In charge-stabilized colloidal suspensions, highly charged macroions, dressed by strongly correlated counterions, carry an effective charge that can be substantially reduced (renormalized) from the bare charge. Interactions between dressed macroions are screened by weakly correlated counterions and salt ions. Thermodynamic and structural properties of colloidal suspensions depend sensitively on the magnitudes of both the effective charge and the effective screening constant. Combining a charge renormalization theory of effective electrostatic interactions with Monte Carlo simulations of a one-component model, we compute osmotic pressures and pair distribution functions of deionized colloidal suspensions. This computationally practical approach yields close agreement with corresponding results from large-scale simulations of the primitive model up to modest electrostatic coupling strengths.

We merge classical kinetic theories [M. Doi and S. F. Edwards, The Theory of Polymer Dynamics, 1986] for viscous dispersions of rigid rods, extended to semi-flexibility [A. R. Khokhlov and A. N. Semenov, Macromolecules, 17 (1984), pp. 2678-2685], and for Rouse flexible chains to model the hydrodynamics of polymer nano-rod composites (PNCs). A mean-field potential for the polymer-rod interface provides the key coupling between the two phases. We restrict this first study to two-dimensional conformational space. We solve the coupled set of Smoluchowski equations for three benchmark experiments. First we explore how rod semi-flexibility and the polymerrod interface alter the Onsager equilibrium phase diagram. Then we determine monodomain phase behavior of PNCs for imposed simple elongation and shear, respectively. These results inform the effects that each phase has on the other as parametric strengths of the interactions are varied in the context of the most basic rheological experiments.

The folding dynamics of small single-domain proteins is a current focus of simulations and experiments. Many of these proteins are 'two-state folders', i.e. proteins that fold rather directly from the denatured state to the native state, without populating metastable intermediate states. A central question is how to characterize the instable, partially folded conformations of two-state proteins, in particular the rate-limiting transition-state conformations between the denatured and the native state. These partially folded conformations are short-lived and cannot be observed directly in experiments. However, experimental data from detailed mutational analyses of the folding dynamics provide indirect access to transition states. The interpretation of these data, in particular the reconstruction of transition-state conformations, requires simulation and modeling. The traditional interpretation of the mutational data aims to reconstruct the degree of structure formation of individual residues in the transition state, while a novel interpretation aims at degrees of structure formation of cooperative substructures such as α-helices and β-hairpins. By splitting up mutation-induced free energies into secondary and tertiary structural components, the novel interpretation resolves some of the inconsistencies of the traditional interpretation.

A comprehensive modeling and simulation study of the first-order isotropic/smectic-A transition is presented and applied to phase diagram computation and two-dimensional spherulite growth. An approach based on nonlinear optimization, that incorporates experimental data (from 12CB, dodecyl-cyanobiphenyl), is used to determine physically realistic model parameters. These parameters are then used in conjunction with an optimized phase diagram computation method. Additionally, a time-dependent formulation is presented and applied to the study of two-dimensional smectic-A spherulite growth. These results show the growth kinetics and defect dynamics of nanoscale smectic-A spherulite growth in an isotropic phase with an initially radial layer configuration.

This paper is concerned with the numerical investigation of a macroscopic model for complex fluids in “1+2” dimension case. We consider the planar pressure driven flow where the direction of the molecules is constrained in the shear plane. The modified Crank-Nicolson finite difference scheme satisfying a discrete energy law will be developed. By using this scheme, it is observed numerically that the direction of the molecules will tumble from the boundary layer and later on the inner layer with a much longer time period. This is consistent with the theoretical prediction. Moreover, we find some complex phenomena, where the tumbling rises from boundary layer and is then embedded into the interior area more clearly when the viscosity coefficient µ of the macro flow has a larger value. The norm of the molecular director d will endure greater change as well. This implies that the viscosity of flow plays the role of an accelerator in the whole complex fluids. Comparing these results with the theoretical analysis, we can find that the gradient of the velocity has direct impact on the tumbling phenomena. These results show that the proposed scheme is capable of exploring some physical phenomena embedded in the macro-micro model.

Phase-field models provide a way to model fluid interfaces as having finite thickness; the interface between two immiscible fluids is treated as a thin mixing layer across which physical properties vary steeply but continuously. One of the main challenges of this approach is in resolving the sharp gradients at the interface. In this paper, moving finite-element methods are used to simulate interfacial dynamics of two-phase viscoelastic flows. The finite-element scheme can easily accommodates complex flow geometry and the moving mesh strategy can cluster more grid points near the thin interfacial areas where the solutions have large gradients. A diffused monitor function is used to ensure high quality meshes near the interface. Several numerical experiments are carried out to demonstrate the effectiveness of the moving mesh strategy.

Phase separation of a two-dimensional van der Waals fluid subject to a gravitational force is studied by numerical simulations based on lattice Boltzmann methods implemented with a finite difference scheme. A growth exponent α=1 is measured in the direction of the external force.

The Cahn-Hilliard equation is often used to describe evolution of phase boundaries in phase field models for multiphase fluids. In this paper, we compare the use of the Cahn-Hilliard equation (of a constant mobility) for the phase variable with that of the singular or modified Cahn-Hilliard equation (of a variable mobility) in the context of physical derivation of the transport equation and numerical simulations of immiscible binary fluids. We show numerically that (i). both equations work fine for interfaces of small to moderate curvature in short to intermediate time scales; (ii) the Cahn-Hilliard equation renders strong dissipation in simulations of small droplets leading to dissolution of small droplets into the surrounding fluid and/or absorption of small droplets by larger droplets nearby, an artifact for immiscible binary fluids; whereas, the singular Cahn-Hilliard equation can significantly reduce the numerical dissipation around small droplets to yield physically acceptable results in intermediate time scales; (iii) the size of droplets that can be simulated by the Cahn-Hilliard equations scale inversely with the strength of the mixing free energy. Since the intermediate timescale is the time scale of interest in most transient fluid simulations, the singular Cahn-Hilliard equation proves to be the more accurate phase transporting equation for immiscible binary fluids.

A general nonhomogeneous extension of the Doi's kinetic theory with translational diffusion and nonlocal potential is proposed to describe the microstructures and defect dynamics of Liquid Crystal Polymer (LCP) solutions. The long-range elasticity of polymer molecules is depicted by a kernel type potential, from which one can derive the well-known Marrucci-Greco potential with weak spatial distortion assumption. Applying quasi-equilibrium closure approximation, we get a second-order moment model for isotropic long-range elasticity, and this reduced moment model maintains the energy dissipation. Implemented by the invariant-based fitting method, the moment model is a decent tool for numerical simulations of defect dynamics and texture evolution in LCP solutions. The numerical results of in-plane rotational case show that the reduced second-order moment model qualitatively predicts complicated nonhomogeneous director dynamics under moderate nematic potential strength, and the translational diffusion plays an important role in defect dynamics.