependent lift and drag on a rigid body in a viscous steady linear flow

Journal article
Authors F. Candelier
Bernhard Mehlig
J. Magnaudet
Published in Journal of Fluid Mechanics
Volume 864
Pages 554-595
ISSN 0022-1120
Publication year 2019
Published at Department of Physics (GU)
Pages 554-595
Language en
Keywords particle/fluid flow, small reynolds, anisotropic particles, stokes resistance, small sphere, orientation dynamics, inertial migration, arbitrary particle, poiseuille, flow, slow motion, shear-flow, Mechanics, Physics, yazaki k, 1995, journal of fluid mechanics, v296, p373, laughlin jb, 1991, journal of fluid mechanics, v224, p261, ildress s, 1964, journal of fluid mechanics, v20, p305, oudman i, 1957, journal of fluid mechanics, v2, p237
Subject categories Condensed Matter Physics


We compute the leading-order inertial corrections to the instantaneous force acting on a rigid body moving with a time-dependent slip velocity in a linear flow field, assuming that the square root of the Reynolds number based on the fluid-velocity gradient is much larger than the Reynolds number based on the slip velocity between the body and the fluid. As a first step towards applications to dilute sheared suspensions and turbulent particle-laden flows, we seek a formulation allowing this force to be determined for an arbitrarily shaped body moving in a general linear flow. We express the equations governing the flow disturbance in a non-orthogonal coordinate system moving with the undisturbed flow and solve the problem using matched asymptotic expansions. The use of the co-moving coordinates enables the leading-order inertial corrections to the force to be obtained at any time in an arbitrary linear flow field. We then specialize this approach to compute the time-dependent force components for a sphere moving in three canonical flows: solid-body rotation, planar elongation, and uniform shear. We discuss the behaviour and physical origin of the different force components in the short-time and quasi-steady limits. Last, we illustrate the influence of time-dependent and quasi-steady inertial effects by examining the sedimentation of prolate and oblate spheroids in a pure shear flow.

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