Effect of internal and external resistances on the swelling of droplets

Abstract

AbstractThe 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 < < 1.0; 10−5 < X < 500; and 0.01 < Bi < ∞ to determine when the more easily applied analytical approximations are valid, and to determine the critical Bi for which internal diffusion resistance or external convective resistance can be ignored. In these limits the simpler low Bi or infinite Bi models can be applied, respectively, in place of the finite Bi model. The results show that the analytical approximations are valid for ≤ 0.05. Furthermore, the infinite Bi numerical solution is accurate for Bi > 100, whereas the low Bi solution is valid for Bi < 1. © 2005 American Institute of Chemical Engineers AIChE J, 51: 379–391, 2005