arXiv subjects

Hervé Henry

Publications and source records attributed to Hervé Henry.

18 recordsLinked to original sources

arXiv2025

Numerical study of the effect of the relative mobilities of chemical components on the Non solvent induced phase separation process for membrane elaboration

The filtration membranes are often elaborated through a phase separation process where a polymer rich phase and a polymer poor phase spontaneously form through spinodal decomposition. One process that is still not well understood from a theoretical point of view is the Non-Solvent induced phase separation where a thermodynamically stable film of a a polymer mixture is put in contact with a bad solvent of the polymer. The invasion of the film by this non-solvent drives the film out of stability and leads to spinodal decomposition. During this phase separation polymer poor and polymer rich regions form. In this article we present a numerical study of the effect of kinetic coefficients: namely the relative mobilities of polymer and solvent/non-solvent on the observed patterns. Using 2D numerical simulations of the ternary Cahn-Hilliard model we show that for a given thermodynamic landscape, this parameter has dramatic effects: depending on its value phase separation can be observed or not. We also show that it can affect the nature of the observed pattern. In addition analysing 3D simulations we analyse the final pattern using a quantitative indicator of its connectivity and show that for a wide range of initial composition of the film the final pattern is bicontinuous. We also quantify the transport properties of both polymer rich and polymer poor domains.

cond-mat.soft↗

arXiv2025

Phase field study of the effective fracture energy increase during dynamic crack propagation in disordered heterogeneous materials

The propagation of a 3D crack in an heterogeneous material is studied using a phase field model. It is shown that in the case of randomly distributed inclusions of soft material in a matrix, the nature of the distribution has little effect on the effective elastic properties. On the opposite it affects significantly crack propagation. The less uniform distribution leads to higher thresholds for crack propagation.

cond-mat.mtrl-sci↗

arXiv2024

Rise and fall of a multicomponent droplet in a surrounrdfing fluid: simulation study of a bumpy path

The coupling between mass transfer and hydrodynamic phenomena in two-phase flow is not necessarily straightforward due to the different effects that can be encountered. The treatment of such coupling is complex and requires particular efforts, especially in the modelling of the interface between phases. In this paper, we consider the case of a droplet composed of two components (one miscible and one immiscible in water) released in a 2D rectangular domain filled with water. Mass transfer occurs between the miscible element and the surrounding water, which leads to a density inversion that directly affects the droplet trajectory through buoyancy. We perform simulations using a ternary Cahn-Hilliard model (implemented in the "phase\_field" model of the TrioCFD code) to capture such coupled phenomena. The Boussinesq approximation for a multicomponent system is used to define the density law and an analytical chemical potential is proposed for the thermodynamic landscape. The effect of the mobility parameter on the flow is highlighted and the results found are in good agreement with the dynamics described from an experimental study of the open literature.

physics.flu-dyn↗

arXiv2024

Numerical study of buoyancy induced arrest of viscous coarsening

The effect of buoyant forces on viscous coarsening is studied numerically. It is shown that at any time buoyant forces induce a vertical flow that scales like the Stokes velocity. This does no induce any noticeable change in the morphology of the coarsening microstructure under a value of the characteristic length of the pattern. Above this threshold the pattern evolves toward a quasi two D pattern and coarsening stops. The characteristic length is shown to scale like $\sqrt{γ/(g Δρ)}$ where $γ$ is he surface tension and $Δρ$ the mass dnsiy difference between the phases.

physics.flu-dyn↗

arXiv2024

Pinning of crack fronts by hard and soft inclusions: a phase field study

Through tridimensonal numerical simulations of crack propagating in material with an elastic moduli heterogeneity it is shown that the presence of a simple inclusion can affect dramatically the propagation of the crack. Both the presence of soft and hard inclusions can lead to the arrest of a crack front. Here the mechanism leading to the arrest of the crack are described and shown to depend on the nature of the inclusion. This is also the case in regimes where the presence of the inclusion leads to a slow down of the crack.

cond-mat.soft↗

arXiv2021

Limitations of the modelling of crack propagating through heterogeneous material using a phase field approach

The modeling of crack propagation in a heterogeneous material using a phase field model is studied numerically in a simple test case: the crack meets a wedge of higher fracture energy. It is shown that when the crack cannot enter the wedge, phase field results are in qualitative agreement with theoretical predictions with moderate quantitative discrepancies. When the crack can propagate in both regions, numerical results show that the interplay of diffuse interface modelling used in the phase field model with the interface between the two regions induces spurious effects that are unphysical.

cond-mat.mtrl-sci↗

arXiv2020

Two- and Three-Dimensional Simulations of Rayleigh-Taylor Instabilities Using a Coupled Cahn-Hilliard / Navier-Stokes Model

