shear alignment and defect dynamics in three-dimensional lamellar mesophase.

The structure-rheology relation in a sheared lamellar mesophase is studied by varying Ericksen number Er (viscous/elastic stress) and Schmidt number Sc (momentum/mass diffusivity) using a mesoscale model of free-energy functional for concentration modulation. The lattice Boltzmann method is used to solve coupled concentration and momentum equations for a three-dimensional system. Due to high layer stiffness, the maximum viscosity is an order of magnitude higher than the steady state value at low Er = 0.003, though there is layer alignment and low viscosity in the final steady state.  A salient observation in this regime is that the layers could align in the cross-stream and span-wise directions.  At moderately high Er = 0.03, there is perfect alignment at steady state for low Sc, because layers formed due to rapid mass diffusion align in the vorticity direction. For Er = 0.03, Sc > 1 and Er = 0.3, the momentum diffusion is faster than the mass diffusion, and the local shear breaks and reforms the layers. That results in the steady state defect density determined by the rates of breakage and reformation. These defects appear on planes whose normal is parallel to the vorticity direction, and hence they do not enhance the effective viscosity.