Brownian coagulation in a field of force

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Abstract
The Fokker–Planck equation for two particles, when reduced to a one-dimensional problem in the radial coordinate, yields a transition state in the effective potential V(R)−2kT ln(R/R′) for potentials exhibiting capture characteristics. Application of Kramers solution to barrier crossing yields an analytic formula for the capture rate constant which applies for all particle sizes relative to the bath mean free path, giving the exact result for large particles for diffusion on V(R) and the kinetic theory result for small particles. The influence of the potential is accounted for by two stability factors W(0) and W(∞). For hard spheres the results are in good agreement with extant theory. Extension to include hydrodynamic interaction and relaxation is indicated.