Distributive Mixing in Extruders

Abstract

Distributive laminar mixing refers to the physical process of two fluids being blended such that the physical separation distances are reduced to a scale where diffusion, or chemical reaction, can occur. The mathematics and nature of distributive mixing have been expressed in terms of the kinematics of the flow — Spencer and Wiley [1] and Erwin [2, 3] — and the continuum mechanics — Aref [4] and Ottino [5,6] Each approach describes “mixing” as the growth of an interfacial line or interface; each approach offers a unique view. The kinematic approach provides an overall view to the mixing process and an understanding as to the nature of mixing. This approach allows one to directly see whether a mixer is “linear” (i.e.; the growth of interfacial area is linear with the applied shear strain) or whether it is “exponential.” In spite of the limitations of the two-dimensional assumptions required in the theoretical development, this approach enables the practitioner insight into the nature of the flow, even for complex three-dimensional flows. The advantage of continuum mechanics is that it provides the mathematics necessary to examine the details of the flow. Given the current computational power readily available and given the current requirements for very tight product properties, knowledge of every aspect of the flow provides the wherewithal to relate the flow dynamics with the product properties. For example, a concern which has become very large is the 1–5% of product that is not acceptable in a process. Continuum mechanics can determine the aspects of the flow which could be causing that result, which can lead to appropriate changes in the flow geometry or operating conditions.