Capillary Interaction between Solid Bodies

First we calculate the force of interaction between the plates at large separations, L a, where a = jfpg is the capillary length, y is the surface tension, p is the density of the liquid, and g is the gravity acceleration. We consider only the case of two partially (or complete) wettable plates, that is, G, Jt/2, 02 n/2, as the case of two nonwettable plates, Gj jt/2, 02 jt/2, can be treated in a similar manner. 

FIGURE 2.41 Liquid profile between two partially wettable plates that are partially 

Displacement of plate 2 through dL while plate 1 is fixed, changes the excess free energy of the system, O, by 

According to the previous consideration, the shape of a liquid surface plates in the gravity field can be described by the following equation  

Close to the position x, the liquid profile has a low slope, that is, h 1, and hence, in the vicinity of this position, the shape of the liquid surface can be described by the linearized equation h = hla, when close to jc = x.  

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B.V. Derjaguin and V.M. Starov, Capillary interaction between solid bodies. Colloid J. USSR (Engl. Transl), 39,383-386 (1977). 

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