Optimization of the rapid supercritical extraction process for aerogels

A partial differential equation is derived that describes the pressure developed in the pores of a gel during the rapid supercritical extraction process. A comparative analysis of the strains caused by syneresis and expansion of the fluid, respectively, suggests that the latter is the dominant effect for this process. Experimental results indicate that the rate of leakage from the mold is equal to the rate of volumetric expansion of the fluid, so this was used as the boundary condition for the calculation. An analytical solution is obtained for the strain produced in a purely elastic gel. The strain is found to develop most rapidly at high temperatures, where the thermal expansion of the fluid increases sharply. The model predicts a temperature dependent heating rate that can be used to avoid irreversible strains by compensating for the increase in thermal expansion coefficient.