Stokes flow around two unequal cylinders: A complex variable approach

TL;DR

This paper develops a complex variable method to analytically solve Stokes flow around two unequal cylinders, generalizing previous solutions and analyzing contact effects on flow separation points.

Contribution

It introduces a complex analysis approach for arbitrary-sized, separated cylinders, extending known solutions for equal cylinders and wall proximity.

Findings

Solutions for flow around unequal cylinders are derived.

Contact between cylinders alters flow separation points.

Flow behavior near contact points is characterized.

Abstract

We solve the Stokes equations for the flow around two parallel translating and rotating cylinders using tools from complex analysis and conformal mapping. By considering cylinders of arbitrary size and separation, we generalise the solutions known for cylinders of equal size, and a cylinder near a plane wall. We then examine the limit when the cylinders are brought into contact, finding that it affects the separation points in the flow. Namely, they move to, and are hidden in, the point of contact between the cylinders.