Modeling Internal Flow Patterns of Sessile Droplets on Horizontally Vibrating Substrates

A three-dimensional Navier-Stokes and continuity equation model is employed to numerically predict the resonant modes of sessile droplets on horizontally vibrating substrates. A dynamic contact angle model is implemented to simulate the contact angle variations during vibrations. The four resonant modes (n = 1, 2, 3 and 4) of a droplet under horizontal vibrations are investigated. Simulations are compared to experimental results for validation. Excellent agreement is observed between predicted results and experiments. The model is used to simulate the internal flow patterns within the droplet under resonant modes. It is found that the flow in all four resonant modes can be divided into the Stokes region, the gas-liquid interface region, and the transition region located in between. Numerical simulations show that the average velocity within the droplet increases with the increase in frequency, while the fluctuations in average velocity after reaching the steady state show different trends with the increase in frequency. It is also found that with an increase in the order of resonant modes, the contact angle difference between the two sides of the droplet increases, and the contact angle difference of the droplet is maximized when the applied frequency is the resonant frequency of the specified mode.