A reciprocal theorem for boundary-driven channel flows

Abstract

In a variety of physical situations, a bulk viscous flow is induced by a distribution of surface velocities, for example in diffusiophoresis (as a result of chemical gradients) and above carpets of cilia (as a result of biological activity). When such boundary-driven flows are used to pump fluids, the primary quantity of interest is the induced flow rate. In this letter we propose a method, based on the reciprocal theorem of Stokes flows, to compute the net flow rate for arbitrary flow distribution and periodic pump geometry using solely stress information from a dual Poiseuille-like problem. After deriving the general result we apply it to straight channels of triangular, elliptic and rectangular geometries and quantify the relationship between bulk motion and surface forcing.

7 pages, 2 figures

References in corpus (5)

• Self-motile colloidal particles: from directed propulsion to random walk
• Designing phoretic micro- and nano-swimmers
• Geometric pumping in autophoretic channels
• The many-body reciprocal theorem and swimmer hydrodynamics
• A note on the reciprocal theorem for the swimming of simple bodies

Cited by in corpus (7)

• Exact solutions for hydrodynamic interactions of two squirming spheres
• Stresslets induced by active swimmers
• Higher-order force moments of active particles
• Universal optimal geometry of minimal phoretic pumps
• Spontaneous onset of convection in a uniform phoretic channel
• First-order analysis of slip flow at the microscale and nanoscale
• Flow rate-pressure drop relation for deformable channels via fluidic and elastic reciprocal theorems