A discrete multicomponent temperature-dependent model for the evaporation of spherical droplets

Abstract

A spherically-symmetric model with temperature-dependent properties has been developed to describe the evaporation of droplets of multicomponent liquids that is suitable for use in large-scale simulations of multiphase droplet-laden flows. In this model, the coupled partial differential equations describing heat transfer and mass diffusion within the liquid droplet are approximated by ordinary differential equations. The temperature and concentration profiles within the droplet are described by an algebraic model which accounts for departures from quasi-steady behavior caused by the coupled transient effects of mass diffusion and thermal diffusion. The interfacial conditions and an auxiliary thermodynamic relationship describing phase equilibrium are solved at each instant as a system of nonlinear algebraic equations, which is coupled to the ordinary differential equations describing heat and mass transfer within the droplet. The evaporation of a droplet comprising n discrete components can then be calculated by solving n+1 ordinary differential equations and, at each time step, 3n+1 algebraic equations. The results of this model appear to be in very good agreement with partial differential equation solutions for small, low-Lewis-number, two-component droplet evaporation driven by modest temperature differences, and can be computed several hundred times faster.