A comparison of closure approximations for the Doi theory of LCPs

The behavior of the Doi model for liquid crystalline polymers, using a closure approximation due to Hinch and Leal (HL1), is studied and compared to the behavior using the simple quadratic closure. It is found that the HL1 closure gives some aphysical results for simple shear flow, but describes a much richer solution structure for this flow than the quadratic closure, including tumbling and wagging phenomena that are found both experimentally, and in solutions of the Doi theory without closure approximations. However, there is a very sharp transition in the predicted behavior as the flow is changed very slightly to one in which the strain rate exceeds the vorticity: the orientation distribution becomes flow aligning for all values of the nematic potential, and the phenomena of tumbling and wagging are suppressed completely. Although the quadratic closure model does not exhibit tumbling in simple shear flow, and thus has been sharply criticized as an approximation of the Doi model, it does exhibit tumblin...