Свободные колебания капли, погруженной в вязкую безграничную жидкость

Abstract

The problem on free oscillations of liquid drop immersed in another liquid filling the whole space is solved analytically. It is assumed that both of liquids are viscous, inert, incompressible and mutually saturated; the shape of drop is slightly deviates from spherical; the amplitude of oscillations is much less than the wavelength. The exact solution of hydrodynamic equations in Stokes approximation is obtained with boundary conditions on the deformable surface of the drop. For the largescale mode decrement, oscillations frequencies, and critical parameters at which an aperiodic mode of motion occurs are determined. It is shown that with an increase in viscosity and density of the drop, the aperiodic mode occurs at lower values of the dimensionless surface tension coefficient.