(412f) Using Convection Dispersion Equations to Model Segregation of Multi-Component and Multi-Mechanism Materials

Segregation is a one of the main causes of poor process operation.  It needs to be understood from a fundamental point of view.  However, segregation is a multi-component and multi-mechanism phenomenon.  Most data in current literature is for simple bimodal systems.  These systems are far too simple to predict real segregation of the complex mixtures created in industry.  One of the key problems is a lack of theory to handle real mixtures of more than two materials.  This paper suggests a framework to accomplish that task.  The convection dispersion framework assumes that dispersion is a set of local velocity flux terms that induce a normal bell shaped concentration distribution off of the average convective velocity.  In dispersion the local convective velocities distribute in a symmetric pattern around the overall average convective velocity, similar to the random scatter of a shotgun fired in an environment where gravity, air drag effects or other external forces were minimal.   Conversely, segregation is a velocity flux term that induces a skewed distribution off of the average convective velocity for each component in the system.  Consider that segregation is always directional and is based on a mechanistic flux that has the form of the derivative (with respect to a spatial dimension) of a characteristic segregation velocity times the local concentration.    We assume that the segregation flux velocities are additive.  Thus, to develop a theory that incorporates multi-mechanisms, the relationship between segregation velocity terms for each type of segregation must be understood.  The overall segregation profile is a sum of a series of skewed concentration distributions from the average dispersion velocities.  These distributions can be combined using the concept of multi-modal distribution functions to yield equivalent overall segregation variance numbers for each component in the mixture.  The overall segregation variance numbers can be measured from segregation potential tests done with spectral reflectance techniques (SPECTester).  The overall segregation variance data can be used with convective dispersion models to quantify the segregation of each component by mechanism, providing a detailed look at the cause of segregation in multi-component and multi-mechanism situations.  The resulting technique allows the quantification of segregation magnitude, segregation pattern, and amount of each segregation mechanism present in the mixture.   Several mixtures were examined using this technique to provide a phase map of segregation.