Solution of population balance equation with pure aggregation in a fully developed turbulent pipe flow

This paper presents our preliminary effort in predicting particle size distributions in particulate processes in turbulent flow systems. The focus has been on processes of pure aggregation, occurring in a turbulent environment. A remarkably simple strategy has been used to solve the population balance equation (PBE) for spatially dependent pure aggregation with insignificant diffusive transport of particles in turbulent flow systems. The method makes use of the solution of a batch PBE through a mathematical transformation linking time to spatial variables. Furthermore, we investigate the self-similar solution of batch aggregation to show scaling behavior of particle size distributions in such flow systems using spatially dependent average particle sizes. Average particle sizes across the pipe cross section have been computed using both averaged frequencies as well as spatially varying frequencies. Comparison of the two solutions shows significant differences between them, establishing the sheer inappropriateness of the use of average aggregation frequencies in the prediction of absolute particle size distribution as done in the past.