Hydrodynamics of smectic-C liquid crystals: Field and flow induced instabilities in confined geometries

Following the Ericksen-Leslie approach, we formulate a complete nonlinear macroscopic theory of the isothermal hydrodynamics of smectic-C liquid crystals. We assume an asymmetric stress tensor and incorporate the essential features of a hydrodynamic theory of a smectic phase, i.e., permeation and variations in layer spacing. Using Onsager's reciprocity relations, we find that entropy production is described by 16 viscosity coefficients and a permeation constant associated with the dissipative dynamics of the layered system. We study the reorientation dynamics of the c vector under the destabilizing influence of an external field. We stress that permeation is important and that transverse flows along and normal to the layers exist. We have also studied certain instabilities that can arise in shear hows. As a consequence of permeation, in Poiseuille flow with the layers parallel to the plates, we find that the length of the inlet section can be very large being many times the lateral dimension. When the layers are perpendicular to the plates, an analog of the nematic Hall effect is shown to exist even in the absence of an aligning external field.