Equilibrium Dynamics of Microemulsion and Sponge Phases

The dynamic structure factor $G({\bf k},\omega)$ is studied in a time-dependent Ginzburg-Landau model for microemulsion and sponge phases in thermal equilibrium by field-theoretic perturbation methods. In bulk contrast, we find that for sufficiently small viscosity $\eta$, the structure factor develops a peak at non-zero frequency $\omega$, for fixed wavenumber $k$ with $k_0 < k {< \atop \sim} q$. Here, $2\pi/q$ is the typical domain size of oil- and water-regions in a microemulsion, and $k_0 \sim \eta q^2$. This implies that the intermediate scattering function, $G({\bf k}, t)$, {\it oscillates} in time. We give a simple explanation, based on the Navier-Stokes equation, for these temporal oscillations by considering the flow through a tube of radius $R \simeq \pi/q$, with a radius-dependent tension.Comment: 24 pages, LaTex, 11 Figures on request; J. Phys. II France 4 (1994) to be publishe

Analytic vortex solutions in an unusual Mexican hat potential

We introduce an unusual Mexican hat potential, a piecewise parabolic one, and we show that its vortex solutions can be found analytically, in contrast to the case of the standard Psi^4 field theory.Comment: 4 pages and 1 figure (missing in this version

Stability of bicontinuous cubic phases in ternary amphiphilic systems with spontaneous curvature

We study the phase behavior of ternary amphiphilic systems in the framework of a curvature model with non-vanishing spontaneous curvature. The amphiphilic monolayers can arrange in different ways to form micellar, hexagonal, lamellar and various bicontinuous cubic phases. For the latter case we consider both single structures (one monolayer) and double structures (two monolayers). Their interfaces are modeled by the triply periodic surfaces of constant mean curvature of the families G, D, P, C(P), I-WP and F-RD. The stability of the different bicontinuous cubic phases can be explained by the way in which their universal geometrical properties conspire with the concentration constraints. For vanishing saddle-splay modulus $\bar \kappa$, almost every phase considered has some region of stability in the Gibbs triangle. Although bicontinuous cubic phases are suppressed by sufficiently negative values of the saddle-splay modulus $\bar \kappa$, we find that they can exist for considerably lower values than obtained previously. The most stable bicontinuous cubic phases with decreasing $\bar \kappa < 0$ are the single and double gyroid structures since they combine favorable topological properties with extreme volume fractions.Comment: Revtex, 23 pages with 10 Postscript files included, to appear in J. Chem. Phys. 112 (6) (February 2000

Swarm behavior of self-propelled rods and swimming flagella

Systems of self-propelled particles are known for their tendency to aggregate and to display swarm behavior. We investigate two model systems, self-propelled rods interacting via volume exclusion, and sinusoidally-beating flagella embedded in a fluid with hydrodynamic interactions. In the flagella system, beating frequencies are Gaussian distributed with a non-zero average. These systems are studied by Brownian-dynamics simulations and by mesoscale hydrodynamics simulations, respectively. The clustering behavior is analyzed as the particle density and the environmental or internal noise are varied. By distinguishing three types of cluster-size probability density functions, we obtain a phase diagram of different swarm behaviors. The properties of clusters, such as their configuration, lifetime and average size are analyzed. We find that the swarm behavior of the two systems, characterized by several effective power laws, is very similar. However, a more careful analysis reveals several differences. Clusters of self-propelled rods form due to partially blocked forward motion, and are therefore typically wedge-shaped. At higher rod density and low noise, a giant mobile cluster appears, in which most rods are mostly oriented towards the center. In contrast, flagella become hydrodynamically synchronized and attract each other; their clusters are therefore more elongated. Furthermore, the lifetime of flagella clusters decays more quickly with cluster size than of rod clusters

Lattice-Boltzmann Model of Amphiphilic Systems

A lattice-Boltzmann model for the study of the dynamics of oil-water-surfactant mixtures is constructed. The model, which is based on a Ginzburg-Landau theory of amphiphilic systems with a single, scalar order parameter, is then used to calculate the spectrum of undulation modes of an oil-water interface and the spontaneous emulsification of oil and water after a quench from two-phase coexistence into the lamellar phase. A comparison with some analytical results shows that the model provides an accurate description of the static and dynamic behavior of amphiphilic systems.Comment: 6 pages, 2 figures, europhysics-letter styl

