Modeling simultaneous deposition and aggregation of colloids

Abstract

Solid formation and particle deposition in chemical and pharmaceutical processes often leads to heat exchanger or reactor fouling, compromising operability. The aim of this work is to propose a mathematical framework, based on population balance equations, to describe the simultaneous colloid aggregation and deposition. The problem is dealt with by accounting for two distinct cluster mass distributions, the first one describing the free clusters, while the second one the deposited aggregates. Three main events are considered: (i) aggregation of two free clusters, (ii) deposition of free clusters on the reactor wall (i.e. a free cluster turns into a deposited one), and (iii) aggregation of a free cluster with a deposited one. To describe the aggregation of free clusters, three typical aggregation kernels (i.e. diffusion-limited and reaction-limited cluster aggregation as well as simple shear aggregation) have been used. Starting from those kernels, aggregation laws to describe the interaction between a free and a deposited cluster were proposed and a simple cluster-mass dependent deposition law was employed. The simulation results are then discussed in the frame of one dimensionless parameter, function of the relevant characteristic time of the process (i.e. aggregation and deposition).