The characteristic equation of an oscillating viscoelastic drop

A study of axisymmetric shape oscillations of a viscoelastic drop in a vacuum using the method of weakly nonlinear analysis is conducted. The work is carried out due to the relevance of the analysis for transport processes across the drop surface and due to fundamental interest. The Oldroyd-B model is used for the characterization of the rheological liquid behaviour. The method applied yields a set of governing equations, boundary and initial conditions for different orders of approximation. In the present paper, the first-order equations and solutions with the characteristic equation for the viscoelastic drop are presented. The characteristic equation yields an infinite number of roots [5], which determine the time dependency in the higher-order solutions. The number of selected roots defines the number of initial conditions needed for the corresponding order of approximation. The solutions of the characteristic equation are selected according to experiments conducted on an acoustically levitated drop. Experimental data are obtained by measuring damping factor and oscillation frequency based on free damped shape oscillations of viscoelastic aqueous polymer solution drops.