Multi-scale Modelling of Lamellar Mesophases

Surfactants are amphiphilic molecules which self-assemble at the interface in oil-water-surfactant mixtures such that the hydrophobic part, called tail, stays in oil and the remaining part, called head, resides in hydrophilic en-vironment. Depending upon concentration of individual components, these mixtures form several microphases, such as bilayers, micelles, columnar and lamellar phases. A lamellar phase, at equilibrium, is made up of alternat-ing layers of water and oil separated by surfactants, or of alternate layers of water and surfactant bilayers such that the hydrophilic heads are in contact with water. This equilibrium state is rarely achieved in macroscopic samples due to thermodynamic and kinetic constraints; instead, a lamellar fluid is usually disordered with a large number of defects. These defects have significant effect on the flow behaviour of the lamellar mesophase systems. They are known to alter the flow field, resulting stresses and in turn could get distorted or annihilated by the flow. In present work, we analyse this two way coupling between lamellar structure and flow field. The structural and rheological evolution of an initially disordered lamellar phase system under a shear flow is examined using a mesoscale model based on a free energy functional for the concentration field, which is the scaled difference in the concentration between the hydrophilic and hydrophobic components. Two distinct modes of structural evolution are observed depending only on Peclet number, which ratio of inertial forces to mass diffusivity, in-dependent of system size. At low Peclet number, local domains are formed which are then rotated and stretched by shear. A balance between defect creation and annihilation is reached due to which the system never reaches the equilibrium layer configuration. In the opposite limit, partially formed layers break and reform so as to form a nearly aligned lamellar phase con-figuration with residual defects. Viscosity of lamellar phase system increases with layer moduli, differences in viscosity of individual components, fluidity of the lamellae due to shear banding and defect pinning. These factors however, do not have any effect on alignment mechanism