Tubular-body theory for viscous flows

TL;DR

This paper introduces an exact slender-body-like theory for viscous flows around cable-like structures, providing a more versatile and extendable approach than traditional asymptotic methods.

Contribution

It develops a new, exact theoretical framework for calculating surface traction on cable-like bodies in viscous flow, overcoming limitations of existing asymptotic theories.

Findings

Provides a series solution to a Fredholm integral equation

Enables straightforward generalization to other systems

Improves accuracy over leading-order asymptotic theories

Abstract

Cable-like bodies play a key role in many interdisciplinary systems but are hard to simulate. Asymptotic theories, called slender-body theories, are effective but apply in specific regimes and can be hard to extend beyond leading order. In this letter we develop an exact slender-body-like theory for the surface traction of cable-like bodies in viscous flow. This theory expresses the traction as a series of solutions to a well-behaved one-dimensional Fredholm integral equation of the second kind. This process can be simply generalised to other systems.