Mathematical Modeling of Binary Nano Scale Diffusion of Molecular Gas Suspensions in Liquid Media

Abstract

A model describing the suspension diffusion process of gas molecules in liquid media is presented in this paper. This process is not yet solved by a satisfactory model for micro-scale applications at this time. The new model allows the simulation of diffusion processes in continuous media considering the molecular mass flux in a suspension/carrier phase mixture. Modelling the diffusion of gas suspensions in liquid media the saturation mass ratio is reached near the liquid/gas surface very quickly. The increase of gas concentration in the liquid domain depends on the elapsed time and the physical properties of gas and liquid media. The molecular gas velocity is described by a Maxwell probability density function. Based on this spectral method macroscopic physical values are modelled to describe time-dependent global concentration changes. Modelling the gas species diffusion the molecular convection is considered. Modelling the mass flux of the molecular gas suspension characteristic time scales are developed describing the completion level of the saturation progress based on non-dimensional formulations of the molecular convection equation. The present model is implemented in a CFD code and validated by a family of parametric simulation results depending on the saturation mass ratio of the suspended gas phase. This simulation result array shows the dependency of saturation time and saturation mass ratio of the suspended gas molecules. Based on this relation macroscopic diffusion processes in micromixers and microchannels are described with this model and without an extra solution of molecule trajectories or spectral fields of molecule velocity.