22 research outputs found
Viscoelastic Phase Separation in Shear Flow
We numerically investigate viscoelastic phase separation in polymer solutions
under shear using a time-dependent Ginzburg-Landau model. The gross variables
in our model are the polymer volume fraction and a conformation tensor. The
latter represents chain deformations and relaxes slowly on the rheological time
giving rise to a large viscoelastic stress. The polymer and the solvent obey
two-fluid dynamics in which the viscoelastic stress acts asymmetrically on the
polymer and, as a result, the stress and the diffusion are dynamically coupled.
Below the coexistence curve, interfaces appear with increasing the quench depth
and the solvent regions act as a lubricant. In these cases the composition
heterogeneity causes more enhanced viscoelastic heterogeneity and the
macroscopic stress is decreased at fixed applied shear rate. We find steady
two-phase states composed of the polymer-rich and solvent-rich regions, where
the characteristic domain size is inversely proportional to the average shear
stress for various shear rates. The deviatoric stress components exhibit large
temporal fluctuations. The normal stress difference can take negative values
transiently at weak shear.Comment: 16pages, 16figures, to be published in Phys.Rev.
Hydrodynamics of domain growth in nematic liquid crystals
We study the growth of aligned domains in nematic liquid crystals. Results
are obtained solving the Beris-Edwards equations of motion using the lattice
Boltzmann approach. Spatial anisotropy in the domain growth is shown to be a
consequence of the flow induced by the changing order parameter field
(backflow). The generalization of the results to the growth of a cylindrical
domain, which involves the dynamics of a defect ring, is discussed.Comment: 12 revtex-style pages, including 12 figures; small changes before
publicatio
An optimization principle for deriving nonequilibrium statistical models of Hamiltonian dynamics
A general method for deriving closed reduced models of Hamiltonian dynamical
systems is developed using techniques from optimization and statistical
estimation. As in standard projection operator methods, a set of resolved
variables is selected to capture the slow, macroscopic behavior of the system,
and the family of quasi-equilibrium probability densities on phase space
corresponding to these resolved variables is employed as a statistical model.
The macroscopic dynamics of the mean resolved variables is determined by
optimizing over paths of these probability densities. Specifically, a cost
function is introduced that quantifies the lack-of-fit of such paths to the
underlying microscopic dynamics; it is an ensemble-averaged, squared-norm of
the residual that results from submitting a path of trial densities to the
Liouville equation. The evolution of the macrostate is estimated by minimizing
the time integral of the cost function. The value function for this
optimization satisfies the associated Hamilton-Jacobi equation, and it
determines the optimal relation between the statistical parameters and the
irreversible fluxes of the resolved variables, thereby closing the reduced
dynamics. The resulting equations for the macroscopic variables have the
generic form of governing equations for nonequilibrium thermodynamics, and they
furnish a rational extension of the classical equations of linear irreversible
thermodynamics beyond the near-equilibrium regime. In particular, the value
function is a thermodynamic potential that extends the classical dissipation
function and supplies the nonlinear relation between thermodynamics forces and
fluxes
Continuum formulation of the Scheutjens-Fleer lattice statistical theory for homopolymer adsorption from solution
Homopolymer adsorption from a dilute solution on an interacting (attractive) surface under static equilibrium conditions is studied in the framework of a Hamiltonian model. The model makes use of the density of chain ends n1,e and utilizes the concept of the propagator G describing conformational probabilities to locally define the polymer segment density or volume fraction 驴; both n1,e and 驴 enter into the expression for the system free energy. The propagator G obeys the Edwards diffusion equation for walks in a self-consistent potential field. The equilibrium distribution of chain ends and, consequently, of chain conformational probabilities is found by minimizing the system free energy. This results in a set of model equations that constitute the exact continuum-space analog of the Scheutjens-Fleer (SF) lattice statistical theory for the adsorption of interacting chains. Since for distances too close to the surface the continuum formulation breaks down, the continuum model is here employed to describe the probability of chain configurations only for distances z greater than 2l, where l denotes the segment length, from the surface; instead, for distances z驴2l, the SF lattice model is utilized. Through this novel formulation, the lattice solution at z=2l provides the boundary condition for the continuum model. The resulting hybrid (lattice for distances z驴2l, continuum for distances z>2l) model is solved numerically through an efficient implementation of the pseudospectral collocation method. Representative results obtained with the new model and a direct application of the SF lattice model are extensively compared with each other and, in all cases studied, are found to be practically identical