Some Features of Capillary Wave Energy Conversion on Liquid Surface in the Presence of Dynamic Surface Tension

The effect of dynamic surface tension on capillary oscillations of a droplet is studied in the theoretical asymptotic calculations of the first order of smallness with respect to the dimensionless amplitude of oscillations of charged droplets of a polar liquid. The calculations are carried out within the framework of a model of an ideal incompressible electrically conducting liquid. It has been shown that allowance for the effect of dynamic surface tension increases the order of the dispersion equation, which acquires one more damping root relevant to the destruction of the near-surface electrical double layer (disordering of molecules in the near-surface layer). What is interesting about the revealed damping is that it takes place in an ideal liquid, while the characteristic damping time coincides with that measured experimentally. Free energy transformations occur between mechanical, thermal, electromagnetic, and mechanical again forms of energy, with all of the transformations being caused by the effect of the dynamic surface tension. It has been shown that the dynamic surface tension has a weak effect on the low-frequency oscillations of the droplets, while it essentially affects the high-frequency oscillations causing their rapid damping.