(4e) Extension to Smoluchowski's Population Balance Equation to Include Liquid Binder

Extension to Smoluchowski's Population Balance Equation to
Include Liquid Binder

P. R. Rynhart, R. McLachlan, J. R. Jones, R. McKibbin

College of Sciences, Massey University, New Zealand

Tel +64 6 3569099 ext 3586 Email: P.R.Rynhart@massey.ac.nz

In 1917 Smoluchowski developed a
mathematical model for the coalescence of particles in a liquid suspension,
which has since become established as the fundamental equation for population
balance modelling of particle agglomeration.  In this paper the Smoluchowski
model is extended to include the effects of binder fluid by adding a system of
differential equations.  The extension uses the premise that the coalescence
kernel is the product of the collision rate function and the sticking
efficiency function, where the sticking efficiency function is dependent on the
binder carried by both particles in each collision.  The amount of binder is
size dependent.  Model results are compared for sticking efficiency functions which
are; (i), size independent; (ii), the product of size µ r_ir_j; (iii), cross section area µ (r_i^1/3 + r_j^1/3)²;
and (iv), equi-partition of kinetic energy µ
(r_i^-1/2 + r_j^-1/2).