Numerical simulations of gas microbubble dynamics in an acoustic field with the influence of rectified diffusion

A numerical method for simulation of the diffusion problem for a single gas bubble oscillating in unbounded weakly compressible liquid in an acoustic field is developed. The method enables computation of nonlinear dynamics of bubbles of variable mass. The total mass of the dissolved gas and the gas in the bubble is conserved by enforcing conservation in the discrete scheme. For this purpose a conservative scheme based on an integro-interpolative method is applied for computation of the diffusion flux. Generally, a study of the effect of rectified diffusion on bubble dynamics requires significant computational time. To reduce it, an approximation based on the assumption on quasistationary character of oscillations of the dissolved gas concentration is developed. This enables investigation of rectified diffusion during millions of periods of oscillations. The numerical results obtained by the proposed method are in good agreement with the available experimental data. Comparison of the bubble mass change using the presented scheme and the standard scheme, which does not conserve the total mass of the gas-liquid system, reveals that in the latter case the numerical error may accumulate and lead to physically incorrect results.