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

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 variation of the undisturbed flow at the body scale is much larger than the slip velocity between the body and the fluid. Motivated by applications to 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.

38 pages, 8 figures

References in corpus (8)

• The Magnus expansion and some of its applications
• Rotation of a spheroid in a simple shear at small Reynolds number
• Effect of weak fluid inertia upon Jeffery orbits
• Time-dependent lift and drag on a rigid body in a viscous steady linear flow
• Numerical analysis of the angular motion of a neutrally buoyant spheroid in shear flow at small Reynolds numbers
• Angular dynamics of a small particle in turbulence
• The role of inertia for the rotation of a nearly spherical particle in a general linear flow
• Angular velocity of a spheroid log rolling in a simple shear at small Reynolds number

Cited by in corpus (12)

• Importance of fluid inertia for the orientation of spheroids settling in turbulent flow
• Theory for the effect of fluid inertia on the orientation of a small particle settling in turbulence
• Time-dependent lift and drag on a rigid body in a viscous steady linear flow
• Inertial drag on a sphere settling in a stratified fluid
• Effect of particle inertia on the alignment of small ice crystals in turbulent clouds
• Inertial torque on a small spheroid in a stationary uniform flow
• Experimental validation of fluid inertia models for a cylinder settling in a quiescent flow
• Second-order inertial forces and torques on a sphere in a viscous steady linear flow
• Fluid inertial torque is an effective gyrotactic mechanism for settling elongated micro-swimmers
• Unsteady and inertial dynamics of an active particle in a fluid
• Inertial torque on a squirmer
• Critical charges for droplet collisions