(141i) System Size Dependent Rheology of Sheared Lamellar Phases

The rheology of a lamellar liquid crystalline medium under shear is studied using a two-dimensional mesoscale simulation technique which distinguishes between the hydrophobic and hydrophilic components of the lamellar phase. The dimensionless parameters in this model are the Reynolds number which is the ratio of inertia and viscosity, the Schmidt number which is the ratio of momentum and mass diffusion, an Ericksen number which provides the ratio of viscous stress which tend to deform the layers an elastic restoring stresses, the viscosity contrast between the hydrophilic and hydrophobic components and the ratio of the system size and the layer spacing. Two distinct types of structural evolution are observed depending on the Schmidt number. At high Schmidt number where momentum diffusion is faster than mass diffusion, shear tends to break and reform the layers; this results in a well-aligned background lamellar phase with embedded defects. The defects are annealed by the shear, resulting in a well ordered lamellar phase in the long time limit. At low Schmidt number where mass diffusion is faster than momentum diffusion, the layers are well formed locally in domains with random orientations. Shear tends to rotate and align the layers, but there is also the creation of defects due to shear, which results in a disordered steady state determined by a balance between the annealing and creation of defects. Complete ordering is not observed even at very long times. The average viscosity (ratio of stress and macroscopic strain rate) shows a strong dependence on system size, proportional to (L/λ)^3/2. The reason for this strong system size dependence is the divergence in the length scale of the region over which there is a distortion of layers due to a point defect, and the consequent divergence in the secondary flow caused due to the disturbance of the linear shear flow by the defect.