Compressible slow viscous flow past a vaporizing droplet.

Abstract

A small rigid spherical droplet is taken to undergo quasi-steady adiabatic vaporization. The droplet, near its boiling temperature, lies in an unbounded expanse of hot ideal gas, which flows slowly past the droplet. Whenever even a slight ambient gaseous flow exists relative to the droplet (that is, for small but finite Reynolds number based on freestream conditions), piecewise-valid asymptotic expansions must be adopted to restore the convective transport to proper importance far from the body. Incipient forced convection thus represents a singular perturbation to the classical limit of sphericosymme tric, diffusion-dominated vaporization. Inner-and-outer (matched asymptotic) expansions here yield the solution in general and two gross flow properties in particular: the modifications to both the Stokes drag and also the Maxwell-Stefan vaporization rate (Sherwood number) owing to ablationlike mass transfer, fluid compressibility, and variability of fluid properties. The dependence of the solution on all problem parameters is studied within the restrictions that the Mach number is taken as vanishingly small, and the Schmidt and Lewis numbers are constant and of order unity.