Modeling of microbubble dissolution in aqueous medium

Abstract

A mathematical model for microbubble dissolution in an aqueous medium containing dissolved gases is presented. None of the models available in the literature take into account the influence of shell elasticity (Es), variation in surface tension (σ) at the gas–liquid interface and shell resistance (Ω) on the kinetics of microbubble dissolution. Moreover, values of these shell parameters are not known/available and hence arbitrary values for these variables have been assumed in many of the reports for estimation of dissolution kinetics. Therefore, in this work, a mathematical model is developed to describe microbubble dissolution which takes into account the effect of shell elasticity (Es), shell resistance (Ω), surface tension (σ) and their variation, on the microbubble dissolution. The values of these shell parameters have then been estimated using the proposed model and the experimental data available in literature. The proposed model accurately predicts the experimental microbubble dissolution data using estimated values of shell parameters. Analysis of the results further show that the surface tension and shell resistances change drastically during the microbubble dissolution process and the variation in these parameters during the dissolution process is highly dependent on the shell elasticity which in turn affects the microbubble dissolution times. The methodology developed in this work can be used to estimate shell parameters for any microbubble formulation, to accurately predict in-vitro/in-vivo dissolution of microbubbles, and hence to design a microbubble system with desired characteristics and performance.