Slip-induced dynamics of patterned and Janus-like spheres in laminar flows

Calculations of force and torque on a sphere with inhomogeneous slip boundary conditions are presented. A theoretical approach introduced previously is employed to explicitly explore two types of azimuthally symmetric boundary-condition patterning of high practical importance. The first is a discontinuous binary surface while the second involves continuously varying slip patterned in stripes, with arbitrary periodicity. These geometries mimic anisotropic spheres, as well as superhydrophobic surfaces applied to a sphere. The dynamics apply for unbounded uniform flow and pure rotational flow of a Newtonian fluid at low Reynolds number. In unbounded uniform flow, torque is maximized for an ideal Janus sphere with a discontinuous equatorial transition between regions of slip and no slip.