Oscillations of an Inviscid Encapsulated Drop

The problem relating to the small-amplitude free capillary oscillations of an encapsulated spherical drop is solved theoretically in the framework of asymptotic methods.Liquids are supposed to be inviscid and immiscible.The formulas derived are presented for different parameters of the inner and outer liquids,including densities,thickness of the outer liquid layer,and the surface and interfacial tension coefficients.The frequencies of oscillation of the encapsulated drop are studied in relation to several“modes”which can effectively be determined in experiments by photo and video analysis.The results are presented in terms of oscillation frequencies reported as a function of the mode number,the spherical layer thickness and the relation between the(surface and interfacial)tension coefficients.It is revealed that the influence of the liquids’parameters(and related variations)on the drop oscillation changes dramatically depending on whether oscillations are“in-phase”or“out-of-phase”.Frequencies for“in-phase”type oscillations can be correlated with linear functions of the shell thickness and the relative values of interfacial tension coefficient whereas the analogous dependencies for the“out-of-phase”type oscillation are essentially non-linear.