Direct numerical simulation of an oscillating droplet in partial contact with a substrate

• Small oscillations of a drop in partial contact with a flat substrate are studied.
• Computational results agree well with the theory for large contact angles.
• The results deviate significantly from the theory for small contact angles.
• Effects of drop size, drop density and surface tension are also examined.

Small-amplitude oscillations of a viscous drop that is in a partial contact with a flat substrate are investigated computationally using a finite-difference/front-tracking method. Emphasis is placed on the first mode resonance frequency response of the droplet for a wide range of contact angles. It is found that numerical results converge to the theoretical predictions of Strani and Sabetta (Strani M, Sabetta F. J Fluid Mech 1984;141:223–47) for high contact angles, whereas considerable discrepancy is observed as contact angle decreases. However, the dependence of the frequency on the drop radius, drop density and surface tension coefficient remains the same as predicted by the Strani and Sabetta theory. It is also found that the effects of density and viscosity ratio become insignificant for the density and viscosity ratios larger than 10. The oscillations are found to be damped exponentially in time due to viscous dissipation similar to the case of an isolated droplet and the damping rate decreases with increasing contact angle.