Wave dynamics of perfluorocarbon droplets in a viscoelastic liquid

The authors have developed a mathematical model and present a numerical study of the growth of a vapor bubble as a result of acoustic evaporation of a spherical perfluorocarbon droplet in a viscoelastic liquid. The Kelvin–Voigt, Maxwell, Zener, and Oldroyd linear rheological models are considered. The problem reduces to solving a system of ordinary differential equations for the radius and temperature of the bubble, the radius of the droplet, and normal stresses at the droplet boundary, together with the heat conduction equations for the internal and external liquid. Spatial discretization of the equations is done with an implicit finite difference scheme. Ordinary differential equations 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 theoretical results are compared with known experimental data. The influence of the shear modulus, relaxation time of the elastic carrier phase, and differences in rheological models on the radial dynamics of a vapor bubble inside a droplet in an external viscoelastic liquid is demonstrated.