Analytical theory of thickness acoustic resonances in liquid drop on solid substrate

The analytical theory of thickness acoustic resonances in a liquid droplet lying on a solid substrate is developed in linear approximation using the following three approaches. The droplet is considered as analog of (i) laser resonator, (ii) plano-convex piezoelectric resonator, (iii) hemi-spheroidal cavity. All three methods in use give the same resonance frequencies and the same eigenmodes for thin drops. The effect of nonlinearity is studied using the perturbation theory based on the complex reciprocity relation (Auld, 1973). The account of nonlinearity shows that the drop on the substrate can behave like a self-controlled acoustic analog of laser resonator in which the vibrations are able to move the upper reflective mirror and to change its shape.