Shrinkage capillary stresses

Drying of the gels can be the most time consuming and difficult step in the overall fabrication route, especially when a monolithic material is required directly from the gel. Normally, the liquid is present in fine channels, typically 2-50 nm in diameter. Removal of the liquid by evaporation has two main consequences large capillary stresses are generated, and the gel undergoes considerable shrinkage under the action of the capillary stress (48,49). If the liquid-filled pore channels in the gel are simplified as a set of parallel cylinders of radius a, then the maximum capillary stress exerted on the solid network of the gel is... 

The amount of shrinkage that precedes the critical point depends on the magnitude of the maximum capillary stress, Pr. As indicated by Eq. 10, Pr increases with the interfacial energy ( lv) and with decreasing pore size. It is not surprising, therefore, to find that the porosity of a dried body is greater... 

The greater the capillary stress, the greater the stress at the critical point. The lower Pr, the less the shrinkage (and therefore the greater the permeability) at the end of the CRP. Thus, factors (such as changes in y v) that reduce Pr also reduce the stress Indirectly through their effect on the permeability. When a > 1, Eq. 25 reduces to... 

Surfactants can be added to the pore liquid to reduce the interfacial energy and thereby decrease the capillary stress. It has been demonstrated for particulate [15] and alkoxide-derived [42] gels that cracking is reduced by surfactants, though it is not necessarily eliminated. The shrinkage at the critical point is reduced by surfactants [23,42], and this will have a beneficial effect on the permeability of the gel, contributing to reduction of the stress during the CRP. 

The most common cause of it is the neglect of 3-dimensional effects as compared with those in two dimensions. Thus, all stresses in a loaded wire or ribbon are disregarded in the shrinkage method, Section III. 1. The work of deformation leading to rupture is a bulk effect which does not receive its due consideration in the calculation of fracture energy, Section III.3. Bulk deformations associated with thermal etching, Section III.4, demand more attention than was alloted to them by many scientists. The method of bubbles, Section III.5, is invalid both because of the above neglect (that is, that of the volume stresses around the bubble) and because of another popular error, namely an erroneous treatment of capillary pressure Pc. 

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