The motion of two cylinders in contact in channel flow

The motion of a doublet consisting of two rigidly connected circular cylinders freely suspended in an incompressible Newtonian fluid in a narrow channel bounded by two parallel planes is studied numerically at zero Reynolds number. The Stokes equations are solved by a finite element method for various positions and orientations of the particle, and the trajectories of the particle are determined for a number of initial configurations. A doublet of equal-sized cylinders is found either to tumble or oscillate in rotation, while a doublet of unequal-sized cylinders possesses a stable, steady equilibrium configuration, at which the particle is located close to the channel centerline with a constant angle of inclination. Thus, doublets of unequal diameters tumble, oscillate in rotation or approach the equilibrium configuration asymptotically, depending on the radius ratio of cylinders, particle size-channel width ratio and initial conditions.