arXiv subjects

Emmanuel Trizac

Publications and source records attributed to Emmanuel Trizac.

At least 73 records · Page 4Linked to original sources

arXiv2011

Colloidal ionic complexes on periodic substrates: ground state configurations and pattern switching

We theoretically and numerically studied ordering of "colloidal ionic clusters" on periodic substrate potentials as those generated by optical trapping. Each cluster consists of three charged spherical colloids: two negatively and one positively charged. The substrate is a square or rectangular array of traps, each confining one such cluster. By varying the lattice constant from large to small, the observed clusters are first rod-like and form ferro- and antiferro-like phases, then they bend into a banana-like shape and finally condense into a percolated structure. Remarkably, in a broad parameter range between single-cluster and percolated structures, we have found stable supercomplexes composed of six colloids forming grape-like or rocket-like structures. We investigated the possibility of macroscopic pattern switching by applying external electrical fields.

cond-mat.soft↗

arXiv2009

Rheological properties for inelastic Maxwell mixtures under shear flow

The Boltzmann equation for inelastic Maxwell models is considered to determine the rheological properties in a granular binary mixture in the simple shear flow state. The transport coefficients (shear viscosity and viscometric functions) are {\em exactly} evaluated in terms of the coefficients of restitution, the (reduced) shear rate and the parameters of the mixture (particle masses, diameters and concentration). The results show that in general, for a given value of the coefficients of restitution, the above transport properties decrease with increasing shear rate.

cond-mat.stat-mech↗

arXiv2008

Ground states of colloidal molecular crystals on periodic substrates

Two dimensional suspensions of spherical colloids subject to periodic external fields exhibit a rich variety of molecular crystalline phases. We study in simulations the ground state configurations of dimeric and trimeric systems, that are realized on square and triangular lattices, when either two or three macroions are trapped in each external potential minimum. Bipartite orders of the checkerboard or stripe types are reported together with more complex quadripartite orderings, and the shortcomings of envisioning the colloids gathered in a single potential minimum as a composite rigid object are discussed. This work also sheds light on simplifying assumptions underlying previous theoretical treatments and that made possible the mapping onto spin models.

cond-mat.soft↗

arXiv2007

The renormalized jellium model for spherical and cylindrical colloids

Starting from a mean-field description for a dispersion of highly charged spherical or (parallel) rod-like colloids, we introduce the simplification of a homogeneous background to include the contribution of other polyions to the static field created by a tagged polyion. The charge of this background is self-consistently renormalized to coincide with the polyion effective charge, the latter quantity thereby exhibiting a non-trivial density dependence, which directly enters into the equation of state through a simple analytical expression. The good agreement observed between the pressure calculated using the renormalized jellium and Monte Carlo simulations confirms the relevance of the {renormalized} jellium model for theoretical and experimental purposes and provides an alternative to the Poisson-Boltzmann cell model since it is free of some of the intrinsic limitations of this approach.

cond-mat.soft↗

arXiv2006

Liquid friction on charged surfaces: from hydrodynamic slippage to electrokinetics

Hydrodynamic behavior at the vicinity of a confining wall is closely related to the friction properties of the liquid/solid interface. Here we consider, using Molecular Dynamics simulations, the electric contribution to friction for charged surfaces, and the induced modification of the hydrodynamic boundary condition at the confining boundary. The consequences of liquid slippage for electrokinetic phenomena, through the coupling between hydrodynamics and electrostatics within the electric double layer, are explored. Strong amplification of electro-osmotic effects is revealed, and the non-trivial effect of surface charge is discussed. This work allows to reconsider existing experimental data, concerning Zeta potentials of hydrophobic surfaces and suggest the possibility to generate ``giant'' electro-osmotic and electrophoretic effects, with direct applications in microfluidics.

cond-mat.soft↗

arXiv2006

Stationary state of a heated granular gas: fate of the usual H-functional

We consider the characterization of the nonequilibrium stationary state of a randomly-driven granular gas in terms of an entropy-production based variational formulation. Enforcing spatial homogeneity, we first consider the temporal stability of the stationary state reached after a transient. In connection, two heuristic albeit physically motivated candidates for the non-equilibrium entropy production are put forward. It turns out that none of them displays an extremum for the stationary velocity distribution selected by the dynamics. Finally, the relevance of the relative Kullbach entropy is discussed.

cond-mat.stat-mech↗

arXiv2005

Onsager-Manning-Oosawa condensation phenomenon and the effect of salt

Making use of results pertaining to Painleve III type equations, we revisit the celebrated Onsager-Manning-Oosawa condensation phenomenon for charged stiff linear polymers, in the mean-field approximation with salt. We obtain analytically the associated critical line charge density, and show that it is severely affected by finite salt effects, whereas previous results focused on the no salt limit. In addition, we obtain explicit expressions for the condensate thickness and the electric potential. The case of asymmetric electrolytes is also briefly addressed.

