Capillary Torque on a Rolling Particle in the Presence of a Thin Liquid Film

A spherical particle rolling on a flat surface in the presence of a thin liquid film experiences a capillary torque that resists the rolling motion. A theory is presented for small values of the capillary number, in which the capillary torque is shown to be caused by two complementary mechanisms. The first mechanism results from the rearward shift of the liquid bridge in the presence of particle rolling, which causes the line of action of the low pressure region within the liquid bridge to shift behind the particle centroid. The second mechanism results from the contact angle asymmetry on the surface tension forces on the advancing and receding sides of the rolling particle. An experiment is described in which we measure the different parameters appearing in the expressions for both types of capillary torque. Using this experimental data, we show that the capillary torque varies with capillary number in accordance with a power law. When combined with a standard expression for viscous torque on a rolling particle, the capillary torque expressions are found to yield predictions for particle terminal velocity that are in good agreement with experimental data for a particle rolling down an inclined surface.