Capillary Torque on a Particle Rotating at an Interface.

Small particles attach to liquid-fluid interfaces due to capillary forces. The influence of rotation on the capillary force is largely unexplored, despite being relevant whenever particles roll at a liquid-fluid interface or on a moist solid. Here, we demonstrate that due to contact angle hysteresis, a particle needs to overcome a resistive capillary torque to rotate at an interface. We derive a general model for the capillary torque on a spherical particle. The capillary torque is given by M = γRLk(cos ΘR - cos ΘA), where γ is the interfacial tension, R is the radius of the particle, L is the diameter of the contact line, k = 24/π3 is a geometrical constant, and ΘR and ΘA are the receding and advancing contact angles, respectively. The expression for the capillary torque (normalized by the radius of the particle) is equivalent to the expression for the friction force that a drop experiences when moving on a flat surface. Our theory predicts that capillary torque reduces the mobility of wet granular matter and prevents small (nano/micro) particles from rotating when they are in Brownian motion at an interface.