Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.

Jorge Arrieta,Jorge Arrieta,Emmanuelle Gouillart,Idan Tuval,Oreste Piro,Julyan H E Cartwright,Nicolas Piro,Emmanuelle Gouillart,Julyan H E Cartwright,Emmanuelle Gouillart

doi:10.1371/journal.pone.0130735

Abstract

Mixing fluid in a container at low Reynolds number— in an inertialess environment—is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the “belly phase,” peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.

Highlights

How may fluid be mixed at low Reynolds number? Such mixing is normally performed with a stirrer, a rotating device within the container that produces a complex, chaotic flow
In this Letter we propose what we term geometric mixing: the use of the geometric phase introduced by nonreciprocal cycling of the deformable boundaries of a container as a tool for fluid mixing at low Reynolds number
We lastly show that peristalsis, besides its contribution to important biological functions such as fluid transport within individual tubular organs [4, 5] or signaling throughout complex biological structures [6], fulfills its central role in gastric mixing and digestion [7,8,9] by operating thanks to a geometric phase in the stomach

Summary

Introduction

How may fluid be mixed at low Reynolds number? Such mixing is normally performed with a stirrer, a rotating device within the container that produces a complex, chaotic flow. At the lowest Reynolds numbers, under what is known as creeping flow conditions, fluid inertia is negligible, fluid flow is reversible, and an inversion of the movement of the stirrer or the walls leads—up to perturbations owing to particle diffusion—to unmixing, as Taylor [1] and Heller [2] demonstrated. This would seem to preclude the use of reciprocating motion to stir fluid at low Reynolds numbers; it would appear to lead to perpetual cycles of mixing and unmixing. In the stomach food and drink are mixed to form a homogeneous fluid termed chyme, which is digested

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Conclusion