Mathematical Modeling of the Wave Dynamics of an Encapsulated Perfluorocarbon Droplet in a Viscoelastic Liquid

Abstract

A mathematical model has been developed and a numerical study of vapor bubble growth as a result of acoustic evaporation of an encapsulated perfluorocarbon droplet in a viscoelastic liquid is presented. The viscoelasticity of the droplet shell and the carrier liquid is taken into account according to the Kelvin–Voigt rheological model. The problem is reduced to solving a system of ordinary differential equations for the radius and temperature of the bubble, the radius of the droplet and the shell together with the thermal conductivity equation for the internal liquid. Spatial discretization of the thermal conductivity equation is carried out using an implicit finite difference scheme. ODEs are solved by the fifth order Runge–Kutta method with an adaptive computational step. To check the correctness of the numerical calculation in a particular case, the theory has been compared with known experimental data. The influence of the shear modulus of the shell and the carrier liquid, and the shell thickness on the radial dynamics of a vapor bubble inside an encapsulated droplet in an external viscoelastic liquid is demonstrated.