Motion of a small bubble in forced vibrating sessile drop

In this letter, the motion of small gas bubbles within sessile water drops on a vibrating substrate is investigated numerically using a two-phase diffuse interface method. Depending on the amplitude of the plate vibration, the motion of the gas bubbles falls into three distinct regimes: oscillating within the drop, sticking to the substrate, or escaping from the drop. In particular, the motion of oscillating bubbles follows a harmonic function, and is found to be closely related to a combined effect of the deformation of the sessile drop and the vibration of the plate. To interpret the underlying mechanism, we analyze the dominant forces acting on the bubbles in the non-inertial framework fixed to the plate, and take account of the periodic deformation of the drop, which effectively induces flow acceleration inside the drop. As a result, we establish a theoretical model to predict the bubble motion, and correlate the amplitude and phase difference of the bubble with the Bond and Strouhal numbers. The theoretical prediction agrees with our numerical results. These findings and theoretical analysis provide new insights into controlling bubble motion in sessile drops.