Equations governing the flow behavior of Sm-C and Sm-${\mathit{C}}^{\mathrm{*}}$ liquid crystals are derived. It is shown that the general theory for the description of the macroscopic flow properties of the system demands 20 viscosity coefficients. Using thermodynamic arguments, one can show that these coefficients must fulfill certain restrictions in terms of inequalities and also, from symmetry arguments, that a specific tilt angle dependence can be assigned to them. With the Sm-C stress tensor as a starting point we discuss the concept of viscous torques. We define the rotational viscosity of the system and write down the proper equations governing the shear flow behavior for two different geometries. Using these equations we discuss the concept of flow alignment and define the effective viscosities of the system. We also show that in most cases backflow (flow induced by director rotations), as well as transverse flow effects (flow or permeation perpendicular to the shear plane induced by the shear), is associated with the macroscopic flow.

• Received 23 March 1994

DOI:https://doi.org/10.1103/PhysRevE.51.4509