41 research outputs found
Well-posedness of the Ericksen-Leslie system
In this paper, we prove the local well-posedness of the Ericksen-Leslie
system, and the global well-posednss for small initial data under the physical
constrain condition on the Leslie coefficients, which ensures that the energy
of the system is dissipated. Instead of the Ginzburg-Landau approximation, we
construct an approximate system with the dissipated energy based on a new
formulation of the system.Comment: 16 page
Coexistence and Phase Separation in Sheared Complex Fluids
We demonstrate how to construct dynamic phase diagrams for complex fluids
that undergo transitions under flow, in which the conserved composition
variable and the broken-symmetry order parameter (nematic, smectic,
crystalline, etc.) are coupled to shear rate. Our construction relies on a
selection criterion, the existence of a steady interface connecting two stable
homogeneous states. We use the (generalized) Doi model of lyotropic nematic
liquid crystals as a model system, but the method can be easily applied to
other systems, provided non-local effects are included.Comment: 4 pages REVTEX, 5 figures using epsf macros. To appear in Physical
Review E (Rapid Communications
Lattice Boltzmann Simulations of Liquid Crystal Hydrodynamics
We describe a lattice Boltzmann algorithm to simulate liquid crystal
hydrodynamics. The equations of motion are written in terms of a tensor order
parameter. This allows both the isotropic and the nematic phases to be
considered. Backflow effects and the hydrodynamics of topological defects are
naturally included in the simulations, as are viscoelastic properties such as
shear-thinning and shear-banding.Comment: 14 pages, 5 figures, Revte
Phase Separation of Rigid-Rod Suspensions in Shear Flow
We analyze the behavior of a suspension of rigid rod-like particles in shear
flow using a modified version of the Doi model, and construct diagrams for
phase coexistence under conditions of constant imposed stress and constant
imposed strain rate, among paranematic, flow-aligning nematic, and log-rolling
nematic states. We calculate the effective constitutive relations that would be
measured through the regime of phase separation into shear bands. We calculate
phase coexistence by examining the stability of interfacial steady states and
find a wide range of possible ``phase'' behaviors.Comment: 23 pages 19 figures, revised version to be published in Physical
Review