arXiv subjects

Umberto Marini Bettolo Marconi

Publications and source records attributed to Umberto Marini Bettolo Marconi.

At least 73 records · Page 4Linked to original sources

arXiv2015

Lattice Boltzmann Method for mixtures at variable Schmidt number

When simulating multicomponent mixtures via the Lattice Boltzmann Method, it is desirable to control the mutual diffusivity between species while maintaining the viscosity of the solution fixed. This goal is herein achieved by a modification of the multicomponent Bhatnagar-Gross-Krook (BGK) evolution equations by introducing two different timescales for mass and momentum diffusion. Diffusivity is thus controlled by an effective drag force acting between species. Numerical simulations confirm the accuracy of the method for neutral binary and charged ternary mixtures in bulk conditions. The simulation of a charged mixture in a charged slit channel show that the conductivity and electro-osmotic mobility exhibit a departure from the Helmholtz-Smoluchowski prediction at high diffusivity.

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arXiv2015

Electro-osmotic flow in coated nanocapillaries: a theoretical investigation

Motivated by recent experiments, we present a theoretical investigation of how the electro-osmotic flow occurring in a capillary is modified when its charged surfaces are coated by charged polymers. The theoretical treatment is based on a three dimensional model consisting of a ternary fluid-mixture, representing the solvent and two species for the ions, confined between two parallel charged plates decorated by a fixed array of scatterers representing the polymer coating. The electro-osmotic flow, generated by a constant electric field applied in a direction parallel to the plates, is studied numerically by means of Lattice Boltzmann simulations. In order to gain further understanding we performed a simple theoretical analysis by extending the Stokes-Smoluchowski equation to take into account the porosity induced by the polymers in the region adjacent the walls. We discuss the nature of the velocity profiles by focusing on the competing effects of the polymer charges and the frictional forces they exert. We show evidence of the flow reduction and of the flow inversion phenomenon when the polymer charge is opposite to the surface charge. By using the density of polymers and the surface charge as control variables, we propose a phase diagram that discriminates the direct and the reversed flow regimes and determine its dependence on the ionic concentration.

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arXiv2015

Steric modulation of ionic currents in DNA translocation through nanopores

Ionic currents accompanying DNA translocation strongly depend on molarity of the electrolyte solution and the shape and surface charge of the nanopore. By means of the Poisson-Nernst-Planck equations it is shown how conductance is modulated by the presence of the DNA intruder and as a result of competing electrostatic and confinement factors. The theoretical results reproduce quantitatively the experimental ones and are summarized in a conductance diagram that allows distinguishing the region of reduced conductivity from the region of enhanced conductivity as a function of molarity and the pore dimension.

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arXiv2015

Kinetic Density Functional Theory: A microscopic approach to fluid mechanics

In the present paper we give a brief summary of some recent theoretical advances in the treatment of inhomogeneous fluids and methods which have applications in the study of dynamical properties of liquids in situations of extreme confinement, such as nanopores, nanodevices, etc. The approach obtained by combining kinetic and density functional methods is microscopic, fully self-consistent and allows to determine both configurational and flow properties of dense fluids. The theory predicts the correct hydrodynamic behavior and provides a practical and numerical tool to determine how the transport properties are modified when the length scales of the confining channels are comparable with the size of the molecules. The applications range from the dynamics of simple fluids under confinement, to that of neutral binary mixtures and electrolytes where the theory in the limit of slow gradients reproduces the known phenomenological equations such as the Planck-Nernst-Poisson and the Smoluchowski equations. The approach here illustrated allows for fast numerical solution of the evolution equations for the one-particle phase-space distributions by means of the weighted density lattice Boltzmann method and is particularly useful when one considers flows in complex geometries.

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arXiv2015

Multidimensional Stationary Probability Distribution for Interacting Active Particles

We derive the stationary probability distribution for a non-equilibrium system composed by an arbitrary number of degrees of freedom that are subject to Gaussian colored noise and a conservative potential. This is based on a multidimensional version of the Unified Colored Noise Approximation. By comparing theory with numerical simulations we demonstrate that the theoretical probability density quantitatively describes the accumulation of active particles around repulsive obstacles. In particular, for two particles with repulsive interactions, the probability of close contact decreases when one of the two particle is pinned. Moreover, in the case of isotropic confining potentials, the radial density profile shows a non trivial scaling with radius. Finally we show that the theory well approximates the "pressure" generated by the active particles allowing to derive an equation of state for a system of non-interacting colored noise-driven particles.

