Academic literature on the topic 'Nernst-Planck-Poisson-Boltzmann problem'

Abstract Classical Poisson-Boltzman and Poisson-Nernst-Planck models can only work when ion concentrations are very dilute, which often mismatches experiments. Researchers have been working on the modification to include finite-size effect of ions, which is non-negelible when ion concentrations are not dilute. One of modified models with steric effect is Bikerman model, which is rather popular nowadays. It is based on the consideration of ion size by putting additional entropy term for solvent in free energy. However, ion size is non-specific in original Bikerman model, which did not consider specific ion sizes. Many researchers have worked on the extension of Bikerman model to have specific ion sizes. A direct extension of original Bikerman model by simply replacing the non-specific ion size to specific ones seems natural and has been acceptable to many researchers in this field.Herewe prove this straight forward extension, in some limiting situations, fails to uphold the basic requirement that ion occupation sites must be identical. This requirement is necessary when computing entropy via particle distribution on occupation sites.We derived a new modified Bikerman model for using specific ion sizes by fixing this problem, and obtained its modified Poisson-Boltzmann and Poisson-Nernst-Planck equations.

A lattice Boltzmann (LB) model is developed, validated and used to study simplified plasma/flow problems in complex geometries. This approach solves a combined set of equations, namely the Navier–Stokes equations for the momentum field, the advection–diffusion and the Nernst–Planck equations for electrokinetic and the Poisson equation for the electric field. This model allows us to study the dynamical interaction of the fluid/plasma density, velocity, concentration and electric field. In this work, we discuss several test cases for our numerical model and use it to study a simplified plasma fluid flowing and reacting inside a packed bed reactor. Inside the packed bed, electric breakdown reactions take place due to the electric field, making neutral species ionize. The presence of the packed beads can help enhance the reaction efficiency by locally increasing the electric field, and the size of packed beads and the pressure drop of the packed bed do influence the outflux. Hence trade-offs exist between reaction efficiency and packing porosity, the size of packing beads and the pressure drop of the packed bed. Our model may be used as a guidance to achieve higher reaction efficiencies by optimizing the relevant parameters. This article is part of the theme issue ‘Fluid dynamics, soft matter and complex systems: recent results and new methods’.

The overall objective of the current analysis is to examine how electroosmotic flow combined with peristaltic pumping phenomenon could ably contribute to intracellular fluid flow. The biofluid is taken as non-Newtonian Couple stress fluid, while micro-passage is approximated as two-dimensional inclined channel comprehending complex peristaltic walls. Following a traditional approach of peristaltic fluid flow problem balance of mass and momentum is utilized. Beside channel waves, flow is also generated by Lorentz force triggered by electric and magnetic fields. To integrate electric potential term Poisson-Boltzmann and Nernst Planck equation are utilized. Finally, a sixth order BVP in term of stream function is obtained by employing creeping flow, long wavelength and Debye-Hückel assumptions. A numerical solution is calculated and analyzed by plotting fluid velocity and level curves in MATLAB 2021b. It is observed that couple stress fluid flows with greater speed (in central region of the channel) as compared to Newtonian fluid. Moreover, electro-osmotic parameter and Debye-Hückel length are assistive factors to the fluid velocity in the lower half of the passage.

Cette thèse propose de coupler deux outils préexistant pour la modélisation mathématique en mécanique : l’homogénéisation périodique et la réduction de modèle, afin de modéliser la corrosion des structures de béton armé exposées à la pollution atmosphérique et au sel marin. Cette dégradation est en effet difficile à simuler numériquement, eu égard la forte hétérogénéité des matériaux concernés, et la variabilité de leur microstructure. L’homogénéisation périodique fournit un modèle multi-échelle permettant de s’affranchir de la première de ces deux difficultés. Néanmoins, elle repose sur l’existence d’un volume élémentaire représentatif (VER) de la microstructure du matériau poreux modélisé. Afin de prendre en compte la variabilité de cette dernière, on est amenés à résoudre en temps réduit les équations issues du modèle multi-échelle pour un grand nombre VER. Ceci motive l’utilisation de la méthode POD de réduction de modèle. Cette thèse propose de recourir à des transformations géométriques pour transporter ces équations sur la phase fluide d’un VER de référence. La méthode POD ne peut, en effet, pas être utilisée directement sur un domaine spatial variable (ici le réseau de pores du matériau). Dans un deuxième temps, on adapte ce nouvel outil à l’équation de Poisson-Boltzmann, fortement non linéaire, qui régit la diffusion ionique à l’échelle de la longueur de Debye. Enfin, on combine ces nouvelles méthodes à des techniques existant en réduction de modèle (MPS, interpolation ITSGM), pour tenir compte du couplage micro-macroscopique entre les équations issues de l’homogénéisation périodique
In this thesis, we manage to combine two existing tools in mechanics: periodic homogenization, and reduced-order modelling, to modelize corrosion of reinforced concrete structures. Indeed, chloride and carbonate diffusion take place their pores and eventually oxydate their steel skeleton. The simulation of this degradation is difficult to afford because of both the material heterogenenity, and its microstructure variability. Periodic homogenization provides a multiscale model which takes care of the first of these issues. Nevertheless, it assumes the existence of a representative elementary volume (REV) of the material at the microscopical scale. I order to afford the microstructure variability, we must solve the equations which arise from periodic homogenization in a reduced time. This motivates the use of model order reduction, and especially the POD. In this work we design geometrical transformations that transport the original homogenization equations on the fluid domain of a unique REV. Indeed, the POD method can’t be directly performed on a variable geometrical space like the material pore network. Secondly, we adapt model order reduction to the Poisson-Boltzmann equation, which is strongly nonlinear, and which rules ionic electro diffusion at the Debye length scale. Finally, we combine these new methods to other existing tools in model order reduction (ITSGM interpolatin, MPS method), in order to couple the micro- and macroscopic components of periodic homogenization

Joule heating is present in electrokinetically driven flow and mass transport in microfluidic systems. Specifically, in the cases of high applied voltages and concentrated buffer solutions, the thermal management may become a problem. In this study, a mathematical model is developed to describe the Joule heating and its effects on electroosmotic flow and mass species transport in microchannels. The proposed model includes the Poisson equation, the modified Navier-Stokes equation, and the conjugate energy equation (for the liquid solution and the capillary wall). Specifically, the ionic concentration distributions are modeled using (i) the general Nernst-Planck equation, and (ii) the simple Boltzmann distribution. These governing equations are coupled through temperature-dependent phenomenological thermal-physical coefficients, and hence they are numerically solved using a finite-volume based CFD technique. A comparison has been made for the results of the ionic concentration distributions and the electroosmotic flow velocity and temperature fields obtained from the Nernst-Planck equation and the Boltzmann equation. The time and spatial developments for both the electroosmotic flow fields and the Joule heating induced temperature fields are presented. In addition, sample species concentration is obtained by numerically solving the mass transport equation, taking into account of the temperature-dependent mass diffusivity and electrophoresis mobility. The results show that the presence of the Joule heating can result in significantly different electroosomotic flow and mass species transport characteristics.