(142cw) Rheology of Lamellar Mesophases

Lamellar fluids typically contain alternating water/surfactant or water/oil/surfactant layers in equilibrium. Under shear, one would expect the layers to align with
unit normal velocity gradient direction. In this alignment, the fluid should have viscosity only a few times that of water by the inverse sum rule for the viscosity. However, real lamellar fluids have viscosities that are several orders of magnitudes higher than water. For this reason, lamellar mesophases are used in products which require very high viscosity, such as hair conditioners and butter substitutes. The reason for these high viscosity is a puzzle.

The modeling of lamellar mesophases is complicated due to the two-way coupling between structure and rheology. A perfectly aligned lamellar phase, for example, exhibits fluid like behaviour when the normal to the lamellae is along the shear or vorticity direction, but has a solid like resistance to flow when the normal is along the flow direction. In addition, even though a perfect defect free stack of layers is the final equilibrium state, real samples are rarely defect free due to kinetic constraints. The lamellar spacing is typically small compared to macroscopic scales (the distance between layers in lyotropic liquid crystalline phases is usually a few hundred Angstroms and a macroscopic sample contains $10^4-10^6$ lamellae), and so a flowing lamellar mesophase cannot be modeled using a microscopic description. It is necessary to use different simulation techniques (molecular, mesoscale, macroscale) for accurately capturing the rheology of lamellar phases.

First, we present a multiscale modeling methodology to link molecular and mesoscale simulations. A mesoscale model based on a concentration field (phase field) description is then used to examine the rheology of a lamellar phase under a linear shear flow. For sufficiently large system sizes, the final steady state is not a perfectly aligned state, but rather a disordered state where there is a dynamical balance between the annealing of defects under shear and
the spontaneous creation of defects. There are two different defect creation mechanisms observed in our simulations, an undulation mechanism along the extension axis and a compressional mechanism along the compression axis. Order parameters are used to quantify the extent of disorder in the system, and these are found to be linked to the rheology.