Mass transition and mass diffusion coefficients in a diffuse interface model

The purpose of this paper is to determine the mass transition and mass diffusion coefficients in the diffuse interface model. By means of the thermodynamic probabilities of molecules transiting (phase change) and shifting (diffusing), the rate of mass transition and the mass diffusion flux are derived first. By comparing them with the corresponding formulas in the diffuse interface model, the two coefficients are then obtained. The mass transition coefficient is proportional to the rate of molecular unidirectional transition under the mutual equilibrium of liquid and vapor species. The mass diffusion coefficient is proportional to the rate of molecular unidirectional travel through a unit surface under the condition that two local elements at two sides of the surface are in mutual equilibrium. This diffusion coefficient can finally be expressed as the product of the Fick concentration diffusion coefficient and the mixing density besides an energy (or temperature) factor. The Fick coefficient obtained at present is reduced to the self-diffusion coefficient at the gas boundary of the binary mixing layer and becomes the Fick diffusion coefficient of gas in pure liquid at the liquid boundary. The present coefficients (including Fick coefficient) are different from the existing ones in the literature.