Van der Waals attraction energy

The van der Waal attraction energy, in a first approximation is inversely proportional to the square of the intercolloid distance. 

Even relatively weak attraction between droplets or solid particles in aerosols suffices to create an enhanced collision rate that can change particle-size distributions and overall stability. Think in kT thermal-energy units. Alone, small suspended bodies do a Brownian bop, randomly jiggling from the kT kicks of the air. Should their mutually random paths bring two particles to separations comparable with their size, their van der Waals attraction energy also approaches kT. To previous randomness, attraction adds strength of purpose and increased chance of collision, aggregation, or fusion.59... 

The van der Waals attractive energy between two spheres of radius a has the form8... 

For particles of different sizes, the greater the difference between the radii of two particles, the smaller the stability ratio. This implies that polydispersed particles are more unstable than monodispersed particles. This is because that the greater the difference in the radii of two interacting particles, the grater the absolute van der Waals attraction energy. 

Hamaker Constant In a description of the London-van der Waals attractive energy between two dispersed bodies, such as droplets, the Hamaker constant is a proportionality constant characteristic of the droplet composition. It depends on the internal atomic packing and polarizability of the droplets. 

Figure 10.6 Variation of the van der Waals attraction energy with separation distance.

The thermal energy of a particle scales as kT, while with a — the van der Waals attractive energy scales as the Hamaker constant A (Eq. 8.1.20). Finally from Eq. (8.1.15), the energy of repulsion is seen to scale as ae for small zeta potentials, say f less than the Nernst potential at standard temperature (26 mV), and for small Debye length to radius ratio. 

Finally, we introduce the shear-attraction number, Nj, which is that group characterizing the magnitude of the viscous energy to the van der Waals attractive energy... 

The free energy of interaction of two interacting bodies may be expressed as a sum of electrical double layer interaction energy (in general, repulsive) and the van der Waals attraction energy (in general, attractive) ... 

The Lifshitz-van der Waals attractive energy of interaction between the same spheres can be computed from (96) ... 

This approach enables the interactions between macroscopic bodies to be calculated, making assumptions about their molecular structure. The van der Waals attraction energy between individual molecules at separation r is given by... 

For most dilute silica sols around pH 2, where there is little ionic charge on the particle, no coagulation by electrolyte is observed, presumably because of the hydration layer. However, Harding (237) has called attention to the fact that relatively large colloidal silica particles 50-100 nm or more in diameter flocculate at low pH, whereas small particles do not. It remains to be determined whether the flocculation Is due to the van der Waals attractive energy between the particles or to the formation of multiple hydrogen bonds between the silanol-covered surfaces over the area of contact at collision. 

Equation (13.8) gives the van der Waals attractive energy, Ga, for two particles or droplets with equal radius R, and surface-to-surface separation h (when h R),... 

Flocculation refers to aggregation of the droplets, without any change in the primary droplet size, into larger units. Flocculation is the result of the van der Waals attraction that is universal with all dispelsed system. For two droplets of equal radii R, the van der Waals attractive energy Ga is given by Eq. (14.20) [60] (when the separation between the droplets h is much smaller than the droplet radius). 

It is the process in which emulsion drops aggregate, without rupture of the stabilizing layer at the interface. Flocculation of emulsions may occur under conditions when the van der Waals attractive energy exceeds the repulsive energy and can be weak or strong, depending on the strength of inter-drop forces. 

The energies can be attractive or repulsive generally, the electrostatic repulsion energy [12] and Van der Waals attraction energy (F ) [13] act between non magnetic particles dispersed in aqueous carriers. 

Particles with anchored surfactant layers cannot come into direct contact. The distance of closest apprrwch can be, at most, two time the adsorption layer thickness. Using nm particles the F<,-energy of particle core no longer acts at closest approach, therefore the Van der Waals attraction energy of the adsorbed layer (F,) [15], the Born repulsive energy (Fb) [16], and the of the external ionic adsorption layer determine the colloidal stability of the dispersed particles. 

The following equation was proposed for the London-van der Waals attraction energy Fa, in /cT units, between the spherical particle and the plate, where A is the Hamaker constant ... 

---