Force-dependence of the rigid-body motion for an arbitrarily shaped particle in a forced, incompressible Stokes flow

Abstract

When a particle moves in a Newtonian flow at low Reynolds number, inertia is irrelevant and a linear relationship exists between velocities and forces. For incompressible flows, any force distribution $\mathbf{f}(\mathbf{r})$ acting in the fluid bulk induces flow and motion only through its solenoidal component. For force distributions that are spatially localized (i.e., vanish sufficiently fast at infinity), we derive the representation of the rigid body motion as an explicit linear functional of $\nabla \times \mathbf{f}$, which complements the usual representation in terms of $\mathbf{f}$. We illustrate the utility of this alternative representation, which has the advantage of having the incompressibility constraint built-in, in avoiding certain ambiguities that arise, e.g., when implementing approximations for swimmers.

arXiv commentThe manuscript proper and the supplemental material have been merged consecutively into a single PDF file

References in corpus (5)

• Generic theory of colloidal transport
• Dynamics and efficiency of a self-propelled, diffusiophoretic swimmer
• Self-diffusiophoresis of Janus particles that release ions
• Self-motility of an active particle induced by correlations in the surrounding solution
• Self-chemophoresis in the thin diffuse interface approximation

Cited by in corpus (1)

• Ionic self-phoresis maps onto correlation-induced self-phoresis