London-van der Waals Force

The London-van der Waals force, which is generally attractive in nature, is a short range force and decays rapidly to zero away from a surface. The origin of the London-van der Waals force lies in the instantaneous dipole generated by the fluctuation of electron cloud surrounding the nucleus of electrically neutral atoms. For a spherical particle of diameter d near a flat surface, the interaction energy is given by:

,

(1)

where x=z/d and z is the distance of the sphere from the surface and A is the Hamaker constant. As the particle approaches the surface,

,   as

(2)

Thus, the energy becomes infinite for z = 0. Hence, the surface acts as a perfect sink for aerosol diffusion. The range of operation of the van der Waals force may be estimated by comparing the thermal energy with . Values of Hamaker constant A are in the range of   to  J. Thus,

for  .

(3)

In Table 1 values for van der Waals force for a number of materials are listed and the values of van der Waals force is compared with the Stokes drag force acting on a particle that is moving with a velocity of 1 m/s in aid and in water. It is seen that the van der Waals force in air is comparatively larger than that in water. Furthermore, van der Waals force is much larger that the drag force. The ratio of the van der Waals force to drag force in water is generally less than that in air.