Numerical simulation of rodlike polymers in extensional and sink/source flows using the order-parameter version of Doi’s theory

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Abstract
Doi’s kinetic equation for the order-parameter tensor is utilized to study the molecular orientation, stability, stress, and pressure distributions in sink/source flows of solutions of rodlike polymers. In these flows, the velocity field can be determined without having to solve the kinetic equation simultaneously with the fluid-dynamical equation of motion. The steady state solution is obtained by Newton’s procedure. The transient problem is solved by Runge–Kutta’s method. All of the bifurcated solutions are tested for their dynamical stability, and the results reveal that the most stable distribution of molecular orientation is axisymmetric (or nearly axisymmetric), with the most probable orientation being the axis of symmetry. For solutions which can be nematic at equilibrium, the simulation also predicts a sudden drop in stress, followed by an immediate recovery, if the initial molecular orientation in sink flow is not in the principal direction of stretching.