Flowing smectics with defects

In this talk, a simple rheology theory of smectic liquid crystals is proposed. The stress induced motion of the dislocation line has a close relation to the layer tilting. The conventional Peach-Koehler force predicts that, the layers originally parallel to the shear plane will tilt toward the unstable direction under the flow. Subsequently convections further tilt and also dilate the layers. The layer dilation eventually will cause the layer undulation, which then presumably leads to the formation of more dislocation lines. The shear stress is shown to be proportional to the screw density. We argue that, in the steady state, the typical defect loop size is decreasing with the increasing shear rate. This decreasing loop size causes the liquid crystal to shear thin. The shear thinning exponent is found to be 2/3. The shear stress fluctuation is also predicted to have a well defined frequency.