Decompositional burning of a droplet in a small Peclet number flow.

Abstract

Asymptotic results for chemical-reaction and forced-convection effects on the quasi-steady adiabatic vaporization of a rigid uniform spherical droplet immersed in an unbounded expanse of gas are obtained by inner-and-outer expansions. The zeroth-order approximation is the radially symmetric solution yielding the classical logarithmic mass transfer rate. The perturbation introduces the corrections arising from 1) first-order decompositional burning for reaction rates small relative to flow rates (small first Damkohler similarity parameter); and 2) the possible wake-generating role of a slight relative flow past the droplet (small Peclet number). For tractable closed-form solution the flow is taken as incompressible with constant properties; the Lewis number is restricted to unity in the perturbational analysis. The first perturbation to the Sherwood number (normalized mass transfer rate) is found to be independent of Schmidt number, but dependent on the reaction rate. The first modification to the Stokes drag (owing to mass transfer) is found to be independent of the reaction rate, but dependent on the Schmidt number. For indefinitely large Schmidt number the Stokes drag is always increased because of mass transfer, and streamlines display no wake; for orderunity Schmidt number entirely different results are anticipated.