THE RIGID-ROD MODEL FOR NEMATIC POLYMERS - TESTING CLOSURE APPROXIMATIONS WITH BIFURCATION-ANALYSIS

The rigid rod model has been proven successful in predicting the rheol ogical response to rodlike polymers in the nematic phase. The model ca n be reduced to constitutive equations written in terms of a set of fi rst-order ordinary differential equations, provided that a mathematica l approximation required to close the problem is introduced. These con stitutive equations are attractive as they are suitable for fast numer ical processing. The required closure approximation, however, may have profound effects on the capabilities of the constitutive equation to retain the features of the original model. A method based on the bifur cation analysis is proposed as an effective test of constitutive equat ions. As an example, the bifurcation analysis of a particular constitu tive equation is presented, and the results are compared with the bifu rcation pattern of the exact model.