Edge effects with liquid droplets deposited on acoustic resonators: Consequences of vortex flow

For small droplets deposited on the surface of an acoustic thickness shear resonator, the shear motion of the substrate induces vortex flow close the three-phase line. There is a rather strong peak of stress right at the line of contact and a more extended region (comparable in size to the penetration depth) where the surface stress is lower than average. Altogether, the vortices lower the integral tangential force, thereby lowering the shifts of frequency and bandwidth. When the droplet size is comparable to the decay depth of the shear wave, the influence of the surface mode onto the frequency shift is sizeable. This results applies to all heterogeneous liquid samples with a lateral scale of heterogeneity comparable to the penetration depth.