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

Fabien Candelier (1) , Bernhard Mehlig (2) , Jacques Magnaudet (3)

1 IUSTI - Institut universitaire des systèmes thermiques industriels
2 GU - Göteborgs Universitet = University of Gothenburg
3 IMFT - Institut de mécanique des fluides de Toulouse

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.

Mots clés: Particle; Fluid flow

Domaines: Mécanique des fluides [physics.class-ph]

Fabien Candelier, Bernhard Mehlig, Jacques Magnaudet. Time-dependent lift and drag on a rigid body in a viscous steady linear flow. Journal of Fluid Mechanics, 2019, 864, pp.554-595. ⟨10.1017/jfm.2019.23⟩. ⟨hal-02052051⟩