Channeling and stress during fluid and suspension flow in self-affine fractures.

The flow of fluids and particulate suspensions in realistic models of geological fractures is investigated by lattice Boltzmann numerical simulations. The walls are synthetic self-affine fractal surfaces combined to produce a tight fracture, the fluid is a viscous Newtonian liquid, and the particles are rigid noncolloidal solid spheres. One focus is channeling phenomena, where we compare the fracture aperture, the preferred paths for fluid flow, and the preferred paths for suspended particles. The preferred paths are found to be somewhat similar for pure fluid and particulates and not immediately related to the fracture aperture map. We further investigate the (tensor) stress exerted on the fracture walls. Wall roughness tends to decrease stress by reducing the flow velocities adjacent to it, an effect enhanced by the presence of particulates. Last, we examine the stress probability distributions and their spatial correlation functions.

Field-induced alignment of flexible polyelectrolytes in solution.

Molecular dynamics simulations are used to study dynamical coupling between conformational fluctuations of a highly charged flexible macromolecule and its surrounding ionic cloud. We find that the basic model of a polyelectrolyte as a chain of charged monomers captures the main experimental findings on the field-induced alignment of polyelectrolytes despite its simplicity. Contrary to current theories, the correlated local charge and field fluctuations in the vicinity of the macromolecule are found to dominate alignment along an external field. We suggest that short-lived monomer-counterion clustering can be probed by measuring the field-induced anisotropy of x-ray and neutron scattering from polymer solutions.

Dynamical clustering of counterions on flexible polyelectrolytes.

Molecular dynamics simulations are used to study the spatiotemporal dynamics of charge fluctuations around a polyelectrolyte molecule at charge densities above and below the classic counterion condensation threshold. Surprisingly, the counterions form weakly interacting clusters which exhibit slowly decaying short range orientational order. Local charge fluctuations create energy fluctuations at the order of k_(B)T that is sufficient to affect the polyelectrolyte interaction with an approaching ligand molecule. The predictions of the classical theory appear to be appropriate only over much longer time scales.

Interfacial slip in sheared polymer blends.

We have developed a dynamic self-consistent field theory, without any adjustable parameters, for unentangled polymer blends under shear. Our model accounts for the interaction between polymers, and enables one to compute the evolution of the local rheology, microstructure, and the conformations of the polymer chains under shear self-consistently. We use this model to study the interfacial dynamics in sheared polymer blends and make a quantitative comparison between this model and molecular dynamics simulations. We find good agreement between the two methods.

Dynamic self-consistent field theory for unentangled homopolymer fluids.

We present a lattice formulation of a dynamic self-consistent field (DSCF) theory that is capable of resolving interfacial structure, dynamics, and rheology in inhomogeneous, compressible melts and blends of unentangled homopolymer chains. The joint probability distribution of all the Kuhn segments in the fluid, interacting with adjacent segments and walls, is approximated by a product of one-body probabilities for free segments interacting solely with an external potential field that is determined self-consistently. The effect of flow on ideal chain conformations is modeled with finitely extensible, nonlinearly elastic dumbbells in the Peterlin approximation, and related to stepping probabilities in a random walk. Free segment and stepping probabilities generate statistical weights for chain conformations in a self-consistent field, and determine local volume fractions of chain segments. Flux balance across unit lattice cells yields mean field transport equations for the evolution of free segment probabilities and of momentum densities on the Kuhn length scale. Diffusive and viscous contributions to the fluxes arise from segmental hops modeled as a Markov process, with transition rates reflecting changes in segmental interaction, kinetic energy, and entropic contributions to the free energy under flow. We apply the DSCF equations to study both transient and steady-state interfacial structure, flow, and rheology in a sheared planar channel containing either a one-component melt or a phase-separated, two-component blend.