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arXiv2013

About an H-theorem for systems with non-conservative interactions

We exhibit some arguments in favour of an H-theorem for a generalization of the Boltzmann equation including non-conservative interactions and a linear Fokker-Planck-like thermostatting term. Such a non-linear equation describing the evolution of the single particle probability $P_i(t)$ of being in state $i$ at time $t$, is a suitable model for granular gases and is indicated here as Boltzmann-Fokker-Planck (BFP) equation. The conjectured H-functional, which appears to be non-increasing, is $H_C(t)=\sum_i P_i(t) \ln P_i(t)/Π_i$ with $Π_i = \lim_{t \to \infty} P_i(t)$, in analogy with the H-functional of Markov processes. The extension to continuous states is straightforward. A simple proof can be given for the elastic BFP equation. A semi-analytical proof is also offered for the BFP equation for so-called inelastic Maxwell molecules. Other evidence is obtained by solving particular BFP cases through numerical integration or through "particle schemes" such as the Direct Simulation Monte Carlo.

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arXiv2013

Weighted density Lattice Boltzmann approach to fluids under confinement

The Enskog-like kinetic approach, recently introduced by us to study strongly inhomogeneous flu- ids, is reconsidered in order to improve the description of the transport coefficients. The approach is based on a separation of the interaction between hydrodynamic and non-hydrodynamic parts. The latter is treated within a simple relaxation approximation. We show that, by considering the non-hydrodynamic part via a weighted density approximation, we obtain a better prediction of the transport coefficients. By virtue of the simplicity of the kinetic equation we are able to solve numer- ically the phase space distribution in the presence of inhomogeneities, such as confining surfaces, via a Lattice Boltzmann method. Analytical estimates of the importance of these corrections to the transport coefficients in bulk conditions is provided. Poiseuille flow of the hard-sphere fluid confined between two parallel smooth walls is studied and their pore-averaged properties are determined.

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arXiv2012

Charge transport in nanochannels: a molecular theory

We introduce a theoretical and numerical method to investigate the flow of charged fluid mixtures under extreme confinement. We model the electrolyte solution as a ternary mixture, comprising two ionic species of opposite charge and a third uncharged component. The microscopic approach is based on kinetic theory and is fully self-consistent. It allows to determine configurational prop- erties, such as layering near the confining walls, and the flow properties. We show that, under appropriate assumptions, the approach reproduces the phenomenological equations used to describe electrokinetic phenomena, without requiring the introduction of constitutive equations to determine the fluxes. Moreover, we model channels of arbitrary shape and nanometric roughness, features that have important repercussions on the transport properties of these systems. Numerical simulations are obtained by solving the evolution dynamics of the one-particle phase- space distributions of each species by means of a Lattice Boltzmann method for flows in straight and wedged channels. Results are presented for the microscopic density, the velocity profiles and for the volumetric and charge flow-rates. Strong departures from electroneutrality are shown to appear at molecular level.

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arXiv2012

Thermally induced directed currents in hard rod systems

We study the non equilibrium statistical properties of a one dimensional hard-rod fluid undergoing collisions and subject to a spatially non uniform Gaussian heat-bath and periodic potential. The system is able to sustain finite currents when the spatially inhomogeneous heat-bath and the periodic potential profile display an appropriate relative phase shift, $ϕ$. By comparison with the collisionless limit, we determine the conditions for the most efficient transport among inelastic, elastic and non interacting rods. We show that the situation is complex as, depending on shape of the temperature profile, the current of one system may outperform the others.

