An exact solution of the mass transport equations for spheroidal evaporating drops

Mathematical modelling of heating and evaporation of a spheroidal droplet

“…At the same time the shapes of most actually observed droplets in engineering and environmental applications are far from spherical [2,3]. The effects of droplet deformation are generally investigated assuming that the droplet shapes can be approximated as prolate or oblate spheroids [4].…”

“…One of the main limitations of that paper is that both mass and heat transfer equations were presented in the form of the Laplace equations, which implies that the effects of the Stefan flow from the surface of the particles were ignored. The latter effects were taken into account in the exact solutions to the mass and heat transfer equations in the gas phase around a spheroidal droplet in the model suggested in [4]. In that paper it was assumed that the temperatures at all points on the surface of the droplet are identical and constant, and that the droplet's shape remains the same.…”

“…In that paper it was assumed that the temperatures at all points on the surface of the droplet are identical and constant, and that the droplet's shape remains the same. A combined problem of spheroidal droplet heating and evaporation, similar to the one studied in [4], was considered in [15]. As in [4], the authors of [15] based their analysis on the solution to the species conservation equation in the gas phase and assumed that the thermal conductivity of droplets is infinitely large.…”

“…A combined problem of spheroidal droplet heating and evaporation, similar to the one studied in [4], was considered in [15]. As in [4], the authors of [15] based their analysis on the solution to the species conservation equation in the gas phase and assumed that the thermal conductivity of droplets is infinitely large. In contrast to [4], the authors of [15] took into account the relative velocities of droplets, assuming that the dependence of the Nusselt and Sherwood numbers on the Reynolds and Prandtl numbers is the same as for spherical droplets.…”

Modelling of spheroidal drop evaporation with non-uniform temperature conditions

“…Numerical investigations on oscillating drops [4,5] have shown that the vapour and heat fluxes on the drop surface are not uniform and they were empirically correlated to the local mean curvature of the surface [1,6]. Analytical modelling of the heating and evaporation of spheroidal drops have shown that the local vapour and heat flux scale with the fourth root of the Gaussian curvature [7,8] and later the same result was extended to a wider class of drop shapes [9]. When dynamical simulation of droplet heating and evaporation is necessary, uniform drop temperature is often assumed, on the basis of a commonly accepted belief that the internal recirculation would maintain uniform conditions.…”