Flow induced by the rotation of two circular cylinders in a viscous fluid

Stokes flow driven by rotation of two parallel cylinders inside a cylinder of large radius R₀ is investigated, and the flow in this triply-connected domain is determined numerically, with particular focus on the narrow-gap situation, when the local behavior is well described by lubrication theory. The asymptotic situation for infinite R₀ is inferred (i) when the cylinder axes are unconstrained, and (ii) when they are held fixed. Contributions to the far-field are identified: a torquelet and a radial quadrupole in the counter- and co-rotating cases, respectively. In the former case, when the cylinders make contact (zero gap) a contact force acting on the cylinder pair is identified.