Deryagin’s theory

Deryagin s Theory and the Possibility of Calculating Adhesive Forces. The forces of adhesion can be calculated without resorting to experiment. Toward this end, let us turn to the theory of Deryagin. The basic premises of this theory are as follows [24] Adhesion takes place under the influence of surface forces and can be regarded as a reversible process in thermodynamic equilibrium, provided that the radii of curvature of both surfaces are considerably greater than the radius of action of the surface forces. 

Deryagin s theory is based on the proposition that the force of adhesion is a function of the clearance H separating spherical surfaces of contiguous bodies F = /(//). As the gap disappears H 0), the force of adhesion is given by... 

Deryagin s Theory and the Possibility of Calculating Forces of Adhesion... 

It follows from Deryagin s theory that the force of adhesion depends on the curvature [formula (1.62)] of the surfaces in contact. The influence of the properties of the surfaces on the adhesion is taken into account by the free energy /(O) the effect of capillary forces and the particle charges on the adhesive force, however, is not taken into consideration (see Chapter II, 12-14 on this point). 

As a basis for the simulation of particle interaction, we can take Deryagin s thermodynamic theory of interaction between surfaces [1], according to which [7,p. 196],... 

The adhesion is proportional to particle size only if the dominant forces are molecular. If (apart from these forces) electrical, capillary, or Coulomb forces predominate, the overall force of adhesion may very well not be proportional to particle size. Deryagin s thermodynamic theory of adhesion regards adhesion as a reversible equilibrium process, and the force of adhesion as a function of the gap separating the contiguous bodies. When this gap is zero, the force of adhesion is proportional to the sizes of the contiguous bodies, as indicated in Eq. (1.39). 

For an aqueous medium, the experimental data on the relationship between adhesive force and particle size are in agreement with theoretical values, thus providing practical support for Deryagin s thermodynamic theory of adhesion (see Section 3). 

In a liquid medium, for which there is a liquid interlayer between the contiguous bodies, and the effects of capillary, electric, and Coulomb forces are excluded (see 11-13), adhesion is due solely to the molecular forces fthe disjoining pressure opposes adhesion). The value of the molecular forces is directly proportional to the dimensions of the particles [see Eqs. (1 47) and (1.49)]. For an aqueous medium the experimental results relating to the dependence of the adhesive forces on particle dimensions coincide with the theoretical data, and Deryagin s thermodynamic theory of adhesion is practically confirmed (see 5). 

Deryagin, B. V., and Landau, L. (1941) Theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solutions of electrolytes. Acta Physi-ochim. U.R.S.S. 14, 633-662. 

Deryagin, B. M. Levi, S. M. Film Coating Theory, The Focal Press New York, 1964. Domingo, C. Berends, E. Van Rosmalen, G. M. Precipitation of Ultrafine Organic Crystals from the Rapid Expansion of Supercritical Solutions over a Capillary and a Frit Nozzle. J. Supercrit. Fluids, 1997, 10, 35-55. 

B. M. Deryagin and S. M. Levi, Film Coating Theory. London Focal, 1964. 

Deryagin, B. M., and Levi, S. M., Film Coating Theory. Focal Press, London, 1964. Deryagin, B. V., and Titievskaya, A. S., Dokl. Akad. Nauk SSSR 60, 307 (1946). Werk-Albers, M. L., and Ring, T. A., unpublished manuscript. 

Deryagin, B.M. and Levi, S.M. (1964) Film Coating Theory The Physical Chemistry of Coating Thin Layers on a Moving Support, The Focal Press, London, pp. 25 -48. 

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