Ionic transfer in charged porous media. Periodic homogenization and parametric study on 2D microstructures

Bourbatache, Khaled; Millet, Olivier; Aït‐Mokhtar, Abdelkarim

doi:10.1016/j.ijheatmasstransfer.2012.06.008

Cited by 40 publications

(18 citation statements)

References 33 publications

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“…We next validate our HSE approach using an electrodiffusion model established by Bourbatache et al 27 In Figure 27 The slowing effect of repulsive interactions was previously attributed to an increased effective radius of the obstacles due to exclusion by the repulsive force, which reduces the accessible volume fraction. 28 These findings not only validate our model, but also suggest the utility of the HSE framework in modeling small-molecule diffusion within lattices of charged cylinders, such as the negatively charged thick (myosin) and thin (actin) filaments comprising muscle cell myofibrils 29 that we previously examined in the absence of electrostatics.…”

Section: A Validation Of Model Using a Cylindrical Periodic Systemmentioning

confidence: 82%

Predicting the influence of long-range molecular interactions on macroscopic-scale diffusion by homogenization of the Smoluchowski equation

Kekenes‐Huskey

Gillette

McCammon

2014

The Journal of Chemical Physics

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The macroscopic diffusion constant for a charged diffuser is in part dependent on (1) the volume excluded by solute "obstacles" and (2) long-range interactions between those obstacles and the diffuser. Increasing excluded volume reduces transport of the diffuser, while long-range interactions can either increase or decrease diffusivity, depending on the nature of the potential. We previously demonstrated [P. M. Kekenes-Huskey et al., Biophys. J. 105, 2130] using homogenization theory that the configuration of molecular-scale obstacles can both hinder diffusion and induce diffusional anisotropy for small ions. As the density of molecular obstacles increases, van der Waals (vdW) and electrostatic interactions between obstacle and a diffuser become significant and can strongly influence the latter's diffusivity, which was neglected in our original model. Here, we extend this methodology to include a fixed (time-independent) potential of mean force, through homogenization of the Smoluchowski equation. We consider the diffusion of ions in crowded, hydrophilic environments at physiological ionic strengths and find that electrostatic and vdW interactions can enhance or depress effective diffusion rates for attractive or repulsive forces, respectively. Additionally, we show that the observed diffusion rate may be reduced independent of non-specific electrostatic and vdW interactions by treating obstacles that exhibit specific binding interactions as "buffers" that absorb free diffusers. Finally, we demonstrate that effective diffusion rates are sensitive to distribution of surface charge on a globular protein, Troponin C, suggesting that the use of molecular structures with atomistic-scale resolution can account for electrostatic influences on substrate transport. This approach offers new insight into the influence of molecular-scale, long-range interactions on transport of charged species, particularly for diffusion-influenced signaling events occurring in crowded cellular environments.

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Section: A Validation Of Model Using a Cylindrical Periodic Systemmentioning

confidence: 82%

Predicting the influence of long-range molecular interactions on macroscopic-scale diffusion by homogenization of the Smoluchowski equation

Kekenes‐Huskey

Gillette

McCammon

2014

The Journal of Chemical Physics

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“…In the mathematical model of ionic diffusion used, we used macroscopic equations (1) to (4) where the influence of the physical phenomena at the microscopic and nanoscopic scales is included in the effective diffusion coefficient (Eq. 2) through the tortuosity factor [29]. In the present study the electric field was assumed to be constant during the simulation [18,23].…”

Section: Transport Phenomenonmentioning

confidence: 99%

Electrokinetic Remediation of Zinc and Copper Contaminated Soil: A Simulation-based Study

Rezaee¹,

Ghomesheh²,

Hosseini

2017

cej

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Electrokinetic is an effective and innovative method to remediate different kinds of soils, especially low permeable finedgrain soils such as silty and clayey soils. In this method, by applying a direct-current electric field into a contaminated soil resulted in different transport phenomena, the soil is remediated. This paper's objective is to propose a numerical model for Electrokinetic remediation of zinc and copper contaminated soils. Different transport phenomena including ion migration, electroosmosis flow, and diffusion were taken into account in the model. Chemical reactions such as precipitation/dissolution, adsorption onto the soil surface, and water chemical equilibrium were considered as well. Furthermore, instead of simplified boundary conditions (Neumann or Dirichlet) that cannot properly reflect the reality of the Electrokinetic remediation process, the realistic boundary conditions were used with consideration of flux and electrolysis reaction at the electrodes. The simulation results compared with the available experimental data in the literature. The coefficient of determination and the index of agreement indicated that the present model is consistent with the tests' results. Thus, the assumptions considered in the present study are acceptable.

