Crack critical drying rate

The microstructure of a sol, in terms of the nature and concentration of sol particles, significantly affect a membrane s properties such as average pore diameter and pore size distribution. Other critical parameters are the temperature and rate of evaporation used in the drying and calcination steps. Even though it is economical to obtain the final product form quickly, too rapid a drying rate forms cracks in the membrane. Crack formation is also dependent on thickness of the membrane. The work of Cini et al. [49], who prepared supported microporous y-A C membranes as catalyst supports, illustrates many of these effects. 

Fracture occurs when > Kjc, where Kjc is the critical stress intensity of the gel. Assuming that the flaw size distribution is independent of the size and drying rate of the gel, the tendency to fracture would be expected to increase with drying rate Ve. Scherer s analysis therefore provides a qualitative explanation for the dependence of cracking on L and Ve. 

Cracks can also appear during the pressure release in the autoclave. In the supercritical drying process, the gel is subjected to high temperature and high pressure. When the critical point is reached, the pressure of the autoclave is decreased while the temperature is kept constant. At this instant, the pressure applied to the supercritical fluid is equal to that within the pores. The supercritical fluid has a very low density and viscosity compared with that of the liquid at room temperature however, the low permeability of the gel resists the flow of the supercritical fluid out of the gel. In other words, if the supercritical fluid release is performed too fast a pressure gradient appears. In this case the supercritical fluid within the gel, which is in compression, suddenly expands and the solid part suffers tensile stress. Experiments show that cracking depends on the pressure release rate, on the nature of the gel (basic or neutral), and on its geometrical dimensions. 

To measure those stresses and their elfect on the breakage rate of glass containers freeze-drying crash tests were performed in a LYOVAC GT3 small-scale lyophilizer with 10% mannitol solution (most critical, i.e., a high breakage and cracking rate, because of its extreme expansion [10] (see Figure 2)). 

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