The role of liquid mixing in evaporation of complex multi-component mixtures: Modelling using continuous thermodynamics.

Abstract

"Continuous thermodynamics" is a technique for modelling mixtures with large numbers of components which uses a probability density function rather than discrete components to represent the mixture composition. It has proved to be a practical and useful technique for modelling mixtures with dozens or even hundreds of components. An unresolved issue in the use of these models so far has been the role of mixing in the liquid phase, all the previous work having assumed a well-mixed droplet. With two- or three-component mixtures it is known that there are significant differences between the two extremes of well-mixed and diffusion limited droplets, the latter referring to mixing which occurs by molecular diffusion only. This paper presents a numerical solution for diffusion within a droplet of multi-component mixture modelled using continuous thermodynamics. Transport equations for the mean and variance of the fuel composition distribution function in the droplet are derived. The molecular diffusivity of the liquid mixture is calculated using a continuous thermodynamics extension of the well-known Wilke-Chang diffusivity correlation. The effects of enhanced mixing caused by internal circulation are modelled by increasing the effective diffusivity of the liquid. Vapour and liquid phase solutions are coupled at the liquid surface by matching the fluxes of the distribution moments. The results are compared to other models, including a continuous mixture version of the quasi-steady liquid phase model of Law and Law (1981). Conclusions for practical spray modelling are drawn.