Pumping by flapping in a viscoelastic fluid

TL;DR

This paper demonstrates that reciprocal flapping motion can generate net flow in viscoelastic fluids, breaking the scallop theorem constraints and enabling micro-pump design without inertia.

Contribution

It provides an analytical demonstration that reciprocal motion can produce net flow in viscoelastic fluids, expanding the understanding of fluid pumping mechanisms.

Findings

Net flow occurs at fourth order in flapping amplitude.

Reciprocal motion can pump polymeric fluids without inertia.

Flow field and pumping efficiency are analytically optimized.

Abstract

In a world without inertia, Purcell's scallop theorem states that in a Newtonian fluid a time-reversible motion cannot produce any net force or net flow. Here we consider the extent to which the nonlinear rheological behavior of viscoelastic fluids can be exploited to break the constraints of the scallop theorem in the context of fluid pumping. By building on previous work focusing on force generation, we consider a simple, biologically-inspired geometrical example of a flapper in a polymeric (Oldroyd-B) fluid, and calculate asymptotically the time-average net fluid flow produced by the reciprocal flapping motion. The net flow occurs at fourth order in the flapping amplitude, and suggests the possibility of transporting polymeric fluids using reciprocal motion in simple geometries even in the absence of inertia. The induced flow field and pumping performance are characterized and optimized analytically. Our results may be useful in the design of micro-pumps handling complex fluids.