Microscale Flow Dynamics of Ribbons and Sheets

TL;DR

This paper introduces a regularised stokeslet method for simulating the hydrodynamics of thin ribbons and sheets, bridging the gap between asymptotic and boundary element methods, and validated through analytical, experimental, and computational examples.

Contribution

The paper develops a novel regularised stokeslet approach for ribbons and sheets, overcoming limitations of existing theories and methods in microscale flow simulations.

Findings

Validated against analytical solutions for plate ellipsoids

Successfully modeled ribbon helices and a microswimmer

Demonstrated flow calculations around a double helix and a microscale 'magic carpet'

Abstract

Numerical study of the hydrodynamics of thin sheets and ribbons presents difficulties associated with resolving multiple length scales. To circumvent these difficulties, asymptotic methods have been developed to describe the dynamics of slender fibres and ribbons. However, such theories entail restrictions on the shapes that can be studied, and often break down in regions where standard boundary element methods are still impractical. In this paper we develop a regularised stokeslet method for ribbons and sheets in order to bridge the gap between asymptotic and boundary element methods. The method is validated against the analytical solution for plate ellipsoids, as well as the dynamics of ribbon helices and an experimental microswimmer. We then demonstrate the versatility of this method by calculating the flow around a double helix, and the swimming dynamics of a microscale "magic carpet".