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arXiv2012

Stabilized Lattice Boltzmann-Enskog method for compressible flows and its application to one and two-component fluids in nanochannels

A numerically stable method to solve the discretized Boltzmann-Enskog equation describing the behavior of non ideal fluids under inhomogeneous conditions is presented. The algorithm employed uses a Lagrangian finite-difference scheme for the treatment of the convective term and a forcing term to account for the molecular repulsion together with a Bhatnagar-Gross-Krook relaxation term. In order to eliminate the spurious currents induced by the numerical discretization procedure, we use a trapezoidal rule for the time integration together with a version of the two-distribution method of He et al. (J. Comp. Phys 152, 642 (1999)). Numerical tests show that, in the case of one component fluid in the presence of a spherical potential well, the proposed method reduces the numerical error by several orders of magnitude. We conduct another test by considering the flow of a two component fluid in a channel with a bottleneck and provide information about the density and velocity field in this structured geometry.

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arXiv2011

Electro-osmotic flows under nanoconfinement: a self-consistent approach

We introduce a theoretical and numerical method to investigate the properties of electro-osmotic flows under conditions of extreme confinement. The present approach, aiming to provide a simple modeling of electrolyte solutions described as ternary mixtures, which comprises two ionic species and a third uncharged component, is an extension of our recent work on binary neutral mixtures. The approach, which combines elements of kinetic theory, density functional theory with Lattice-Boltzmann algorithms, is microscopic and self-consistent and does not require the us e of constitutive equations to determine the fluxes. Numerical solutions are obtained by solving the resulting coupled equations for the one-particle phase-space distributions of the species by means of a Lattice Boltzmann discretization procedure. Results are given for the microscopic density and velocity profiles and for the volumetric and charge flow.

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arXiv2011

Multicomponent Diffusion in Nanosystems

We present the detailed analysis of the diffusive transport of spatially inhomogeneous fluid mixtures and the interplay between structural and dynamical properties varying on the atomic scale. The present treatment is based on different areas of liquid state theory, namely kinetic and density functional theory and their implementation as an effective numerical method via the Lattice Boltzmann approach. By combining the first two methods it is possible to obtain a closed set of kinetic equations for the singlet phase space distribution functions of each species. The interactions among particles are considered within a self-consistent approximation and the resulting effective molecular fields are analyzed. We focus on multispecies diffusion in systems with short-range hard-core repulsion between particles of unequal sizes and weak attractive long-range interactions. As a result, the attractive part of the potential does not contribute explicitly to viscosity but to diffusivity and the thermodynamic properties. Finally, we obtain a practical scheme to solve the kinetic equations by employing a discretization procedure derived from the Lattice Boltzmann approach. Within this framework, we present numerical data concerning the mutual diffusion properties both in the case of a quiescent bulk fluid and shear flow inducing Taylor dispersion.

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arXiv2011

Non-local kinetic theory of inhomogeneous liquid mixtures

In this work we investigate the dynamical properties of a mixture of mutually interacting spherical molecules of different masses and sizes. From an analysis of the microscopic laws governing the motion of the molecules we derive a set of non-local self-consistent equations for the singlet phase-space distribution functions. The theory is shown to reproduce the hydrodynamic equations for the densities of each species, the total momentum and the local temperature. The non ideal gas interaction term is separated into a contribution due to the repulsive part, which is treated by means of the revised Enskog theory for hard spheres, and an attractive contribution treated within the random phase approximation. The present formulation accounts for the effects of the density and velocity inhomogeneities both on the thermodynamic and transport properties of the fluid. In a special limit, where one species is massive and diluted, the theory leads to a description which is formally identical to the dynamic density functional equation governing the time evolution of a colloidal system. The derivation also determines the dependence of the friction coefficient, appearing in the dynamic density functional theory, on the microscopic parameters of the solvent. However, the predicted value takes into account only the collisional contributions to the friction and not the Stokes friction of hydrodynamic origin, suggesting that velocity correlations should be incorporated in a more complete treatment.

