Abstract
The role of biaxiality in the dynamics of a nematic liquid crystal under shear flow is systematically examined within a rigid-rod model. The non-linear partial differential equation that governs the evolution of the orientational distribution function is solved numerically by using a Galerkin method on an expansion in spherical harmonics. Examples are given for various types of solutions and different values of the free parameters. The limit of low shear rates is further examined analytically on the basis of a relaxation equation for the alignment tensor of the second rank. Several qualitative features of the different types of solutions are derived. In the important case of in-plane tumbling at low shear rates a remarkable behaviour is found in the numerical calculations: namely, whenever the scalar order parameter reaches its equilibrium value and the in-plane angle is either zero or π/2, the evolution traverses a uniaxial state. An explanation is also given for this fact within our analytical model.
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