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

Published online by Cambridge University Press:  11 February 2019

Fabien Candelier ,
Bernhard Mehlig Open the ORCID record for Bernhard Mehlig [Opens in a new window]  and
Jacques Magnaudet Open the ORCID record for Jacques Magnaudet [Opens in a new window]
Fabien Candelier*
Affiliation:
Aix-Marseille Univ., CNRS, IUSTI (Institut Universitaire des Systèmes Thermiques et Industriels) F-13013 Marseille, France
Bernhard Mehlig
Affiliation:
Department of Physics, Gothenburg University, SE-41296 Gothenburg, Sweden
Jacques Magnaudet*
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, Toulouse, France
*
†Email addresses for correspondence: fabien.candelier@univ-amu.fr, jmagnaud@imft.fr
†Email addresses for correspondence: fabien.candelier@univ-amu.fr, jmagnaud@imft.fr
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Abstract

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.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 864 , 10 April 2019 , pp. 554 - 595
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© 2019 Cambridge University Press 

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