Kinetics of heterogeneous magnetic flocculation using a bivariate population-balance equation

The discrete bivariate population-balance equation is formulated and solved to describe the kinetics of heterogeneous magnetic flocculation of colloidal paramagnetic particles in a uniform magnetic field. The particles are allowed to have various sizes and values of magnetic susceptibility. Computations show the importance of particle size and magnetic susceptibility on the flocculation rate and the transient bivariate (size/magnetic susceptibility) density function. The particle size distribution of certain magnetic-susceptibility particles and the magnetic-susceptibility distribution of certain size particles are calculated as functions of time and initial and operating conditions. The composition of a floc at any time depends on magnetic, van der Waals, double layer, and hydrodynamic forces among pairs of particles. The magnetic force is a function of the particle size, magnetic susceptibility, and strength of the magnetic field. Results are presented for various initial conditions of particles after ten minutes of flocculation. The results are of significance in understanding the forces among the particles and designing efficient magnetic separation processes.