A mathematical model of coagulation

Abstract A simplified mathematical model of floc growth in a stirred suspension is developed with the aid of the Smoluchowski equation for orthokinetic coagulation. Particles are assumed to be spherical and to conjoin into spheres of proportionate volume upon contact. Particle growth is restricted to different maximum sizes or multiple volumes, larger particles breaking up into smaller ones which are returned to the system. A smooth growth pattern asymptotically approaching a steady-state mean size results when a model parameter of gross contact opportunity is less than 0.04 in magnitude; as it approaches 0.10, the growth pattern becomes oscillatory. Oscillatory growth was observed also experimentally when a controlled shear gradient was imposed on a suspension of iron flocs.