Modeling of stress development in aerogel preparation

Abstract

Aerogels are prepared by sol-gel method associated with supercritical drying. They are used in different areas due to their special characteristics such as high porosity, low density, low thermal conductivity. Drying is one of the critical steps in producing aerogels with desired properties, since drying stresses can cause shrinkage and cracking during the process. In the study, stress development during heating to the critical temperature of pore liquid is modeled for an elastic, isotropic, circular plate. The flow of pore liquid in the radial direction is neglected and Darcy's Law is applied for the flux in the axial direction. The model, which is an integro-differential equation, derived for a free circular plate is analyzed where radial constraint is in effect. Radial constraint prevents the pore liquid from escaping the network in the radial direction. Also, the expansion of the network in this direction is prevented. When radial constraint is applied, the difference between a circular plate and a cylinder of high thickness disappears since the flow is in the axial direction and the most significant stress occurs in the radial direction in both cases. The model equations are solved to observe the effects of heating rates, shear moduli and permeability of the network. The presence of syneresis, spontaneous shrinkage due to condensation reactions, is also examined. The magnitudes of stresses determined at different conditions for the cylindrical silica gel are compared to the modulus of rupture which is 0.2 MPa for the alcogel and 2 MPa for the aerogel. The aim is to determine whether or not production of crack-free monolithic materials is possible under specified conditions. It is observed that, radial constraint increases stress development significantly and fracture of the cylinder is inevitable. Therefore, heating rate is decreased to a very low value (0.04 C/min). Actually, increasing temperature 0.04 C per minute doesn't have a physical meaning since with that rate, it takes about four days to reach the critical temperature. Even at this low heating rate, themagnitude reaches about 0.4 MPa at low temperatures and it even exceeds 2MPa when syneresis is taken into account. The analysis is repeated for a circular plate. The effect of heating rate, shear modulus and permeability are studied. It is observed that stress formation is lower in comparison to the cylindrical silica gel. Since the modulus of rupture of the circular plate is not known, a comparison with the mahnitudes of the computed stresses could not be made. The model can be applied to any porous material and used to find the optimum heating rates for aerogel production.