(368f) Quantifying the Root Causes of Segregation in Multi-Mechanism Segregation Systems

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 where more than one cause of segregation is present. It would be very useful to understand and quantify the amount of each type of segregation present within a given material on a component basis. This understanding will allow formulators to perform simple tests and determine the root cause(s) of segregation and then determine what to change in the formulation to mitigate the segregation. This paper suggests a framework to accomplish that task. Modified versions of the convection dispersion equations can be used to understand segregation of a particular mechanism on a component-by-component basis. In these equations segregation is often handled by adding a segregation flux term to offset the symmetric dispersion term. This segregation flux velocity is always directional and there are different segregation flux terms for each type of segregation occurring in the system.

This paper examines the relationship between segregation velocities when there are multiple causes of segregation. The main question to answer is: what percent of the overall segregation dispersion coefficients are due to the individual mechanisms of segregation? In dispersion, the local convective velocities distribute in a symmetric pattern around the overall average convective velocity. When segregation flux terms are added to the dispersion equations they cause a skewed concentration distribution off of those caused by average convective velocities for each component in the system. 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 then 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 a component-by-component characterization showing how much segregation is caused by a prescribed set of individual mechanisms in a mixture consisting of more than two components.