Brownian Coagulation and External Force Fields

In our discussion of Brownian motion and the resulting coagulation, we did not include the effect of external force fields on the particle motion. Here we extend our treatment of coagulation to include interparticle forces. 

The force F12 between particles 1 and 2 can be written as the negative of the gradient of a potential  

Now let us assume that — b(r), where r is the distance between the particle centers. Then one can show that the steady-state coagulation flux is given by 

Let us now apply the above theory to two specific types of interactions van der Waals forces and Coulomb forces. 

Van der Waals Forces Van der Waals forces are the result of the formation of momentary dipoles in uncharged, nonpolar molecules. They are caused by fluctuations in the electron cloud, which can attract similar dipoles in other molecules. The potential of the attractive force can be expressed as 

Now let US assume that where r is the distance between the particle centers. 

Then one can show that the steady-state coagulation flux is given by 

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