Competing drying and reaction mechanisms in the formation of sol-to-gel films, fibers, and spheres

Drying of films, fibers, and spheres undergoing sol-to-gel transformation is greatly affected by the strong dependence of the diffusion coefficients on composition, molecular weight, and temperature. This dependence is probed by solving the equations of mass and heat transfer by diffusion or conduction and associated convection, along with chemical reaction. A one-dimensional analysis is used that encompasses the planar, cylindrical, and spherical configurations. The solutions are obtained by Galerkin’s method with finite element basis functions and entail large-scale computation. Skinning and solidification phenomena in silica sol-to-gel systems are greatly affected not only by falling diffusion coefficients, but also by the competition between drying and reaction. The kinetics of silica reactions are modeled with the statistical scheme of Kay and Assink (1988). Gelation is predicted by the recursive technique of Bailey et al. (1990). Results show that at intermediate reaction rates, high molecular weight silica polymers are formed first near the evaporating free surface and gelation proceeds from that surface inwards, but at high or low reaction rates, gelation occurs before or after drying, respectively. These results help predict conditions in which uniform films can be cast, uniform fibers can be drawn, and uniform microspheres can be formed by spray drying.