Dynamics of liquid films exposed to high-frequency surface vibration

We derive a generalized equation that governs the spreading of liquid films under high-frequency (MHz-order) substrate vibration in the form of propagating surface waves and show that this single relationship is universally sufficient to collectively describe the rich and diverse dynamic phenomena recently observed for the transport of oil films under such substrate excitation, in particular, Rayleigh surface acoustic waves. In contrast to low-frequency (Hz- to kHz-order) vibration-induced wetting phenomena, film spreading at such high frequencies arises from convective drift generated by the viscous periodic flow localized in a region characterized by the viscous penetration depth β(-1)≡(2μ/ρω)(1/2) adjacent to the substrate that is invoked directly by its vibration; μ and ρ are the viscosity and the density of the liquid, respectively, and ω is the excitation frequency. This convective drift is responsible for driving the spreading of thin films of thickness h≪k(l)(-1), which spread self-similarly as t(1/4) along the direction of the drift corresponding to the propagation direction of the surface wave, k(l) being the wave number of the compressional acoustic wave that forms in the liquid due to leakage of the surface wave energy from the substrate into the liquid and t the time. Films of greater thicknesses h∼k(l)(-1)≫β(-1), in contrast, are observed to spread with constant velocity but in a direction that opposes the drift and surface wave propagation due to the attenuation of the acoustic wave in the liquid. The universal equation derived allows for the collective prediction of the spreading of these thin and thick films in opposing directions.