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“…We prove here that the steady states of Nernst-Planck-Poisson system correspond to a Boltzmann charge distribution, as is it often assumed a priori in the literature [10][33] [34]. We have the following proposition that will be commented on after.…”

Section: Boltzmann Distribution Of Chargesmentioning

confidence: 52%

“…The ionic drift diffusion of aggressive agents in saturated porous media, as chlorides diffusion in concrete, are generally modeled with Nernst-Planck-Poisson (NPP) or Nernst-Planck-Poisson-Boltzmann (NPPB) system [10]- [13][33] [34]. The mathematical study of these systems of nonlinear partial differential equations is fundamental for civil engineering applications, such as the prediction of service life of mortar structures (building, bridges, etc.).…”

Section: Introductionmentioning

confidence: 99%

A survey on properties of Nernst–Planck–Poisson system. Application to ionic transport in porous media

Gagneux

Millet

2016

Applied Mathematical Modelling

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The aim of this paper is to study the properties of Nernst-Planck-Poisson system describing the evolution of ionic concentrations in porous media. In particular, the well-posedness character of the system is proved and some qualitative properties of the global solution are established (energy and entropy laws, stationary states, Boltzmann distribution, influence of an external electrical field). We prove also that a superficial accumulation of ions occurs when an important external electrical field is applied.Nernst-Planck-Poisson system, cementitious materials, wellposedness, energy and entropy laws 1 Corresponding author. Email address : olivier.millet@univ-lr.fr (O. Millet). 2 The condition of non-negativity, linked to the well-posedness character of the system, is also crucial in the numerical solution of NPP system. 1 analysis of the macroscopic system is due to H. Gajewski and K. Gröger [20] in 1986. Specifically, the crucial step of their proofs consists in finding appropriate a priori estimates in a analytical relevant framework (Dubinskii's compactness results and Schauder's fixed point theorem, Banach and Hilbert spaces, Sobolev functions, in spirit of J.-L. Lions variational methods [30]): boundedness properties by the Moser's iteration technique ([24], p.21-24), estimates by means of a physically motived Liapunov function. A nonlinear version is obtained in 1997 by Dıaz, J.I., Galiano, G. and Jungel, A. [15][16] for a quasilinear degenerate system arising in semiconductors theory; a degenerate parabolic system consisting in two equations for densities of charged particles and in the Poisson equation for an electric field is considered. The proof are based on energy methods. In this vein, M. Schmuck provided a particularly interesting extension by investigating the Navier-Stokes-Nernst-Planck-Poisson system ([41] and his doctoral dissertation [43]). However, these purely mathematical papers need to be adapted to the physical framework and to the context of electrochemistry in order to respect consistency of formulas with the physical units and the dimensionnal analysis without loss of mathematical rigor. Due to their technological relevance and the industrial stakes, these systems received and are currently receiving considerable emphasis on the side of numerical analysis. A. Prohl and M. Schmuck [36][37] propose different finite element convergent discretizations in order to reproduce such sui generis behaviors as the energy and entropy principles by means of suitable fixed point algorithms and stopping criteria. Further finite element convergent discretizations are presented by these authors in the broader framework of the Navier-Stokes-Nernst-Planck-Poisson system [36][37]. Generally, it is convenient to assume that porous media have a periodic microstructure. Consequently, many papers are concerned with the Nernst-Planck-Poisson model posed in periodic porous media since the continuity equations of the system are written at the microscopic level whereas only macroscopic physical quantities are of ...

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Ionic transfer in charged porous media. Periodic homogenization and parametric study on 2D microstructures

Cited by 40 publications

References 33 publications

Predicting the influence of long-range molecular interactions on macroscopic-scale diffusion by homogenization of the Smoluchowski equation

Predicting the influence of long-range molecular interactions on macroscopic-scale diffusion by homogenization of the Smoluchowski equation

Electrokinetic Remediation of Zinc and Copper Contaminated Soil: A Simulation-based Study

A survey on properties of Nernst–Planck–Poisson system. Application to ionic transport in porous media

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