(513j) System Size Dependence of the Structure and Rheology in a Sheared Lamellar Liquidcrystalline Medium | AIChE

(513j) System Size Dependence of the Structure and Rheology in a Sheared Lamellar Liquidcrystalline Medium


Kumaran, P. V. - Presenter, Indian Institute of Science
Jaju, S., Indian Institute of Science
The shear alignment and rheology of a sheared lamellar liquid crystalline system is studied to determine the effect of system size on the rheology. A mesoscale model based on a phase field representation of the concentration field and a free energy functional is used to obtain a sinusoidal modulation of the concentration field at equilibrium. The coupled concentration and momentum equations are solved to determine the evolution of the lamellar phase from an initially disordered state. The relevant dimensionless parameters are a dimensionless parameter Σ = (A λ2 / ρ ν2), the Schmidt number (ν / D), the Reynolds number (γ L2 / ν), a parameter μr which represents the relative viscosity of the hydrophilic and hydrophobic components, and the ratio of system size and layer spacing (L/λ), where A is the energy density in the free energy functional which is proportional to the compression modulus, and ρ, ν and D are the density, kinematic viscosity (ratio of viscosity and density) and the mass diffusivity. There are two qualitatively different modes for the structural evolution the intermediate range of Σ depending only
on the combination Sc Σ, and independent of system size. For Sc Σ 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 Σ greater than about 10, layers are deformed by the mean shear before they are fully formed, and a well aligned lamellar phase with edge dislocations 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 system size proportional to (L/λ)3/2. For large values of Σ, 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 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 γ-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.