One-dimensional diffusion equation for the particle size distribution of perlite filter granulation

Abstract

Many filtration systems employing perlite granulations have been designed so far. Size distribution of perlite particles directly influences the retention properties of filter media. The information on the size distribution of perlite particles, used in each specific dead-end filtration process (the flow of fluid being filtered is perpendicular to the surface of filter medium), is crucial for the adequate design of filter medium. In order to facilitate the design of filter systems possessing filter media of this kind, a new and particular mathematical model has been developed for this present study. It is based on an appropriate partial differential equation and additional mathematical conditions, whose solution is an exponential function describing the probability density distribution of perlite particle sizes. The formulated model was experimentally verified by measuring the particle sizes of a perlite granulation using the morphometric method, based on the application of a standard light microscope and digital image analysis software. The fitting procedure of experimental data gave acceptable values of accuracy parameters - high R-square factor (R-2 = 0,905) and small value of the root-mean square error (MSE = 0,490).