Incompressibility Conditions in Liquid Crystals

We discuss the implications of the incompressibility approximation on the num-ber of relevant transport parameters, like viscosities, flow alignment coefficients, and rotational viscosities in uniaxial and biaxial nematic liquid crystals. A comparison between the hydrodynamic and the Leslie-Ericksen approach is given. Agreement is found, if in the latter description a redefinition of the pressure is assumed. For sys-tems with positional order, like smectic and columnar liquid crystals and crystals, we show that, generally, incompressibility does not imply that the displacement field is source-free. PACS: 05.70.Ln, 46.05.+b, 83.10.-y