The small clear (but cracked) gel on the right had the same diameter as the white one on the left before it was dried. As the solvent evaporated, its volume decreased by about an order of magnitude, and the stresses resulting from capillary pressure caused the fractures. The other samples contained colloidal silica particles, increasing in volume fraction from right to left. (Those with ≥ 20 vol% particles did not shrink at all. These gels were prepared in a study of consolidants for stone.)
The following papers deal with the theory of drying. The theory was originally developed for gels, but the principles are the same for any drying material, so some of the later papers include consideration of ceramics and whitewares.
My first paper on this topic, with the grandiose title, “Drying Gels: I. General Theory” was full of errors. Most unfortunate was an error in the formulation that was not corrected until after the sixth paper in the “Drying Gels” series. This was sorted out in a major mea culpa published as “Drying Gels: VIII. Revision and Review”. If you are interested in this subject, I suggest that you start with Part VIII, and ignore the first six papers; Part VII was written at the same time as VIII, so it is correct. The theory that I worked out was actually developed decades earlier by Maurice Biot, as acknowledged in Part VIII and in the text, Sol-Gel Science.
The analysis of stresses in gels is simplified by the fact that the gel network is so soft that the stresses is can bear are far too small to cause significant dilatation of the liquid or solid phases. That is not true for more rigid materials, such as porous glass or cement paste, so the theory presented in the following papers does not apply to them. I am presently extending the model to include that case.
Papers that deal with supercritical drying, and predicting drying shrinkage, are listed separately.
Relevant papers:
Sol-Gel Science
C.J. Brinker and G.W. Scherer (Academic Press, New York, 1990) 908 pp.
Theory of Drying
"Drying Mechanics of Gels", G.W. Scherer, pp. 225-230 in Better Ceramics Through Chemistry II, eds. C.J. Brinker, D.E. Clark, D.R. Ulrich (Mat. Res. Soc., Pittsburgh, PA, 1986)
Parts I-VI of this series contain errors that are corrected in Part VIII.
"Drying Gels: I. General Theory", G.W. Scherer, J. Non-Cryst. Solids 87 (1986) 199-225 ; "Correction of 'Drying Gels: I. General Theory'", J. Non-Cryst. Solids 92 (1987) 375-382
"Drying Gels: II. Film and Flat Plate", G.W. Scherer, J. Non-Cryst. Solids 89 (1987) 217-238
"Drying Gels: III. Warping Plate", G.W. Scherer, J. Non-Cryst. Solids 91 (1987) 83-100
"Drying Gels: IV. Cylinder and Sphere", G.W. Scherer, J. Non-Cryst. Solids 91 (1987) 101-121
"Drying Gels: V. Rigid Gels", G.W. Scherer, J. Non-Cryst. Solids 92 (1987) 122-144
"Drying Gels: VI. Viscoelastic Plate", G.W. Scherer, J. Non-Cryst. Solids 99 (1988) 324-358
"Drying Gels: VII. Diffusion During Drying", G.W. Scherer, J. Non-Cryst. Solids 107 (1989) 135-148
"Drying Gels: VIII. Revision and Review", G.W. Scherer, J. Non-Cryst. Solids 109 (1989) 171-182
“Cavitation during drying of a gel”, G.W. Scherer and D.M. Smith, J. Non-Cryst. Solids 189 (1995) 197-211
Effect of Drying on Properties
"Aging and Drying of Gels", G.W. Scherer, J. Non-Cryst. Solids 100 (1988) 77-92
“Effect of Inclusions on Shrinkage”, G.W. Scherer, pp. 503-514 in Better Ceramics Through Chemistry IV, eds. B.J.J. Zelinski, C.J. Brinker, D.E. Clark, and D.R. Ulrich (Mat. Res. Soc., Pittsburgh, PA, 1990)
“Drying of Ceramics Made by Sol-Gel Processing”, G.W. Scherer, pp. 92-113 in Drying ‘92 Part A, ed. A.S. Mujumdar (Elsevier, Amsterdam, 1992)
“Effect of drying on viscoelasticity and permeability of gel”, G.W. Scherer, pp. 209-215 in Better Ceramics Through Chemistry VI, eds. A.K. Cheetham, C.J. Brinker, M.L. Mecartney, and C. Sanchez (Mat. Res. Soc., Pittsburgh, PA, 1994)
“Stress development during drying of Conservare OH®”, G.W. Scherer and G. Wheeler, pp. 355-362 in Proc. 4th Int. Symp. Conservation of Monuments in the Mediterranean, Vol. 3, eds. A. Moropoulou, F. Zezza, E. Kollias, I. Papachristodoulou (Tech. Chamber Greece, Athens, 1997)
“Effect of drying on properties of silica gel”, G.W. Scherer, J. Non-Cryst. Solids, 215 [2,3] (1997) 155-168
Reviews
“Drying of Gels”, G.W. Scherer, pp. 181-220 in Sol-Gel Science and Technology, eds. M.A. Aegerter, M. Jafelicci Jr., D.F. Souza, and E.D. Zanotto (World Scientific, New Jersey, 1990)
“Theory of Drying”, G.W. Scherer, J. Am. Ceram. Soc. 73 [1] (1990) 3-14
“Physics of Drying”, G.W. Scherer, pp. 561-572 in Ceramic Powder Science III, Ceramic Transactions, Vol. 12 (Am. Ceram. Soc., Westerville, OH, 1990)
“Recent Progress in Drying of Gels”, G.W. Scherer, J. Non-Cryst. Solids 147&148 (1992) 363-374
“Physics of Drying”, pp. 179-199 in Ultrastructure Processing of Advanced Materials, eds. D.R. Uhlmann and D.R. Ulrich (Wiley, New York, 1992)
“Fundamentals of drying and shrinkage”, G.W. Scherer, pp. 199-211 in Science of Whitewares, eds. V.E. Henkes, G.Y. Onoda, and W.M. Carty (Am. Ceram. Soc., Westerville, OH, 1996)
“Drying, Shrinkage, and Cracking of Cementitious Materials”, G.W. Scherer, Transp. Porous Med., 110 [2] (2015) 311-331
DOI 10.1007/s11242-015-0518-5
Fracture
“Stress and Fracture During Drying of Gels”, G.W. Scherer, J. Non-Cryst. Solids 121 (1990) 104-109
“Crack-tip stress in gels”, G.W. Scherer, J. Non-Cryst. Solids 144 (1992) 210-216