cond-mat.soft↗

arXiv2005

Dynamics of a tracer granular particle as a non-equilibrium Markov process

The dynamics of a tracer particle in a stationary driven granular gas is investigated. We show how to transform the linear Boltzmann equation describing the dynamics of the tracer into a master equation for a continuous Markov process. The transition rates depend upon the stationary velocity distribution of the gas. When the gas has a Gaussian velocity probability distribution function (pdf), the stationary velocity pdf of the tracer is Gaussian with a lower temperature and satisfies detailed balance for any value of the restitution coefficient $α$. As soon as the velocity pdf of the gas departs from the Gaussian form, detailed balance is violated. This non-equilibrium state can be characterized in terms of a Lebowitz-Spohn action functional $W(τ)$ defined over trajectories of time duration $τ$. We discuss the properties of this functional and of a similar functional $\bar{W}(τ)$ which differs from the first for a term which is non-extensive in time. On the one hand we show that in numerical experiments, i.e. at finite times $τ$, the two functionals have different fluctuations and $\bar{W}$ always satisfies an Evans-Searles-like symmetry. On the other hand we cannot observe the verification of the Lebowitz-Spohn-Gallavotti-Cohen (LS-GC) relation, which is expected for $W(τ)$ at very large times $τ$. We give an argument for the possible failure of the LS-GC relation in this situation. We also suggest practical recipes for measuring $W(τ)$ and $\bar{W}(τ)$ in experiments.

cond-mat.soft↗

arXiv2005

Maxwell and very hard particle models for probabilistic ballistic annihilation: hydrodynamic description

The hydrodynamic description of probabilistic ballistic annihilation, for which no conservation laws hold, is an intricate problem with hard sphere-like dynamics for which no exact solution exists. We consequently focus on simplified approaches, the Maxwell and very hard particles (VHP) models, which allows us to compute analytically upper and lower bounds for several quantities. The purpose is to test the possibility of describing such a far from equilibrium dynamics with simplified kinetic models. The motivation is also in turn to assess the relevance of some singular features appearing within the original model and the approximations invoked to study it. The scaling exponents are first obtained from the (simplified) Boltzmann equation, and are confronted against Monte Carlo simulation (DSMC technique). Then, the Chapman-Enskog method is used to obtain constitutive relations and transport coefficients. The corresponding Navier-Stokes equations for the hydrodynamic fields are derived for both Maxwell and VHP models. We finally perform a linear stability analysis around the homogeneous solution, which illustrates the importance of dissipation in the possible development of spatial inhomogeneities.

cond-mat.stat-mech↗

arXiv2004

Hydrodynamics of probabilistic ballistic annihilation

We consider a dilute gas of hard spheres in dimension $d \geq 2$ that upon collision either annihilate with probability $p$ or undergo an elastic scattering with probability $1-p$. For such a system neither mass, momentum, nor kinetic energy are conserved quantities. We establish the hydrodynamic equations from the Boltzmann equation description. Within the Chapman-Enskog scheme, we determine the transport coefficients up to Navier-Stokes order, and give the closed set of equations for the hydrodynamic fields chosen for the above coarse grained description (density, momentum and kinetic temperature). Linear stability analysis is performed, and the conditions of stability for the local fields are discussed.

cond-mat.stat-mech↗

arXiv2004

Granular gases: dynamics and collective effects

We present a biased review of some of the most "spectacular" effects appearing in the dynamics of granular gases where the dissipative nature of the collisions leads to a rich phenomenology, exhibiting striking differences with equilibrium gases. Among these differences, the focus here is on the illustrative examples of ``Maxwell Demon''-like experiment, modification of Fourier's law, non-equipartition of energy and non-Gaussianity of the velocity distributions. The presentation remains as non technical as possible.

cond-mat.stat-mech↗

arXiv2004

Hydrodynamics within the Electric Double Layer on slipping surfaces

We show, using extensive Molecular Dynamics simulations, that the dynamics of the electric double layer (EDL) is very much dependent on the wettability of the charged surface on which the EDL develops. For a wetting surface, the dynamics, characterized by the so-called Zeta potential, is mainly controlled by the electric properties of the surface, and our work provides a clear interpretation for the traditionally introduced immobile Stern layer. In contrast, the immobile layer disappears for non-wetting surfaces and the Zeta potential deduced from electrokinetic effects is considerably amplified by the existence of a slippage at the solid substrate.

cond-mat.soft↗

arXiv2004

Non-linear screening of spherical and cylindrical colloids: the case of 1:2 and 2:1 electrolytes