We report on two- and three-dimensional numerical simulations of Rayleigh-Taylor instabilities in immiscible fluids. A diffuse-interface model that combines the Cahn-Hilliard equation, governing the evolution of the volume fraction of one fluid, and the Navier-Stokes equations, governing the bulk velocity and pressure, is used. The study is limited to low Atwood numbers owing to the use of the Boussinesq approximation. The code is based on a pseudo-spectral method. A linear analysis is first performed in a two-dimensional case of Rayleigh-Taylor instability to confirm that the model very well captures this phenomenon in the case of inviscid or viscid fluids. One key aspect of this work is that the influence of the thermodynamic parameters related to the Cahn-Hilliard equation (interface thickness and mobility) is quantitively studied. Three-dimensional results of Rayleigh-Taylor instabilities in viscous fluids are then presented to show the possibilities of this modeling. We observe the effect of the viscosity and the wavelength of an initial single-mode perturbation on the mass transport during the nonlinear regime.

physics.flu-dyn↗

arXiv2019

On topological defects in two-dimensional orientation-field models for grain growth

Standard two-dimensional orientation-field based phase-field models rely on a continuous scalar field to represent crystallographic orientation. The corresponding order parameter space is the unit circle, which is not simply-connected. This topological property has important consequences for the resulting multi-grain structures: (i) trijunctions may be singular; (ii) for each pair of grains, there exist two different grain boundary solutions that cannot continuously transform to one another; (iii) if both solutions appear along a grain boundary, a topologically stable, singular point defect must exist between them. While (i) can, (ii) and therefore (iii) cannot be interpreted in the classical picture of grain boundaries. In addition, singularities cause difficulties, such as lattice pinning in numerical simulations. To overcome these problems, we propose two new formulations of the model. The first is based on a 3-component unit vector field, while in the second we utilise a 2-component vector field with an additional potential. In both cases, the additional degree of freedom introduced make the order parameter space simply-connected, which removes the topological stability of these defects.

cond-mat.mtrl-sci↗

arXiv2019

Nucleation of crystal surfaces with corner energy regularization

The thermodynamics of strongly anisotropic crystalline surfaces is analogous to that of a binary mixture exhibiting phase separation. On a metastable planar surface, formation of stable orientations requires a nucleation process, in which the energy associated with the presence of corners must be considered. In this context, a nucleation event corresponds to the formation of a critical shape for the crystalline surface before the system enters the growth regime. We first derive the Euler-Lagrange equation for crystal surface nucleation, in two dimensions, and show that the saddle-point condition corresponds to a vanishing chemical potential along this critical surface. We then perform numerical simulation of the equation of motion for the crystal surface and show that, as compared with saddle point nucleation, ridge crossing is dynamically favoured.

cond-mat.mtrl-sci↗

arXiv2019

Kinetics of coarsening have dramatic effects on the microstructure: self-similarity breakdown induced by viscosity contrast

The viscous coarsening of a phase separated mixture is studied and the effects of the viscosity contrast between the phases are investigated. From an analysis of the microstructure, it appears that for moderate departure from the perfectly symmetric regime the self-similar bicontinuous regime is robust. However, the connectivity of one phase decreases when its volume fraction decreases or when it is becoming less viscous than the complementary phase. Eventually self-similarity breakdown is observed and characterized.

cond-mat.soft↗

arXiv2018

On self similarity and coarsening rate of a convecting bicontinuous phase separating mixture: effect of the viscosity contrast

We present a computational study of the hydrodynamic coarsening in 3D of a critical mixture using the Cahn-Hilliard/Navier-Stokes model. The topology of the resulting intricate bicontinuous microstructure is analyzed through the principal curvatures to prove self-similar morphological evolution. We find that the self similarity exists for both systems: iso-viscous and with variable viscosity. However the two system have distinct topological character. Our simulations confirm that the predicted viscous growth regime exists in both cases. Moreover the coarsening rate is inversely proportional to an \textit{effective viscosity} that is the geometrical average of the viscosities of the two phases.

cond-mat.soft↗

arXiv2016

Crack front instabilities under mixed mode loading in three dimensions

The evolution of a crack front under mixed mode loading (I+III) is studied using a phase field model in 3 dimensions with no stress boundary conditions. As previously observed experimentally in gels, there is a relaxation toward a geometry where $K_{III}=0$ without any front fragmentation even for high values of the initial mode mixity $K_{III}/K_{I}$. The effects of the initial condition is studied and it is shown that irregularities in the initial slit can lead to front fragmentation for smaller values of the ratio $K_{III}/K_{I}$ as is observed in experiments.

