Coagulation repulsive force

Small metal particles are unstable with respect to agglomeration to the bulk. At short interparticle distances, two particles would be attracted to each other by van der Waals forces and, in the absence of repulsive forces to counteract this attraction, an unprotected sol would coagulate. To counteract this, stabilization can be achieved in two ways electrostatic stabilization and steric stabilization. 

Repulsive forces between Fe oxide particles can be established by adsorption of suitable polymers such as proteins (Johnson and Matijevic, 1992), starches, non-ionic detergents and polyelectrolytes. Adsorption of such polymers stabilizes the particles at electrolyte concentrations otherwise high enough for coagulation to occur. Such stabilization is termed protective action or steric stabilization. It arises when particles approach each other closely enough for repulsive forces to develop. This repulsion has two sources. 1) The volume restriction effect where the ends of the polymer chains interpenetrate as the particles approach and lose some of their available conformations. This leads to a decrease in the free energy of the system which may be sufficient to produce a large repulsive force between particles. 2) The osmotic effect where the polymer chains from two particles overlap and produce a repulsion which prevents closer approach of the particles. 

In aqueous suspension, the stability is discussed in reference to the DLVO (Deryaguin-Landau-Verway-Overbeek) theory. Within this framework, all solid substances have a tendency to coagulate due to their large van der Waals attractive force. The coulombic repulsive force among colloidal particles more or less prevents this tendency. These two opposite tendencies determine the stability of suspensions. What kind of parameters are concerned in the present nonaqueous system, for which little is known about the stability This is an interest in this section. 

Calculation of Coagulation Rate. Here we discuss an interaction potential of two charged particles in a liquid within a framework of DLVO theory. Following this theory, the overall interaction potential U, of charged spherical particles of the same radius R and surface distance d is a sum of a coulombic repulsive force of charged particles and a van der Waals attractive force given by the equation (28) ... 

If an emulsion is stabilized by electrical repulsive forces, then demulsification could be brought about by overcoming or reducing these forces. In this context the addition of electrolyte to an O/W emulsion could be used to achieve the critical coagulation concentration, in accord with the Schulze-Hardy rule. 

As repulsive forces decrease with increasing salinity, van der Waals forces will dominate and flocculation will proceed. Strong salinity gradients in estuaries make them ideal environments for coagulation processes. 

As pointed out earlier, the present treatment attempts to clarify the connection between the sticking probability and the mutual forces of interaction between particles. The van der Waals attraction and Bom repulsion forces are included in the analysis of the relative motion between two electrically neutral aerosol particles. The overall interaction potential between two particles is calculated through the integration of the intermolecular potential, modelled as the Lennard-Jones 6-12 potential, under the assumption of pairwise additivity. The expression for the overall interaction potential in terms of the Hamaker constant and the molecular diameter can be found in Appendix I of (1). The Brownian motions of the two particles are no longer independent because of the interaction force between the two. It is, therefore, necessary to describe the relative motion between the two particles in order to predict the rate of collision and of subsequent coagulation. 

Hydrodynamic Models. The coagulation kernels are usually calculated for solid spheres with hydrodynamic models of different sophistication. The simplest calculation uses fluid flow in the absence of any effect of either particle on the flow. This flow level is known as rectilinear flow. The next level of sophistication involves calculating the flow around one particle, usually the larger of the two interacting particles. This level of calculation is known as curvilinear flow. Further levels of sophistication can be obtained by considering the particle trajectories as affected by the interacting flow fields of the particles, as well as any attractive or repulsive forces between them. 

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