Diffusion Through a Membrane from a Sessile Droplet-Limiting Case of the LargeDroplet Approximation for Short Times

摘要

We review briefly the singular perturbation problem arising in the approximatesolution of diffusion from a large, neat, sessile agent droplet through a thin membrane. We obtain the zeroth order short time solution(which has a definite thickness scaling) but this solution is only valid for short times. The agent droplet can be neat or polymer thickened. The numerical solutions make clear both qualitatively and quantitatively (for suitably chosen parameters) the overall expected behavior and the results are in overall agreement with observations. While for the polymer thickened agent droplet problem there is a more extensive region of scaling with regard to initial droplet radius, R, and membrane thickness, L, this is not the case for the neat droplet. Specifically we showed that simple scaling relations apply only for a rather limited parameter ranges: (a) The more ubiquitous (under field conditions) case where the agent is deposited as an aerosol of tiny droplets which spread on the membrane, for the small droplet case.