The relationship between structure and rheology in a three-dimensional sheared lamellar mesophase

Abstract

The evolution of a lamellar mesophase from an initially disordered state under shear is examined using simulations of a mesoscale model based on a concentration field ψ that distinguishes the hydrophilic and hydrophobic components. The Landau–Ginzburg free-energy functional is augmented by a term that is minimised for sinusoidal modulations in the concentration field with wavelength λ = (2π/k), and the dynamical equations are the model H equations. The structure and rheology are determined by the relative magnitudes of the diffusion time for coarsening, (λ²/D) and the inverse of the strain rate ⁻¹, and the Ericksen number, which is the ratio of the shear stress and the layer stiffness. When the diffusion time is small compared with the inverse of the strain rate, there is a local formation of misaligned layers, which are deformed by the imposed flow. There is near-perfect ordering with isolated defects at low values of the Ericksen number, but the defects result in a significant increase in viscosity due to the high layer stiffness. At high values of the Ericksen number, the concentration field is deformed by the mean shear before layers form via diffusion. Cylindrical structures aligned along the flow direction form after about 8–10 strain units, and these evolve into layers with disorder through diffusion perpendicular to the flow. The layers are not perfectly ordered, even after hundreds of strain units, due to the creation and destruction of defects via shear. The excess viscosity is low because the layer stiffness is small compared with the applied shear at a high Ericksen number. This study provides guidance on how the material parameters and imposed flow can be tailored to achieve the desired rheological behaviour.