Defect interactions in a two-dimensional sheared lamellar mesophase.

The interaction between two edge dislocations in a sheared lyotropic lamellar liquid-crystalline medium is examined. The model is a mesoscale hydrodynamic model based on a free-energy functional that is minimised for a sinusoidal concentration modulation coupled with concentration and momentum equations. The defect dynamics are analysed as a function of the system size and the Ericksen number, the ratio of the shear stress and the characteristic free-energy density for deformation. Three different regimes are observed as the Ericksen number is increased when the edge dislocations are sheared towards each other, such that there is compression of layers between the defects: (a) defect motion that reduces the cross-stream separation till there is a steady spacing with plug flow between the defects, (b) defect attraction and cancellation resulting in a well-aligned state, and (c) defect creation due to a compressional instability between the defects resulting in an increase in the disorder. When the edge dislocations are sheared away from each other, such that there is extension of the layers between the defects, two distinct regimes are observed as the Ericksen number is increased: (a) bending of layers and a plug flow between the defects at their initial separation, and (b) buckling of the layers leading to creation of more defects and a dynamical steady state between defect creation and cancellation. These regimes are found to be robust for different values of the system size, from 32 to 128 layers, and for different values of the dimensionless groups that characterise the ratio of mass/momentum convection and diffusion.