Modeling of Continuous Mixers in Polymer Processing

The numerical modeling of creeping flow and continuous mixing in polymer processing equipment is considered. The decoupling of axial and transverse flow problems is the main subject of analysis. The conditions under which and the procedures whereby a steady three-dimensional mixing problem can be modeled via numerical procedures in two dimensions are discussed. The flow through a Kenics Static Mixer is chosen as a sample problem. Symmetry is exploited by formulating the problem in a nonorthogonal helical coordinate system, and a splitting method is devised for the resulting finite-difference equations which solves the axial and transverse problems alternately until convergence is reached. Three criteria are postulated as necessary and sufficient conditions for such decoupling. Finally, a method is presented whereby the result of the flow analysis can be used to model mixing. Graphical representations of the progress of mixing with down-channel displacement in the Kenics are obtained, and its mechanism of mixing is discussed.