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arXiv2011

Dynamics of Fluid Mixtures in Nanospaces

A multicomponent extension of our recent theory of simple fluids [ U.M.B. Marconi and S. Melchionna, Journal of Chemical Physics, 131, 014105 (2009) ] is proposed to describe miscible and immiscible liquid mixtures under inhomogeneous, non steady conditions typical of confined fluid flows. We first derive from a microscopic level the evolution equations of the phase space distribution function of each component in terms of a set of self consistent fields, representing both body forces and viscous forces (forces dependent on the density distributions in the fluid and on the velocity distributions). Secondly, we solve numerically the resulting governing equations by means of the Lattice Boltzmann method whose implementation contains novel features with respect to existing approaches. Our model incorporates hydrodynamic flow, diffusion, surface tension, and the possibility for global and local viscosity variations. We validate our model by studying the bulk viscosity dependence of the mixture on concentration, packing fraction and size ratio. Finally we consider inhomogeneous systems and study the dynamics of mixtures in slits of molecular thickness and relate structural and flow properties.

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arXiv2010

Dynamic density functional theory versus Kinetic theory of simple fluids

By combining methods of kinetic and density functional theory, we present a description of molecular fluids which accounts for their microscopic structure and thermodynamic properties as well as for the hydrodynamic behavior. We focus on the evolution of the one particle phase space distribution, rather than on the evolution of the average particle density, which features in dynamic density functional theory. The resulting equation can be studied in two different physical limits: diffusive dynamics, typical of colloidal fluids without hydrodynamic interaction, where particles are subject to overdamped motion resulting from the coupling with a solvent at rest, and inertial dynamics, typical of molecular fluids. Finally, we propose an algorithm to solve numerically and efficiently the resulting kinetic equation by employing a discretization procedure analogous to the one used in the Lattice Boltzmann method.

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arXiv2009

A unified framework for dynamic density functional and Lattice Boltzmann methods

Using methods of kinetic theory and liquid state theory we propose a description of the non-equilibrium behavior of molecular fluids which takes into account their microscopic structure and thermodynamic properties. The present work represents an alternative to the recent dynamic density functional theory which can only deal with colloidal fluids and is not apt to describe the hydrodynamic behavior of a molecular fluid. The method is based on a suitable modification of the Boltzmann transport equation for the phase space distribution and provides a detailed description of the local structure of the fluid and of the transport coefficients under inhomogeneous conditions. Finally, we propose a practical scheme to solve numerically and efficiently the resulting kinetic equation by employing a discretization procedure analogous to the one used in the Lattice Boltzmann method.

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arXiv2008

Beyond the Dynamic Density Functional theory for steady currents. Application to driven colloidal particles in a channel

Motivated by recent studies on the dynamics of colloidal solutions in narrow channels, we consider the steady state properties of an assembly of non interacting particles subject to the action of a traveling potential moving at a constant speed while the solvent is modeled by a heat bath at rest in the laboratory frame. Since the description, we propose here, takes into account the inertia of the colloidal particles it is necessary to consider the evolution of both positions and momenta and study the governing equation for the one-particle phase-space distribution. We first derive the asymptotic form of its solutions as an expansion in Hermite polynomials and their generic properties, such as the force and energy balance and then we particularize our study to the case of an inverted parabolic potential barrier. We obtain numerically the steady state density and temperature profile and show that the expansion is rapidly convergent for large values of the friction constant and small drifting velocities. The present results on the one hand confirm the previous studies based on the dynamic density functional theory (DDFT) when the friction constant is large, on the other hand display effects such as the presence of a wake behind the barrier and a strong inhomogeneity in the temperature field which are beyond the DDFT description.

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arXiv2008

Fluctuation-Dissipation: Response Theory in Statistical Physics

General aspects of the Fluctuation-Dissipation Relation (FDR), and Response Theory are considered. After analyzing the conceptual and historical relevance of fluctuations in statistical mechanics, we illustrate the relation between the relaxation of spontaneous fluctuations, and the response to an external perturbation. These studies date back to Einstein's work on Brownian Motion, were continued by Nyquist and Onsager and culminated in Kubo's linear response theory. The FDR has been originally developed in the framework of statistical mechanics of Hamiltonian systems, nevertheless a generalized FDR holds under rather general hypotheses, regardless of the Hamiltonian, or equilibrium nature of the system. In the last decade, this subject was revived by the works on Fluctuation Relations (FR) concerning far from equilibrium systems. The connection of these works with large deviation theory is analyzed. Some examples, beyond the standard applications of statistical mechanics, where fluctuations play a major role are discussed: fluids, granular media, nano-systems and biological systems.

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