Isothermal Hydrodynamics of Orthorhombic Nematics

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Abstract
Differential equations governing elastic and flow behaviour of compressible orthorhombic biaxial nematics are derived using the Ericksen-Leslie approach for uniaxial nematics. The preferred direction of orientation is represented by a mutually orthogonal triad of unit vectors (directors), each of which is a diad axis of symmetry. The expression for non-dissipative stress is deduced as a consequence of entropy inequality; the free energy density is found to satisfy a symmetry relation similar to that for uniaxial nematics. The expression for viscous stress derived on general symmetry assumptions depends on 21 viscosity coefficients. Use of the dissipative function approach reduces this number to 15 via three Onsager relations and three symmetry relations; the viscous stress becomes identical to that derived by Saupe.2 Under uniaxial symmetry about one director, the expression for the viscous stress reduces to that for a compressible uniaxial nematic. It seems possible to determine combinations of some of the viscosity coefficients through the determination of apparent viscosity in shear flow and plane Poiseuille flow. It also seems reasonable to expect transverse flow effects in plane Poiseuille flow, similar to those observed for uniaxial nematics.

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