capillary stress
Dip a narrow glass tube into water and the water climbs up inside it, its surface curving into a little bowl-shaped dip called a meniscus. That climb is capillary action, and it comes from a real pulling force: the water's surface tension, wrapped around a curved surface, puts the liquid under tension and sucks it up. Now picture that same suction inside the millions of tiny gaps between the particles of a drying ceramic. Every little meniscus at the surface is pulling on the water — and through the water, squeezing the particles together. That squeeze is capillary stress, the hidden villain of drying.
The Young-Laplace relation gives the size of the suction: the pressure jump across a curved liquid surface, written delta-P, is delta-P = 2 gamma cos(theta) / r, where gamma is the liquid's surface tension, theta is the contact angle (how well the liquid wets the solid), and r is the radius of the pore or gap. The smaller the pore, the tighter the meniscus curves, and the harder it pulls. For water (gamma about 0.072 N/m) fully wetting a pore of radius 0.1 micron (that is 1e-7 m), delta-P works out to about 2 x 0.072 / 1e-7, which is roughly 1.4 MPa. Shrink the pore to 10 nm and the stress climbs to about 14 MPa — a serious squeeze on a fragile green body.
Capillary stress is the engine that drives useful drying shrinkage — it is what pulls the particles into tight packing during the constant-rate period. But the same force turns destructive the instant it acts unevenly: a surface drying faster develops finer, more sharply curved menisci and therefore higher suction than the wetter interior, and that mismatch is exactly the tension that cracks and warps a body. Notice the punishing lesson in the equation: because stress scales as 1/r, the fine, sub-micron powders prized in advanced ceramics have the smallest pores and so the most dangerous capillary stresses — which is why the most refined bodies are often the hardest to dry.
Two blotting papers, one soaked with water and one with alcohol, dry very differently: water, with roughly three times the surface tension of alcohol, pulls its fibres together far harder as it leaves. Ceramists use the same trick in reverse, sometimes drying troublesome bodies with a low-surface-tension liquid to soften the capillary squeeze and avoid cracks.
Capillary stress = 2 gamma cos(theta) / r: smaller pores and higher surface tension mean a harder squeeze on the drying body.
Capillary stress is not all bad — without it there would be no drying shrinkage and green bodies would stay loose. The goal is never to eliminate it but to keep it uniform: even suction packs a body neatly, uneven suction tears it.