LIOUVILLE EQUATIONS FOR AGGLOMERATION AND DISPERSION PROCESSES

The probability distribution of a collection of discrete subsystems, or particles, has a density which satisfies a continuity equation, or Liouville equation, described here for particles undergoing collisional interactions. From this equation, a set of equations for the moments of the distribution are derived. Solution of these moment equations by expansion in series of orthogonal functions is applied to coagulation processes in shear flow and to chemical reaction in coalescing dispersed media. Approximation methods applicable to realistic problems are described which require much less numerical computation than direct numerical methods. © 1969, American Chemical Society. All rights reserved.