Numerical and theoretical study of natural oscillations of supported drops with free and pinned contact lines.

The oscillation of drops supported by solid surfaces is important to a wide variety of applications, such as dropwise condensation. Identification of the natural frequencies of supported drops of different sizes and liquids on different material surfaces is essential to developing techniques to enhance drop shedding using acoustics or surface vibration. This dissertation presents a systematic investigation of the effect the contact angle, the gravitational Bond number, the contact line mobility, and the perturbation force angle on the natural frequencies of the drop through parametric direct numerical simulation. The open-source multiphase flow solver, Basilisk, has been used for both 2D-axisymmetric and full 3D simulation. The geometric volume-of-fluid method has been used to capture the drop surface. Two asymptotic limits of contact line mobility, the free and pinned contact lines are considered. The results show that the for all the oscillation modes, the frequency scales with the capillary frequency. For the axisymmetric longitudinal modes, normalized frequency decreases with the contact angle, increases with the gravitational Bond number, and increases when the contact line changes from the free to pinned conditions. For the lateral oscillation mode, the variation trends of the oscillation frequency with the contact angle and contact line mobility remain the same, but the frequency slightly decreases with the Bond number. The simulation results match with inviscid theory remarkably well and also agree well with the experimental data on different material surfaces. An inviscid theoretical model is also established. The model yields expressions for the frequency as a function of the contact angle and the Bond number, with all parameters involved fully determined by the equilibrium drop theory and the simulation. The model predictions are compared with the simulation results and excellent agreement is achieved.