General Solution of Drop Evaporation Modelling in Non-Viscous Steady-State Gaseous Environment

The problem of steady-state mass transport from a spherical mono-component droplet immersed in gaseous environment is addressed to find a solution for the expected vaporisation rate under general ambient conditions. The continuity, momentum and energy equations are written on a radial coordinate system. The effect of thermal gradient in the vapour phase is taken into account, while the viscous and dissipation terms in the momentum and energy equations are neglected. The model yields a non-linear second order ODE that is numerically and analytically solved to calculate the steady-state vaporisation rate. The description in terms of non-dimensional variables introduces some new parameters that are expected to influence the vaporisation rate. The model is then compared to the existing simplified Maxwell equation and the well-known Stefan-Fuchs model. Quantitative comparisons are presented and discussed and an application to water droplets floating in hot gas environment, under the operating conditions typical of fire protection spray scenarios, is presented.