Stokes flow around two unequal cylinders: A complex variable approach

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.