Biomedical subjects

Emmanuel Trizac

Publications and source records attributed to Emmanuel Trizac.

At least 19 recordsLinked to original sources

PubMed2007

The renormalized jellium model for spherical and cylindrical colloids.

Starting from a mean-field description for a dispersion of highly charged spherical or (parallel) rodlike 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 nontrivial density dependence, which directly enters into the equation of state through a simple analytical expression. The good agreement observed between the pressures 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.

Colloids↗

PubMed2006

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 nontrivial effect of surface charge is discussed. This work allows us to reconsider existing experimental data, concerning zeta potentials of hydrophobic surfaces and suggests the possibility to generate "giant" electro-osmotic and electrophoretic effects, with direct applications in microfluidics.

Journal Article↗

PubMed2006

Dynamics of a tracer granular particle as a nonequilibrium 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 on 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 alpha. As soon as the velocity PDF of the gas departs from the Gaussian form, detailed balance is violated. This nonequilibrium state can be characterized in terms of a Lebowitz-Spohn action functional W(tau) defined over trajectories of time duration tau. We discuss the properties of this functional and of a similar functional W(tau), which differs from the first for a term that is nonextensive in time. On the one hand, we show that in numerical experiments (i.e., at finite times tau), the two functionals have different fluctuations and 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(tau) at very large times tau. We give an argument for the possible failure of the LS-GC relation in this situation. We also suggest practical recipes for measuring W(tau) and W(tau) in experiments.

Journal Article↗

PubMed2006

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

Making use of results pertaining to Painlevé 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.

Biopolymers↗

PubMed2005

Fluctuations of internal energy flow in a vibrated granular gas.

The nonequilibrium fluctuations of power flux in a fluidized granular media have been recently measured in an experiment [Phys. Rev. Lett. 92, 164301 (2004)], which was announced to be a verification of the fluctuation relation (FR) by Gallavotti and Cohen. An effective temperature was also identified and proposed to be a useful probe for such nonequilibrium systems. We explain these results in terms of a two-temperature Poisson process. Within this model, supported by independent molecular dynamics simulations, power flux fluctuations do not satisfy the FR and the nature of the effective temperature is clarified. In the pursuit of a hypothetical global quantity fulfilling the FR, this points to the need of considering candidates other than the power flux.

Journal Article↗

PubMed2005

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 spherelike dynamics for which no exact solution exists. We consequently focus on simplified approaches, the Maxwell and very-hard-particle (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 direct Monte Carlo simulations. 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.

Journal Article↗

PubMed2005

Electrostatic potential around charged finite rodlike macromolecules: nonlinear Poisson-Boltzmann theory.

In this paper, we show that the far field electrostatic potential created by a highly charged finite size cylinder within the nonlinear Poisson-Boltzmann (PB) theory, is remarkably close to the potential created within the linearized PB approximation by the same object at a well-chosen fixed potential. Comparing the nonlinear electrostatic potential with its linear counterpart associated to a fixed potential boundary condition (called the effective surface potential), we deduce the effective charge of the highly charged cylinder. Values of the effective surface potential are provided as a function of the bare surface charge and Debye length of the ionic solution. This allows to compute the anisotropic electrostatic interaction energy of two distant finite rods.

Journal Article↗

PubMed2004

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 nonwetting surfaces, and the zeta potential deduced from electrokinetic effects is considerably amplified by the existence of a slippage at the solid substrate.

Computer Simulation↗

PubMed2004

Hydrodynamics of probabilistic ballistic annihilation.

We consider a dilute gas of hard spheres in dimension d> or =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 is a conserved quantity. 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.

Journal Article↗

PubMed2004

Nonlinear 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 coions, divalent counterions) and a 2:1 (reversed situation) electrolyte. Our approach consists of an expansion in powers of rescaled curvature 1/ (kappaa), where a is the colloidal radius and 1/kappa 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 kappaa>1. We also report an unusual overshooting effect where the colloidal effective charge is larger than the bare one.

Journal Article↗

PubMed2004

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 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 our equation of state can be used to shed light on the surprising results found in recent sedimentation experiments.

Journal Article↗

PubMed2004

Interaction between charged anisotropic macromolecules: application to rod-like polyelectrolytes.

In this paper we propose a framework allowing one to compute the effective interactions between two anisotropic macromolecules, thereby generalizing the Derjaguin, Landau, Verwey, and Overbeek theory [E. J. W. Verwey and J. T. G. Overbeek, Theory of the Stability of Lyophobic Colloids (Elsevier, Amsterdam, 1948)] to nonspherical 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.

