Dynamics of evaporating drops. Part II: free oscillations

Free oscillations of evaporating drops are investigated using a combination of numerical and theoretical analyses. The investigation is based on an evaporation model that expresses the mass flux as a function of the surface curvature and is valid for surface amplitudes up to 10% of the drop radius. The results show that, the period of oscillation is decreased by evaporation, however, the dominant mode of oscillation remains the same as that for a non-evaporating drop. For low evaporation rates, it is shown that the recoil force is responsible for modifications in the period. At high evaporation rates, the period of oscillation also varies significantly in time, due to the decrease of the drop size. The theoretical analysis is mainly concerned with infinitesimal-amplitude oscillations via invoking simplifying assumptions which are supported by numerical results. Closed-form expressions are derived for the period and the kinetic energy of the drop. The predictions of the theory are compared with the results of the numerical simulations and excellent agreements are observed. The effect of oscillations on the rate of evaporation is also investigated, and it is shown that the rate of evaporation decreases for an oscillating drop as compared to a deformed but non-oscillating drop.