Rheological Properties of Coagulation Structures

For a large number of disperse systems with a globular structure mechanical characteristics, such as strength, (N/m ), and the ability to resist the action of external stresses in general are manifested by the cohesive forces between the particles at points of their contact. Experiments have confirmed [11,12] that the strength can be estimated using the additivity approximation, P = xPi, where p is the strength (the force measured in N) of individual contacts between particles, and x (m ) is the number of such contacts per unit area of the fracture surface. Estimates for both p and x can be obtained on the basis of both theory and experimental data. 

For moderately dense structures (such as those described by a primitive cubic lattice with a coordination number of 6, employing a first and most crude approximation yields an estimate of X l/(2r). This provides one with the means to estimate the order of magnitude of x in real systems, namely, for particles having a diameter 2r 100 pm, we get a value of x lO -lO contacts per cm  

FIGURE 3.17 Models describing 2D (a) and 3D (b) globular disperse structures. (From Shchukin, E.D., Physical-chemical theory of the strength of disperse structures and materials, in Physical-Chemical Mechanics of Natural Disperse Systems, E.D. Shchukin, N.V. Pertsov, V.I. Osipov, and R.I. Zlochevskaya (eds.), Izd. MGU, Moscow, Russia, 1985, pp. 72-90.) 

For typical lyophobic colloidal systems with a complex Hamaker constant 10 J and a particle-particle separation of 0.2-1 nm, the adhesive energy in the contact is significantly larger than kT, which indicates that thermodynamics favors the formation of coagulation contacts. The primary potential energy minimum is even deeper in systems conposed of coarser particles. At the same time, for the case of low values of the complex Hamaker constant, 10 -10 J, the adhesion between the particles in systems that are not too coarse (particles with a diameter up to a micron) is overcome by the Brownian motion, and the formation of structures with coagulation contacts is impossible. 

The strength of a coagulation contact, that is, the adhesive force between particles, is determined primarily by the molecular forces. For spherical particles, this force is given by 

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