Potential Energy

In many cases it is desirable to calculate potential energy due to repulsion  per unit area. By definition potential energy may be given as the product of force and distance, thus we may write energy as

where D is a dummy variable. Substituting FR from equation (9.34) in equation (9.35) we get

Integrating with boundary conditions we get:

(9.36)

Total energy between 2 plates then can be evaluated as a summation of energy due to acid base interaction, van der Waal interaction and electrostatic interaction. Thus,

For spherical particle potential energy can be calculated by Deryaguin’s approximation.

Fig. 9.3:   for spherical particles.

(9.37)

Note that if radius of two spheres is different, then instead of using R in the above equation we would have used . Again we see that the total energy is equal to