Coupled two-phase model of a gas microbubble containing suspended light absorbing nonoparticles

A mathematical model of a micrometer size gas bubble containing nanometer size light absorbing nanoparticles is presented. A description of such a system can be obtained in terms of a two-coupled phase model with the solid particles in suspension in a fluid phase, i.e. the gas. It is assumed that the suspension is diluted so that particle-particle interaction can be ignored. Because the heat exchange between the nanoparticles and the gas is of main interest in this calculation, it is assumed in first approximation that the gas and the particles have the same velocity and pressure. The pressure is assumed to be function of time only. In this case, only the equations of continuity and energy for both the particulate phase and the gas phase. The two-coupled model is then solved in linear approximation and a system of four differential equations with constant coefficients is obtained. The system is diagonalized and the general solution of the two coupled system is obtained. The general solution is a combination of exponential decaying oscillatory functions for the temperature of the two phases, the pressure and the microbubble radial oscillations. It was found that the oscillatory behavior takes place in the MHz range.