Interparticle forces total potential energy

Solvent friction is measured by the Stokes friction coefficient = 6 r)is H- The interparticle forces = — d/dr, U ( rj ) derive from potential interactions of particle i with all other colloidal particles U is the total potential energy. The solvent shear-flow is given by v ° (r) = yyx, and the Gaussian white noise force satisfies (with a,j8 denoting directions)... 

A theoretical derivation of the Schulze-Hardy rule can be developed on the basis of the interparticle forces described in Sec. 6.2. Each of the three forces is associated with a potential energy that contributes additively to the total potential energy between two planar particle surfaces a distance d apart. If (p(d) is the total potential energy per unit area of planar surface, then... 

The classical DLVO theory of interparticle forces considers the interaction between two charged particles in terms of the overlap of their electric double layers leading to a repulsive force which is combined with the attractive London-van der Waals term to give the total potential energy as a function of distance for the system. To calculate the potential energy of attraction Va between solid spherical particles we may use the Hamaker expression ... 

Assuming we know the form of the interparticle potential functions, Uy = u( rj-q ), the total potential energy, V (r) = Y Uij, and the conservative forces, fj = -3V(r)/3rj, can be calculated. Equations [2] and [3] can be numerically integrated forward in time using finite difference techniques, given a suitable initial condition. Various algorithms are described in the literature. ... 

Figure 10.2 Total potential energy (V)-interparticle distance (Hj curves. Various combinations of attractive and repulsive forces are shown here. In case V( /) repulsive forces dominate and we have a stable dispersion, but in case V(2) (weaker repulsive forces) the attractive forces dominate at all separations and thus we have an unstable dispersion. In the figure, V(l) = Vr(/) + and V(2) = Vr(2) + Va- Shaw (1992). Reproduced with permission from Elsevier...

The physical mechanisms underlying the effect of moisture on interparticle cohesion have received considerable attention in the soil physics literature and now are well understood. The total potential energy of soil water arises from both capillary and adsorptive forces and is represented as the matric potential (rlfm)- The relation of (Pa) to the humidity of the air within the soil voids is modeled by the Kelvin equation ... 

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