Mesoscale Modelling of sheared lamellar mesophases
The lamellar phase or smectic lyotropic liquid crystalline medium, which is made up of alternating flat sheets of water and surfactant bilayers shearing past each other in an imposed flow. Surprisingly, In practical applications, the viscosity is two to three orders of magnitude larger than that of water. This is because the stacking of the bilayers is not perfect, and there is disorder and different kinds of defects like edge, screw, and focal conic defects. A mesoscopic continuum model is developed consisting of free-energy functional for concentration modulation. The structure-rheology relationship is studied for lamellar systems by simultaneous solution of the coupled advection-diffusion and momentum equations by Lattice Boltzmann simulation method. In this simulation study, the coupling between the structure and rheology of a sheared lamellar phase is examined in a cubic simulation box by varying Er(viscous stress/elastic stress) and product of Sc(momentum diffusivity/mass diffusivity) and Σ (ratio of inertial and viscous force at layer scale. At low Er, when diffusion time is smaller compared to the inverse of strain rate, there is the formation of local misaligned layer-like domains, which are stretched and rotated by imposed shear. There is near-perfect ordering with titled layers and isolated defects which causes a high excess viscosity. At high Er, the formation of layers is disrupted by shear. Cylindrical structures aligned along the flow are formed after tens of strain units. The system does not reach a perfectly aligned state even after hundreds of strains as defects persist at steady state. It is also observed dynamics is dependant on ScΣ only at moderate Er. The effect of viscosity contrast between the hydrophobic and hydrophilic parts on the dynamics has also been studied three dimensions. At high Er, the viscosity contrast has no effect on the concentration evolution as initial shear-mixed states has hardly any viscosity variation. At moderate Er the coarsening after layer formation depends on viscosity contrast which results different steady state disordered steady-state configurations with high excess viscosity compared to no contrast. At Low Er at low ScΣ the steady state configuration has tilted layers parallel always which otherwise stochastic depending on initial condition. The interaction of edge-defects in two-dimensions is also studied by shearing of a configuration with two edge defects of opposite signs at a finite cross-stream separation. The interaction dynamics and rheological behavior are very different when the portion pinned between defects are extended compared to when it is compressed.