From a multiple scale analysis, we find an analytic solution of spherical and cylindrical Poisson-Boltzmann theory for both a 1:2 (monovalent co-ions, divalent counter-ions) and a 2:1 (reversed situation) electrolyte. Our approach consists in an expansion in powers of rescaled curvature $1/(κa)$, where $a$ is the colloidal radius and $1/κ$ the Debye length of the electrolytic solution. A systematic comparison with the full numerical solution of the problem shows that for cylinders and spheres, our results are accurate as soon as $κa>1$. We also report an unusual overshooting effect where the colloidal effective charge is larger than the bare one.

cond-mat.soft↗

arXiv2004

On the fluid-fluid phase separation in charged-stabilized colloidal suspensions

We develop a thermodynamic description of particles held at a fixed surface potential. This system is of particular interest in view of the continuing controversy over the possibility of a fluid-fluid phase separation in aqueous colloidal suspensions with monovalent counterions. The condition of fixed surface potential allows in a natural way to account for the colloidal charge renormalization. In a first approach, we assess the importance of the so called ``volume terms'', and find that in the absence of salt, charge renormalization is sufficient to stabilize suspension against a fluid-fluid phase separation. Presence of salt, on the other hand, is found to lead to an instability. A very strong dependence on the approximations used, however, puts the reality of this phase transition in a serious doubt. To further understand the nature of the instability we next study a Jellium-like approximation, which does not lead to a phase separation and produces a relatively accurate analytical equation of state for a deionized suspensions of highly charged colloidal spheres. A critical analysis of various theories of strongly asymmetric electrolytes is presented to asses their reliability as compared to the Monte Carlo simulations.

cond-mat.soft↗

arXiv2003

Renormalized Jellium model for charge-stabilized colloidal suspensions

We introduce a renormalized Jellium model to calculate the equation of state for charged colloidal suspensions. An almost perfect agreement with Monte Carlo simulations is found. Our self-consistent approach naturally allows to define the effective charge of particles {\em at finite colloidal density}. Although this quantity may differ significantly from its counterpart obtained from the standard Poisson-Boltzmann cell approach, the osmotic pressures for both models are in good agreement. We argue that by construction, the effective charge obtained using the Jellium approximation is more appropriate to the study of colloidal interactions. We also discuss a possibility of a fluid-fluid critical point and show how the new equation of state can be used to shed light on the surprising results found in recent sedimentation experiments.

cond-mat.soft↗

arXiv2003

Interaction between charged anisotropic macromolecules: Application to rod-like polyelectrolytes

In this paper we propose a framework allowing to compute the effective interactions between two anisotropic macromolecules, thereby generalizing the DLVO theory to non spherical finite size colloids. We show in particular that the effective interaction potential remains anisotropic at all distances and provide an expression for the anisotropy factor. We then apply this framework to the case of finite rod-like polyelectrolytes. The calculation of the interaction energy requires the numerical computation of the surface charge profiles, which result here from a constant surface potential on the rod-like colloids. However, a simplified analytical description is proposed, leading to an excellent agreement with the full numerical solution. Conclusions on the phase properties of rod-like colloids are proposed in this context.

cond-mat.soft↗

arXiv2003

Probabilistic ballistic annihilation with continuous velocity distributions

We investigate the problem of ballistically controlled reactions where particles either annihilate upon collision with probability $p$, or undergo an elastic shock with probability $1-p$. Restricting to homogeneous systems, we provide in the scaling regime that emerges in the long time limit, analytical expressions for the exponents describing the time decay of the density and the root-mean-square velocity, as continuous functions of the probability $p$ and of a parameter related to the dissipation of energy. We work at the level of molecular chaos (non-linear Boltzmann equation), and using a systematic Sonine polynomials expansion of the velocity distribution, we obtain in arbitrary dimension the first non-Gaussian correction and the corresponding expressions for the decay exponents. We implement Monte-Carlo simulations in two dimensions, that are in excellent agreement with our analytical predictions. For $p<1$, numerical simulations lead to conjecture that unlike for pure annihilation ($p=1$), the velocity distribution becomes universal, i.e. does not depend on the initial conditions.

cond-mat.stat-mech↗

arXiv2003

A density functional theory study of electric potential saturation: planar geometry

We investigate the possibility of electrostatic potential saturation, which may lead to the phenomenon of effective charge saturation. The system under study is a uniformly charged infinite plane immersed in an arbitrary electrolyte made up of several micro-species. To describe the electric double layer, we use a generic density functional theory in which the local micro-ionic density profiles are arbitrary functions of the local electrostatic potential. A necessary and sufficient condition is obtained for saturation, whereby the electrostatic potential created by the plane becomes independent of its bare charge, provided the latter is large enough.

cond-mat.soft↗