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By Shchukin, Evgeniĭ Dmitrievich; Zelenev, Andrei S
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Extra info for Physical-chemical mechanics of disperse systems and materials
Example text
At the same time, to identify the numerical coefficient, that is, π, one needs a rigorous approach. To do that, we utilize the following scheme for calculating the force p(h) from the known Π(h) dependence. The approach illustrated here is a simpler one than that utilized by Derjaguin. 25. 25 The derivation of Derjaguin’s theorem. 37) pR It is assumed here that the particle surface is molecularly smooth and that the gap h << R; “infinity” as the integration limit has the meaning of distances comparable to h.
The description of this case is analogous to the one mentioned earlier, if the contact angle θ (in this case, measured outside the meniscus) is replaced by an (π – θ) angle inside the cavity, but with one principal difference: The formation of a wetting meniscus implies a particular volume of a liquid, while in the case of a cavity, the liquid volume depends on the external pressure. The analysis of meniscus formation upon the contact of particles in a nonwetting liquid has been studied and has been discussed in detail in a study by Shchukin et al.
It is, however, worth pointing out that for macroscopic particles, this is valid only in the case of molecularly smooth surfaces. In this case, the equations for the molecular adhesive forces and for the capillary contraction force both contain the same macroscopic value of Rg. The situation is different for rough surfaces. Namely, the value of Rg in the expression for the molecular forces may be determined by the radii of microheterogeneities between which the contact is formed, while the value of Rg in the expression for the capillary adhesion force may be determined by the macroscopic radii of the particles.