Pumping by flapping in a viscoelastic fluid

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.

References in corpus (6)

• The hydrodynamics of swimming microorganisms
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• Propulsion in a viscoelastic fluid
• A basic swimmer at low Reynolds number
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• Swimming in Complex Fluids
• Viscoelastic propulsion of a rotating dumbbell
• Fluid-Induced Propulsion of Rigid Particles in Wormlike Micellar Solutions
• Micropropulsion and microrheology in complex fluids via symmetry breaking
• Viscoelastic levitation
• Microswimming in viscoelastic fluids