Theory of vaporization of a rigid spherical droplet in slowly varying rectilinear flow at low Reynolds numbers

Abstract

The vaporization of a droplet in rectilinear motion relative to a stagnant gaseous atmosphere is addressed for the limit of low Reynolds numbers and slow variation of the droplet velocity. Approximations are introduced that enable a formal asymptotic analysis to be performed with a minimum of complexity. It is shown that, under the conditions addressed, there is an inner region in the vicinity of the droplet within which the flow is nearly quasi-steady except during short periods of time when the acceleration changes abruptly, and there is a fully time-dependent outer region in which departures of velocities and temperatures from those of the ambient medium are small. Matched asymptotic expansions, followed by a Green's function analysis of the outer region enable expressions to be obtained for the velocity and temperature fields and for the droplet drag and vaporization rate. The results are applied to problems in which the droplet experiences constant acceleration, constant deceleration and oscillatory motion. The results, which identify dependences on the Prandtl number and the transfer number, are intended to be compared with experimental measurements on droplet behaviours in time-varying flows.