A Solution to Smoluchowski’s Coagulation Equation Based on Experimental Data and a Model to Describe the Frequency of Particle Collisions

Use of coagulants in treatment of wastewater from food industry is one of the most promising techniques to establish environment-friendly industries. To date, however, the coagulation process is not yet fully described in a manner which is conducive to practical applications and results. In fact, the coagulation process theoretical basis, i.e. the classical Smoluchowski’s equation published in 1916, is so complex to solve that virtually no practical application exists in the field of applied chemistry. This article illustrates the Authors’ endeavor to overcome this impasse. This has been achieved by constructing a mathematical model of the guiding force in the phenomenon, i.e. the frequency of particles collisions, and then utilizing this model to define, starting from Smoluchowski’s equation, a function which describes both the coagulation and sedimentation processes depending on space (vertical coordinate z) and the concentration of coagulant. This study can be considered as the first step of a methodology of practical application of the Smoluchowski’s equation to process and equipment design.Â