Dynamical regimes and hydrodynamic lift of viscous vesicles under shear

The dynamics of two-dimensional viscous vesicles in shear flow, with different fluid viscosities $\eta_{\rm in}$ and $\eta_{\rm out}$ inside and outside, respectively, is studied using mesoscale simulation techniques. Besides the well-known tank-treading and tumbling motions, an oscillatory swinging motion is observed in the simulations for large shear rate. The existence of this swinging motion requires the excitation of higher-order undulation modes (beyond elliptical deformations) in two dimensions. Keller-Skalak theory is extended to deformable two-dimensional vesicles, such that a dynamical phase diagram can be predicted for the reduced shear rate and the viscosity contrast $\eta_{\rm in}/\eta_{\rm out}$. The simulation results are found to be in good agreement with the theoretical predictions, when thermal fluctuations are incorporated in the theory. Moreover, the hydrodynamic lift force, acting on vesicles under shear close to a wall, is determined from simulations for various viscosity contrasts. For comparison, the lift force is calculated numerically in the absence of thermal fluctuations using the boundary-integral method for equal inside and outside viscosities. Both methods show that the dependence of the lift force on the distance $y_{\rm {cm}}$ of the vesicle center of mass from the wall is well described by an effective power law $y_{\rm {cm}}^{-2}$ for intermediate distances $0.8 R_{\rm p} \lesssim y_{\rm {cm}} \lesssim 3 R_{\rm p}$ with vesicle radius $R_{\rm p}$. The boundary-integral calculation indicates that the lift force decays asymptotically as $1/[y_{\rm {cm}}\ln(y_{\rm {cm}})]$ far from the wall.Comment: 13 pages, 13 figure

Dynamic regimes of fluids simulated by multiparticle-collision dynamics

We investigate the hydrodynamic properties of a fluid simulated with a mesoscopic solvent model. Two distinct regimes are identified, the `particle regime' in which the dynamics is gas-like, and the `collective regime' where the dynamics is fluid-like. This behavior can be characterized by the Schmidt number, which measures the ratio between viscous and diffusive transport. Analytical expressions for the tracer diffusion coefficient, which have been derived on the basis of a molecular-chaos assumption, are found to describe the simulation data very well in the particle regime, but important deviations are found in the collective regime. These deviations are due to hydrodynamic correlations. The model is then extended in order to investigate self-diffusion in colloidal dispersions. We study first the transport properties of heavy point-like particles in the mesoscopic solvent, as a function of their mass and number density. Second, we introduce excluded-volume interactions among the colloidal particles and determine the dependence of the diffusion coefficient on the colloidal volume fraction for different solvent mean-free paths. In the collective regime, the results are found to be in good agreement with previous theoretical predictions based on Stokes hydrodynamics and the Smoluchowski equation.Comment: 15 pages, 15 figure

A Ternary Lattice Boltzmann Model for Amphiphilic Fluids

A lattice Boltzmann model for amphiphilic fluid dynamics is presented. It is a ternary model, in that it conserves mass separately for each chemical species present (water, oil, amphiphile), and it maintains an orientational degree of freedom for the amphiphilic species. Moreover, it models fluid interactions at the microscopic level by introducing self-consistent forces between the particles, rather than by positing a Landau free energy functional. This combination of characteristics fills an important need in the hierarchy of models currently available for amphiphilic fluid dynamics, enabling efficient computer simulation and furnishing new theoretical insight. Several computational results obtained from this model are presented and compared to existing lattice-gas model results. In particular, it is noted that lamellar structures, which are precluded by the Peierls instability in two-dimensional systems with kinetic fluctuations, are not observed in lattice-gas models, but are easily found in the corresponding lattice Boltzmann models. This points out a striking difference in the phenomenology accessible to each type of model.Comment: 12 pages, 6 figures included with graphic

Budding and vesiculation induced by conical membrane inclusions

Conical inclusions in a lipid bilayer generate an overall spontaneous curvature of the membrane that depends on concentration and geometry of the inclusions. Examples are integral and attached membrane proteins, viruses, and lipid domains. We propose an analytical model to study budding and vesiculation of the lipid bilayer membrane, which is based on the membrane bending energy and the translational entropy of the inclusions. If the inclusions are placed on a membrane with similar curvature radius, their repulsive membrane-mediated interaction is screened. Therefore, for high inclusion density the inclusions aggregate, induce bud formation, and finally vesiculation. Already with the bending energy alone our model allows the prediction of bud radii. However, in case the inclusions induce a single large vesicle to split into two smaller vesicles, bending energy alone predicts that the smaller vesicles have different sizes whereas the translational entropy favors the formation of equal-sized vesicles. Our results agree well with those of recent computer simulations.Comment: 11 pages, 12 figure