Solutions of the Smoluchowski Equation for Nematic Polymers under Imposed Fields
Abstract: We solve the Smoluchowski equation for nematic polymers and suspensions under imposed elongational flow fields, magnetic or electric fields. We show that the equation can be cast into a generic form under the three imposed fields and, in all three cases, we show that the probability density function solution is of the Boltzmann type, parameterized by two order parameters and the material parameters, where the order parameters satisfy two algebraic equations. Then, all order parameters solution can be studied by solving the algebraic equations and their stability are inferred from the free energy. The solution method is extended to dilute solutions of nematic polymers under imposed electric field. The solution