Quantifying fluid transitions for different strokes with applications to micro-organisms swimming in viscoelastic fluids

Becca Thomases,

University of California, Davis, USA

Abstract

We ask the question: Why is the fluid response to small amplitude and large amplitude strokes different in viscoelastic fluids? It is well known that elastic stresses accumulate in viscoelastic fluids and where stretching outpaces relaxation. For example, large fluid stresses develop at steady extensional points for sufficiently large Weissenberg number. It is more difficult to understand how stress accumulates near swimmer bodies in part because the flows around moving micro-organisms, or waving cilia, cannot be characterized by a single Weissenberg number. In addition, it is not currently possible to measure the fluid elastic stress near motile cells in viscoelastic fluids. We use theory and numerical simulations to guide our intuition on where elastic stresses develop in the flows around organisms. By examining the flows around idealized undulating flagella or waving cilia in our numerical simulations we find that fluid regions near tips of these objects experience an effective oscillating extensional point from which we can define a local Weissenberg number. This can help us quantify what high amplitude means in terms of large stress accumulation around the body.

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