Brownian Coagulation at High Concentration

Abstract

Particle growth by Brownian coagulation at high concentration in the continuum regime is investigated by solving the Langevin dynamics (LD) equations for each particle trajectory of polydisperse suspensions. By monitoring the LD attainment of the self-preserving size distribution (SPSD), it is shown that the classic Smoluchowski collision frequency function is accurate for dilute particle volume fractions, phis, below 0.1%. At higher phis, coagulation is about 4 and 10 times faster than for the classic theory at phis = 10 and 20%, respectively. For complete particle coalescence upon collision, SPSDs develop even in highly concentrated suspensions (up to phis = 35%), as with dilute ones, but are broadened with increasing phis. At high particle concentration, an overall coagulation rate is proposed that reduces to the classic one at low concentration. Detailed collision frequency functions are also obtained at various phis values. Fractal-like agglomerates undergoing coagulation at constant fractal dimension attain an SPSD only temporarily because their effective volume fraction continuously increases, approaching gelation in the absence of restructuring or fragmentation.