(244d) Defect Dynamics in a Sheared Lamellar Mesophase

Lamellar mesophases typically contain alternating water/surfactant, water/oil/surfactant layers or immiscible segments of a block coopolymer. Under shear, one would expect the layers to align with unit normal velocity gradient direction. In this alignment, the fluid should have viscosity only a few times that of water by the inverse sum rule for the viscosity. However, real lamellar fluids have viscosities that are orders of magnitudes higher than water.  The reason for this is the spontaneous generation of disorder in the system due to applied shear. For sufficiently large system sizes, the final steady state is not a perfectly aligned state, but rather a disordered state where there is a dynamical balance between the annealing of defects under shear and the spontaneous creation of defects. In the present analysis, order parameters are used to quantify the extent of disorder in the system, and these are found to be linked to the rheology. The motion and interaction of edge dislocations, and the mechanism of defect cancellation and defect creation, and their effects on rheology are analysed. Edge dislocations acts as centers of elastic stress concentration as in the case of solids, but they also acts as flow generating centers and they generate liquid stresses as well in lamellar mesophases. These are treated in as defect suspensions (similar to particle suspensions) with highly anisotropic interactions and creation/destruction mechanisms to model their effect on rheology.