Patrick Grosfils

Dependence of the liquid-vapor surface tension on the range of interaction: A test of the law of corresponding states

The validity of the principle of corresponding states is investigated for the case of a potential with more than one intrinsic length scale. The planar surface tension of coexisting liquid and vapor phases of a fluid of Lennard-Jones atoms is studied as a function of the range of the potential using both Monte Carlo simulations and density functional theory (DFT). The interaction range is varied from r(c)(*) = 2.5 to r(c)(*) = 6 and the surface tension is determined for temperatures ranging from T(*) = 0.7 up to the critical temperature in each case. The simulation results are consistent with previous studies and are shown to obey the law of corresponding states even though the potential has two intrinsic length scales. It is further shown that the corresponding states principle can also be used to enhance the accuracy of some, but not all, DFT calculations of the surface tension. The results show that most of the cutoff dependence of the surface tension can be explained as a result of changes in the cutoff-dependent phase diagram and that corresponding states can be a useful tool for explaining differences between theory and simulation.

The structure of an infinitely strong shock wave

The structure of a shock wave propagating through a hard-sphere gas is obtained by the Direct Simulation Monte Carlo method (DSMC), in the limit of infinitely large Mach number. The shock profiles and the distribution function of molecular velocities f are compared with Grad’s and Mott–Smith approximations. It is shown that the “regular” part of f, exhibits a singularity in the velocity space at the location of the upstream bulk speed.

Structural and dynamical characterization of Hele-Shaw viscous fingering.

Viscous fingering occurs in the interfacial zone between two fluids confined between two plates with a narrow gap (Hele–Shaw geometry) when a highly viscous fluid is displaced by a fluid with relatively low viscosity. Using a mesoscopic approach—the lattice Boltzmann method—we investigate the dynamics of spatially extended Hele–Shaw flow under conditions corresponding to various experimental systems by tuning the ‘surface tension’ and the reactivity between the two fluids. We discuss the onset of the fingering instability (dispersion relation), analyse the structural properties (characterization of the interface) and the dynamical properties (growth of the mixing zone) of the Hele–Shaw systems, and show the effect of reactive processes on the structure of the interfacial zone.

Is the Tsallis entropy stable

The question of whether the Tsallis entropy is Lesche-stable is revisited. It is argued that when physical averages are computed with the escort probabilities, the correct application of the concept of Lesche-stability requires use of the escort probabilities. As a consequence, as shown here, the Tsallis entropy is unstable but the thermodynamic averages are stable. We further show that Lesche stability as well as thermodynamic stability can be obtained if the homogeneous entropy is used as the basis of the formulation of non-extensive thermodynamics. In this approach, the escort distribution arises naturally as a secondary structure.

Dark-field digital holographic microscopy to investigate objects that are nanosized or smaller than the optical resolution

We describe a transmission dark-field digital holographic microscope based on a Mach-Zehnder configuration for the detection of nanosize objects or objects smaller than the optical resolution limit. An optical stop adequately placed in the object beam removes the nondiffracted beam while keeping the light scattered by the object. This configuration combines an improved detection of objects smaller than the optical resolution with the refocusing capability yielded by digital holography. A theoretical analysis and an experimental demonstration are provided.

Evidence of an inverted temperature gradient during evaporation/condensation of a Lennard-Jones fluid

Molecular dynamics simulations of the Lennard-Jones fluid have been performed to study the vapor flow between two liquid slabs kept at slightly different temperatures. For the first time, direct evidence is found of the onset of inverted gradient temperature profiles in the vapor. The simulations results also show good agreement with a kinetic theory analysis of the vapor phase flow field.

VISCOUS FINGERING IN MISCIBLE, IMMISCIBLE AND REACTIVE FLUIDS

With the Lattice Boltzmann method (using the BGK approximation) we investigate the dynamics of Hele-Shaw flow under conditions corresponding to various experimental systems. We discuss the onset of the instability (dispersion relation), the static properties (characterization of the interface) and the dynamic properties (growth of the mixing zone) of simulated Hele-Shaw systems. We examine the role of reactive processes (between the two fluids) and we show that they have a sharpening effect on the interface similar to the effect of surface tension.

Nonextensive statistics in viscous fingering

Measurements in turbulent flows have revealed that the velocity field in nonequilibrium systems exhibits q-exponential or power-law distributions in agreement with theoretical arguments based on nonextensive statistical mechanics. Here we consider Hele–Shaw flow as simulated by the lattice Boltzmann method and find similar behavior from the analysis of velocity field measurements. For the transverse velocity, we obtain a spatial q-Gaussian profile and a power-law velocity distribution over all measured decades. To explain these results, we suggest theoretical arguments based on Darcys law combined with the nonlinear advection–diffusion equation for the concentration field. Power-law and q-exponential distributions are the signature of nonequilibrium systems with long-range interactions and/or long-time correlations, and therefore provide insight to the mechanism of the onset of fingering processes.

Propagation and organization in lattice random media

We show that a signal can propagate in a particular direction through a model random medium regardless of the precise state of the medium. As a prototype, we consider a point particle moving on a one-dimensional lattice whose sites are occupied by scatterers with the following properties: (i) the state of each site is defined by its spin (up or down); (ii) the particle arriving at a site is scattered forward (backward) if the spin is up (down); (iii) the state of the site is modified by the passage of the particle, i.e., the spin of the site where a scattering has taken place, flips (↑⇔↓). We consider one-dimensional and triangular lattices, for which we give a microscopic description of the dynamics, prove the propagation of a particle through the scatterers, and compute analytically its statistical properties. In particular we prove that, in one dimension, the average propagation velocity is 〈c(q)〉=1/(3−2q), with q the probability that a site has a spin ↑, and, in the triangular lattice, the average propagation velocity is independent of the scatterers distribution: 〈c〉=1/8. In both cases, the origin of the propagation is a blocking mechanism, restricting the motion of the particle in the direction opposite to the ultimate propagation direction, and there is a specific reorganization of the spins after the passage of the particle. A detailed mathematical analysis of this phenomenon is, to the best of our knowledge, presented here for the first time.

Coarse-grained modelling of surface nanobubbles

Surface nanobubbles are nanoscale gaseous objects that form on hydrophobic surfaces in contact with water. Understanding nanobubble formation and stability remains challenging due to the lack of appropriate theoretical framework and adequate modelling. Here we present a non-equilibrium coarse-grained model for nanobubbles at hydrophobic surfaces. The model is based on a lattice-gas model that has been proposed to understand the hydrophobic effect to which dynamical properties are added. The results presented demonstrate the ability of the model to reproduce the basic features of stable surface nanobubbles, which, thereby, supports the dynamical origin of these objects.