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The structure-rheology relationship in the shear alignment of a lamellar fluid is studied using a mesoscale model which provides access to the lamellar configurations and the rheology. Based on the equations and free energy functional, the complete set of dimensionless groups that characterize the system are the Reynolds number (rho gamma L-2/mu), the Schmidt number (mu/rho D), the Ericksen number (mu(gamma)/B), the interface sharpness parameter r, the ratio of the viscosities of the hydrophilic and hydrophobic parts mu(r), and the ratio of the system size and layer spacing (L/lambda). Here, rho and mu are the fluid density and average viscosity, (gamma) over dot is the applied strain rate, D is the coefficient of diffusion, B is the compression modulus, mu(r) is the maximum difference in the viscosity of the hydrophilic and hydrophobic parts divided by the average viscosity, and L is the system size in the cross-stream direction. The lattice Boltzmann method is used to solve the concentration and momentum equations for a two dimensional system of moderate size (L/lambda = 32) and for a low Reynolds number, and the other parameters are systematically varied to examine the qualitative features of the structure and viscosity evolution in different regimes. At low Schmidt numbers where mass diffusion is faster than momentum diffusion, there is fast local formation of randomly aligned domains with ``grain boundaries,'' which are rotated by the shear flow to align along the extensional axis as time increases. This configuration offers a high resistance to flow, and the layers do not align in the flow direction even after 1000 strain units, resulting in a viscosity higher than that for an aligned lamellar phase. At high Schmidt numbers where momentum diffusion is fast, the shear flow disrupts layers before they are fully formed by diffusion, and alignment takes place by the breakage and reformation of layers by shear, resulting in defects (edge dislocations) embedded in a background of nearly aligned layers. At high Ericksen number where the viscous forces are large compared to the restoring forces due to layer compression and bending, shear tends to homogenize the concentration field, and the viscosity decreases significantly. At very high Ericksen number, shear even disrupts the layering of the lamellar phase. At low Ericksen number, shear results in the formation of well aligned layers with edge dislocations. However, these edge dislocations take a long time to anneal; the relatively small misalignment due to the defects results in a large increase in viscosity due to high layer stiffness and due to shear localization, because the layers between defects get pinned and move as a plug with no shear. An increase in the viscosity contrast between the hydrophilic and hydrophobic parts does not alter the structural characteristics during alignment. However, there is a significant increase in the viscosity, due to pinning of the layers between defects, which results in a plug flow between defects and a localization of the shear to a part of the domain.

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. The dimensionless numbers which affect the shear evolution are the Reynolds number (((gamma) over bar )over dotL(2) = nu), the Schmidt number (nu/D), a dimensionless parameter Sigma = (A lambda(2)/rho nu(2)), a parameter mu(r) which represents the viscosity contrast between the hydrophilic and hydrophobic components, and (L/lambda), the ratio of system size and layer spacing. Here, rho, nu, and D are the density, kinematic viscosity (ratio of viscosity and density), and the mass diffusivity, and A is the energy density in the free energy functional which is proportional to the compression modulus. Two distinct modes of structural evolution are observed for moderate values of the parameter Sigma depending only on the combination Sc Sigma and independent of system size. For Sc Sigma less than about 10, the layers tend to form before they are deformed by the mean shear, and layered but misaligned domains are initially formed, and these are deformed and rotated by the flow. In this case, the excess viscosity (difference between the viscosity and that for an aligned state) does not decrease to zero even after 1000 strain units, but appears to plateau to a steady state value. For Sc Sigma greater than about 10, layers are deformed by the mean shear before they are fully formed, and a well aligned lamellar phase with edge dislocation orders completely due to the cancellation of dislocations. The excess viscosity scales as t(-1) in the long time limit. The maximum macroscopic viscosity (ratio of total stress and average strain rate over the entire sample) during the alignment process increases with the system size proportional to (L/lambda)(3/2). For large values of Sigma, there is localisation of shear at the walls, and the bulk of the sample moves as a block. The thickness of the shearing region appears to be invariant with the system size, leading to an increase of viscosity proportional to L. The time for structural evolution is found to be the inverse of the strain rate (gamma)over dot(-1). In the case of a significant viscosity contrast between the hydrophilic and hydrophobic parts, the average viscosity increases by 1-2 orders of magnitude due to the defect pinning mechanism, where the regions between defects move as a block, and shear localisation at the wall. Published by AIP Publishing.