Agglomeration of particles in a fluid environment is an integral part of many industrial processes and has been the subject of scientific investigation. One model of the fundamental mathematical problem of determining the number of particles of each particle-size as a function of time for a system of particles that may agglutinate during two particle collisions uses the coagulation or Smoluchowski’s equation. With initial conditions, it is called the discrete agglomeration model. Several problems have been associated with this model allowing progress to proceed separately. To facilitate this progress, in this paper, we develop and solve the fixed agglomeration problem and establish the fundamental agglomeration problem for all cases of the autonomous quadratic kernel.

agglomeration, coagulation, Smoluchowski, differential equations.