Theoretical Investigation of the Shear Flow of Nematic Liquid Crystals with the Leslie Viscosityα3> 0: Hydrodynamic Analogue of First Order Phase Transitions

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Abstract
The shear flow of nematic Liquid crystals with a positive value of the Leslie viscosity α3 is studied theoretically. Under the assumption that the director will remain in the plane of shear, the equations governing the flow are solved numerically and the director- and velocity-profile are calculated. The validity of this “in-plane” assumption is discussed, and it is shown that there are at least two situations where it is correct. For some values of the shear the solution of the equations is multi-valued. By study of the entropy production of the system it is deduced which one of these solutions will be adopted by the system. It is also demonstrated that as a consequence of these multi-valued solutions the system in some cases will behave like a system is undergoing a first-order phase transition.

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