Effect of internal and external resistances on the swelling of droplets

The diffusion equation is solved, subject to a quasi-steady approximation, to determine the swelling rate of a spherical drop in an infinite medium. External convective mass transfer to the growing drop surface is accounted for as a boundary condition. Three cases are considered: the general case of finite Biot number (Bi), and the limiting cases of infinite Bi (negligible external convective resistance), and low Bi (negligible internal diffusion resistance). Analytical approximations and numerical solutions are developed and detailed results are presented. The dimensionless swelling rate is governed by a dimensionless mass driving force (), a dimensionless time (X), and the Biot number. The various models are compared over the range 0.001 100, whereas the low Bi solution is valid for Bi < 1. © 2005 American Institute of Chemical Engineers AIChE J, 51: 379–391, 2005