Mathematical modeling of gel drying with supercritical carbon dioxide

Abstract

The most complex step in the production of aerogels is the supercritical drying step, and it is therefore important to study its dynamics using mathematical models. Alumina/silica aerogel was obtained using a one step sol-gel synthesis and subsequent drying with supercritical carbon dioxide. The wet gel weight change with time was monitored. The dry aerogel sample porous structure was determined using the BET method and nitrogen adsorption/desorption. Supercritical drying of the wet gel sample was represented as the unsteady and one dimensional diffusion of 1-butanol through aerogel pores filled with supercritical carbon dioxide. Different mathematical models describing supercritical drying of the wet gel cylindrical sample were developed. Shrinking core models used one value of the effective diffusivity for the whole material, and they failed to describe the drying experiment correctly. Parallel pore models used different effective diffusivity values for each pore size. The best simulation results were obtained using the parallel pore model with local porosity or tortuosity values for each pore size.