Journal Article↗

PubMed2004

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 (nonlinear 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, which are in excellent agreement with our analytical predictions. For p<1, numerical simulations lead to the conjecture that unlike for pure annihilation (p=1), the velocity distribution becomes universal, i.e., does not depend on the initial conditions.

Journal Article↗

PubMed2003

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 microspecies. To describe the electric double layer, we use a generic local density functional theory in which the local microionic density profiles are arbitrary functions of the local electrostatic potential. A general 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. As a consequence, for most situations, the following simple and practical sufficient condition follows: if, as the electric potential psi--> infinity, the local theory predicts that the highest valency counterions density diverges as psi(nu) with some nu>1 or faster, then the electrostatic potential will saturate. Otherwise, if the counterion density diverges as psi or slower, or does not diverge as psi--> infinity, the electric potential will not saturate. Using this condition, we investigate the possibility of the saturation phenomenon within the framework of recent theories proposed in the literature to describe electrical double layer beyond the Poisson-Boltzmann description.

Journal Article↗

PubMed2003

Some exact results for Boltzmann's annihilation dynamics.

The problem of ballistic annihilation for a spatially homogeneous system is revisited within Boltzmann's kinetic theory in two and three dimensions. Analytical results are derived for the time evolution of the particle density for some isotropic discrete bimodal velocity modulus distributions. According to the allowed values of the velocity modulus, different behaviors are obtained: power law decay with nonuniversal exponents depending continuously upon the ratio of the two velocities, or exponential decay. When one of the two velocities is equal to zero, the model describes the problem of ballistic annihilation in the presence of static traps. The analytical predictions are shown to be in agreement with the results of two-dimensional molecular dynamics simulations.

Journal Article↗

PubMed2002

Dynamics of ballistic annihilation.

The problem of ballistically controlled annihilation is revisited for general initial velocity distributions and an arbitrary dimension. An analytical derivation of the hierarchy equations obeyed by the reduced distributions is given, and a scaling analysis of the corresponding spatially homogeneous system is performed. This approach points to the relevance of the nonlinear Boltzmann equation for dimensions larger than 1 and provides expressions for the exponents describing the decay of the particle density n(t) proportional, variant t(-xi) and the root-mean-square velocity v proportional, variant t(-gamma) in terms of a parameter related to the dissipation of kinetic energy. The Boltzmann equation is then solved perturbatively within a systematic expansion in Sonine polynomials. Analytical expressions for the exponents xi and gamma are obtained in arbitrary dimension as a function of the parameter mu characterizing the small velocity behavior of the initial velocity distribution. Moreover, the leading non-Gaussian corrections to the scaled velocity distribution are computed. These expressions for the scaling exponents are in good agreement with the values reported in the literature for continuous velocity distributions in d=1. For the two-dimensional case, we implement Monte Carlo and molecular dynamics simulations that turn out to be in excellent agreement with the analytical predictions.

Journal Article↗

PubMed2002

Simple approach for charge renormalization in highly charged macroions.

We revisit the notion of renormalized charge, which is a concept of central importance in the field of highly charged colloidal or polyelectrolyte solutions. Working at the level of a linear Debye-Hückel-like theory only, we propose a versatile method to predict the saturated amount of charge renormalization, which is, however, a nonlinear effect arising at strong electrostatic coupling. The results are successfully tested against nonlinear Poisson-Boltzmann theory for polyions of various shapes (planar, cylindrical, and spherical), both in the infinite dilution limit or in confined geometry, with or without added electrolyte. Our approach, accurate for monovalent microions in solvents such as water, is finally confronted against experimental results on charged colloids and B-DNA solutions.

Journal Article↗

PubMed2002

Molecular dynamics simulations of vibrated granular gases.

We present molecular dynamics simulations of monodisperse or bidisperse inelastic granular gases driven by vibrating walls, in two dimensions (without gravity). Because of the energy injection at the boundaries, a situation often met experimentally, density and temperature fields display heterogeneous profiles in the direction perpendicular to the walls. A general equation of state for an arbitrary mixture of fluidized inelastic hard spheres is derived and successfully tested against numerical data. Single-particle velocity distribution functions with non-Gaussian features are also obtained, and the influence of various parameters (inelasticity coefficients, density, etc.) are analyzed. The validity of a recently proposed random restitution coefficient model is assessed through the study of projected collisions onto the direction perpendicular to that of energy injection. For the binary mixture, the nonequipartition of translational kinetic energy is studied and compared both to experimental data and to the case of homogeneous energy injection ("stochastic thermostat"). The rescaled velocity distribution functions are found to be very similar for both species.

Journal Article↗