Flow Properties of Smectic A Liquid Crystals

Characteristic flow geometries for smectic A phases. A pressure head Ap promotes the flow, (a) Velocity parallel and gradient is perpendicular to the layers, (b) Velocity and the gradient are parallel to the layers, (c) Both the velocity and the gradient are perpendicular to the layers. 

In geometry (b) one does not find a purely viscous behavior, but rather that of a Bingham fluid, and the shear stress then can be described as  

Experimentally, J] was found to be in the order of nematic viscosity, with value depending on the shear rate and history, indicating the effect of defects on the flow properties. It was also found that IN/m, which is comparable to azz = B na/L) n-3N/m with n 3, where a is the layer thickness, and L is the width of the film ( 1 cm). Because (Tq, tire effect of residual stress may explain the observations. We will see a bit later, however, that more subtle explanation of the existence of may be connected to the breakdown of the hydrod5mamics. Results obtained under periodic shears, however, show pure viscous behavior with no frequency dependence. This shows the importance of working with small amplitudes, which reduces the residual effects due to the thickness variations and of the nonlinear effects. 

In geometry (c), close to the boundary in a range controlled by tire characteristic length S, which is in the order of molecular size, the speed varies from zero given by the boimdary condition to the imiform velocity of the bulk dictated by the plug flow. In this range, the viscous friction is important. 

This range has been called the distal region. Although the layer compression modulus is about two orders of magnitude larger than in tire short-pitch cholesterics (see (4.31)), permeation-type flow similar to that observed in cholesterics was observed near the nematic phase, ° shovdng that the apparent viscosity maybe smaller than in the cholesteric, probably due to defects that cause plastic behavior. This and measurements imder periodic deformations indicate the importance of layer defects, which are hard to regulate. 

---