cond-mat.soft↗

arXiv2015

An individual-based model for biofilm formation at liquid surfaces

The bacterium {\em Bacilus subtilis} frequently forms biofilms at the interface between the culture medium and the air. We develop a mathematical model that couples a description of bacteria as individual discrete objects to the standard advection-diffusion equations for the environment. The model takes into account two different bacterial phenotypes. In the motile state, bacteria swim and perform a run-and-tumble motion that is biased toward regions of high oxygen concentration (aerotaxis). In the matrix-producer state they excrete extracellular polymers, which allows them to connect to other bacteria and to form a biofilm. Bacteria are also advected by the fluid, and can trigger bioconvection. Numerical simulations of the model reproduce all the stages of biofilm formation observed in laboratory experiments. Finally, we study the influence of various model parameters on the dynamics and morphology of biofilms.

q-bio.CB↗

arXiv2012

An orientation-field model for polycristalline solidification with a singular coupling between order and orientation

The solidification of polycrystalline materials can be modelled by orientation-field models, which are formulated in terms of two continuous fields: a phase field that describes the thermodynamic state and an orientation field that indicates the local direction of the crystallographic axes. The free-energy functionals of existing models generally contain a term proportional to the modulus of the orientation gradient, which complicates their mathematical analysis and induces artificial long-range interactions between grain boundaries. We present an alternative model, in which only the square of the orientation gradient appears, but in which the phase and orientation fields are coupled by a singular function that diverges in the solid phase. We show that this model exhibits stable grain boundaries whose interactions decay exponentially with their distance. Furthermore, we demonstrate that the anisotropy of the surface energy can be included while preserving the variational structure of the model. Illustrative numerical simulations of two-dimensional examples are also presented.

cond-mat.mtrl-sci↗

arXiv2011

Tensorial mobilities for accurate solution of transport problems in models with diffuse interfaces

The general problem of two-phase transport in phase-field models is analyzed: the flux of a conserved quantity is driven by the gradient of a potential through a medium that consists of domains of two distinct phases which are separated by diffuse interfaces. It is shown that the finite thickness of the interfaces induces two effects that are not present in the analogous sharp-interface problem: a surface excess current and a potential jump at the interfaces. It is shown that both effects can be eliminated simultaneously only if the coefficient of proportionality between flux and potential gradient (mobility) is allowed to become a tensor in the interfaces. This opens the possibility for precise and efficient simulations of transport problems with finite interface thickness.

cond-mat.mtrl-sci↗

arXiv2010

Study of three-dimensional crack fronts under plane stress using a phase field model

The shape of a crack front propagating through a thin sample is studied using a phase field model. The model is shown to have a well defined sharp interface limit. The crack front is found to be an ellipse with large axis the width of the sample and small axis a function of the Poisson ratio and the width of the sample. Numerical results also indicate that the front shape is independent of the crack speed and of the sample extension perpendicular to its width.

cond-mat.mtrl-sci↗

arXiv2009

Phase-field simulations of viscous fingering in shear-thinning fluids

A phase-field model for the Hele-Shaw flow of non-Newtonian fluids is developed. It extends a previous model for Newtonian fluids to a wide range of shear-dependent fluids. The model is applied to perform simulations of viscous fingering in shear- thinning fluids, and it is found to be capable of describing the complete crossover from the Newtonian regime at low shear rate to the strongly shear-thinning regime at high shear rate. The width selection of a single steady-state finger is studied in detail for a 2-plateaux shear-thinning law (Carreau law) in both its weakly and strongly shear-thinning limits, and the results are related to previous analyses. In the strongly shear-thinning regime a rescaling is found for power-law (Ostwald-de-Waehle) fluids that allows for a direct comparison between simulations and experiments without any adjustable parameters, and good agreement is obtained.

cond-mat.soft↗

arXiv2004

The role of M cells and the long QT syndrome in cardiac arrhythmias: simulation studies of reentrant excitations using a detailed electrophysiological model

In this numerical study, we investigate the role of intrinsic heterogeneities of cardiac tissue due to M cells in the generation and maintenance of reentrant excitations using the detailed Luo-Rudy dynamic model. This model has been extended to include a description of the long QT 3 syndrome, and is studied in both one dimension, corresponding to a cable traversing the ventricular wall, and two dimensions, representing a transmural slice. We focus on two possible mechanisms for the generation of reentrant events. We first investigate if early-after-depolarizations occurring in M cells can initiate reentry. We find that, even for large values of the long QT strength, the electrotonic coupling between neighboring cells prevents early-after-depolarizations from creating a reentry. We then study whether M cell domains, with their slow repolarization, can function as wave blocks for premature stimuli. We find that the inclusion of an M cell domain can result in some cases in reentrant excitations and we determine the lifetime of the reentry as a function of the size and geometry of the domain and of the strength of the long QT syndrome.

q-bio.TO↗