Contact line moving over a sinking sphere

Spreading dynamics of a contact line over a sinking sphere with a constant speed into a liquid reservoir are studied both experimentally and theoretically. A high-speed camera system with X-ray illumination is employed to accurately characterize contact line motions. Over a range of Reynolds number from 30 to 1000, the spreading speed of the contact line is linearly dependent on the sinking speed of the sphere. A simple scaling equation from the force balance between the drag-induced pressure and inertia agrees with the experimental results. In addition, the numerical solution of Navier-Stokes equation, showing pressure distribution and streamline near the sinking sphere, validates our scaling equation.