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

TL;DR

This paper demonstrates how cyclical boundary movements, like stomach peristalsis, can induce geometric phases to effectively mix fluids at low Reynolds numbers, offering insights into biological and technological mixing processes.

Contribution

It introduces the concept of geometric mixing via boundary deformation and applies it to biological stomach mixing, highlighting a novel mechanism for low Reynolds number fluid mixing.

Findings

Geometric phase enables mixing with cyclical boundary motions.

Simulations show stomach peristalsis effectively mixes fluids.

Boundary deformation can be a general tool for low Reynolds number mixing.

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.