Modeling of Granular Material Mixing Using Fractional Calculus

Abstract

Particulate and granular materials are found in different chemical processes. Measuring and characterizing the mixing degree remains a challenge, s it is an important variable for process performance. The availability of reliable sensors for real time control is still incipient or expensive, an alternative remains on the development of mathematical models for mixing prediction.The most commonly used approach for solid mixing concern on either diffusive or advective/convective processes. Fractional calculus represents a novel approach and a growing research field for process modeling, being based on derivates of arbitrary order. Therefore, it represents an important and alternative tool for mixing process modeling. This work study the use of a fractional diffusion model to describe granular mixing in a rotary cylinder, considering finite type of boundary conditions. Experimental data previously reported were used for validation purposes. The proposed approach could successfully describe the experimental data, thus, can be used as an alternative tool for mixing evaluation.