Addressing an inverse problem of classifier size distributions

Abstract

One input and two output stream classifiers are commercially employed for the classification of particles. A mass balance equation for a classifier suggests that the feed size distribution can be evaluated from measured product size distributions if and only if the flow split of the feed particles to one of the product streams is also known. Moreover, the mass balance equation used to reconcile measured size distributions indicates that flow split of solid particles is in turn a function of all the three size distributions and is then redundantly expressed over the mass fraction of particles retained in various discrete size classes. Therefore for an operating classifier under steady state, the so far recognized approaches fail to address the profile of feed size distribution from the knowledge of measured fine and coarse product size distributions alone. In the forward approach of estimation of product size distributions, the feed distribution is integrated with efficiency curve of the classifier. Thus as an inverse problem, the feed distribution and efficiency curve need to be identified from the measured product size distributions. This paper attempts to address this inverse problem when flow split of feed particles to product streams is not known. However the method considers additional information regarding the functional forms of the classifier distributions due to inadequacy of product distributions alone to address the inverse problem.