Theory for the band structures in liquid crystal polymers under shear

Abstract

A theory for the shear flow instability in a liquid crystal aligned by the initial flow is presented. We have investigated a periodic distortion of the director and the velocity field in the plane perpendicular to the velocity gradient. We present solutions for the director and velocity field and make a connection with the optical image observed under a polarizing microscope. We include the convective terms in the basic equations neglected previously, and show that they alter the values of the critical parameters, but do not change the instability mechanism. Comparison with experimental data is made and further experiments are suggested.