COAGULATION AND FRAGMENTATION - THE VARIATION OF SHEAR RATE AND THE TIME-LAG FOR ATTAINMENT OF STEADY-STATE

The dynamic behavior and the attainment of steady state by a flocculat ing suspension in a stirred tank are evaluated using a population bala nce model. At long times, shear-induced coagulation and fragmentation reach a steady state, resulting in a particle size distribution (PSD) that is invariant (self-preserving) with respect to shear. The geometr ic standard deviations, sigma(g), of the self-preserving number or vol ume PSDs are 2.22 or 1.79, respectively, for the employed coagulation and fragmentation rates of flocculation. The time required to reach a steady-state PSD (time lag) is determined as a function of a dimension less group comprised of the relative rates of coagulation and fragment ation. The effect of the omnipresent variable shear rate in stirred ta nks during shear-induced flocculation is investigated through a sinuso idal function of the spatially averaged velocity gradient. increasing the amplitude of the shear rate fluctuation decreases the steady-state mass mean floc size, the maximum sigma(g), and the time lag for attai nment of steady state. The asymptotic (self-preserving) sigma(g) is no t affected by the shear rate amplitude provided that >99% of the prima ry particles have grown to larger sizes.