Relevant bibliographies by topics / Poisson-Nernst-Planck (PNP) equations

Academic literature on the topic 'Poisson-Nernst-Planck (PNP) equations'

Author: Grafiati
Published: 10 December 2022
Last updated: 29 January 2023

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Journal articles on the topic "Poisson-Nernst-Planck (PNP) equations"

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Meng, Da, Bin Zheng, Guang Lin, and Maria L. Sushko. "Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment." Communications in Computational Physics 16, no. 5 (November 2014): 1298–322. http://dx.doi.org/10.4208/cicp.040913.120514a.

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AbstractWe have developed efficient numerical algorithms for solving 3D steady-state Poisson-Nernst-Planck (PNP) equations with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are discretized by a finite difference scheme and solved iteratively using the Gummel method with relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Then, the algebraic multigrid method is applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations. A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed, which reduces computational complexity from O(N2) to O(NlogN), where N is the number of grid points. Integrals involving the Dirac delta function are evaluated directly by coordinate transformation, which yields more accurate results compared to applying numerical quadrature to an approximated delta function. Numerical results for ion and electron transport in solid electrolyte for lithiumion (Li-ion) batteries are shown to be in good agreement with the experimental data and the results from previous studies.
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Hashemi Amrei, S. M. H., Gregory H. Miller, Kyle J. M. Bishop, and William D. Ristenpart. "A perturbation solution to the full Poisson–Nernst–Planck equations yields an asymmetric rectified electric field." Soft Matter 16, no. 30 (2020): 7052–62. http://dx.doi.org/10.1039/d0sm00417k.

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Sun, Ning, and Dilip Gersappe. "Simulation of diffuse-charge capacitance in electric double layer capacitors." Modern Physics Letters B 31, no. 01 (January 10, 2017): 1650431. http://dx.doi.org/10.1142/s0217984916504315.

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We use a Lattice Boltzmann Model (LBM) in order to simulate diffuse-charge dynamics in Electric Double Layer Capacitors (EDLCs). Simulations are carried out for both the charge and the discharge processes on 2D systems of complex random electrode geometries (pure random, random spheres and random fibers). The steric effect of concentrated solutions is considered by using a Modified Poisson–Nernst–Planck (MPNP) equations and compared with regular Poisson–Nernst–Planck (PNP) systems. The effects of electrode microstructures (electrode density, electrode filler morphology, filler size, etc.) on the net charge distribution and charge/discharge time are studied in detail. The influence of applied potential during discharging process is also discussed. Our studies show how electrode morphology can be used to tailor the properties of supercapacitors.
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MATEJCZYK, B., J. F. PIETSCHMANN, M. T. WOLFRAM, and G. RICHARDSON. "Asymptotic models for transport in large aspect ratio nanopores." European Journal of Applied Mathematics 30, no. 3 (June 6, 2018): 557–84. http://dx.doi.org/10.1017/s0956792518000293.

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Ion flow in charged nanopores is strongly influenced by the ratio of the Debye length to the pore radius. We investigate the asymptotic behaviour of solutions to the Poisson–Nernst–Planck (PNP) system in narrow pore like geometries and study the influence of the pore geometry and surface charge on ion transport. The physical properties of real pores motivate the investigation of distinguished asymptotic limits, in which either the Debye length and pore radius are comparable or the pore length is very much greater than its radius This results in a quasi-one-dimensional (1D) PNP model, which can be further simplified, in the physically relevant limit of strong pore wall surface charge, to a fully 1D model. Favourable comparison is made to the two-dimensional (2D) PNP equations in typical pore geometries. It is also shown that, for physically realistic parameters, the standard 1D area averaged PNP model for ion flow through a pore is a very poor approximation to the (real) 2D solution to the PNP equations. This leads us to propose that the quasi-1D PNP model derived here, whose computational cost is significantly less than 2D solution of the PNP equations, should replace the use of the 1D area averaged PNP equations as a tool to investigate ion and current flows in ion pores.
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SINGER, A., D. GILLESPIE, J. NORBURY, and R. S. EISENBERG. "Singular perturbation analysis of the steady-state Poisson–Nernst–Planck system: Applications to ion channels." European Journal of Applied Mathematics 19, no. 5 (October 2008): 541–60. http://dx.doi.org/10.1017/s0956792508007596.

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Ion channels are proteins with a narrow hole down their middle that control a wide range of biological function by controlling the flow of spherical ions from one macroscopic region to another. Ion channels do not change their conformation on the biological time scale once they are open, so they can be described by a combination of Poisson and drift-diffusion (Nernst–Planck) equations called PNP in biophysics. We use singular perturbation techniques to analyse the steady-state PNP system for a channel with a general geometry and a piecewise constant permanent charge profile. We construct an outer solution for the case of a constant permanent charge density in three dimensions that is also a valid solution of the one-dimensional system. The asymptotical current–voltage (I–V) characteristic curve of the device (obtained by the singular perturbation analysis) is shown to be a very good approximation of the numerical I–V curve (obtained by solving the system numerically). The physical constraint of non-negative concentrations implies a unique solution, i.e., for each given applied potential there corresponds a unique electric current (relaxing this constraint yields non-physical multiple solutions for sufficiently large voltages).
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Sheu, Tony W. H., Yogesh G. Bhumkar, S. T. Yuan, and S. C. Syue. "Development of a High-Resolution Scheme for Solving the PNP-NS Equations in Curved Channels." Communications in Computational Physics 19, no. 2 (February 2016): 496–533. http://dx.doi.org/10.4208/cicp.230914.040615a.

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AbstractA high-order finite difference scheme has been developed to approximate the spatial derivative terms present in the unsteady Poisson-Nernst-Planck (PNP) equations and incompressible Navier-Stokes (NS) equations. Near the wall the sharp solution profiles are resolved by using the combined compact difference (CCD) scheme developed in five-point stencil. This CCD scheme has a sixth-order accuracy for the second-order derivative terms while a seventh-order accuracy for the first-order derivative terms. PNP-NS equations have been also transformed to the curvilinear coordinate system to study the effects of channel shapes on the development of electroos-motic flow. In this study, the developed scheme has been analyzed rigorously through the modified equation analysis. In addition, the developed method has been computationally verified through four problems which are amenable to their own exact solutions. The electroosmotic flow details in planar and wavy channels have been explored with the emphasis on the formation of Coulomb force. Significance of different forces resulting from the pressure gradient, diffusion and Coulomb origins on the convective electroosmotic flow motion is also investigated in detail.
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KHAIR, ADITYA S., and TODD M. SQUIRES. "Ion steric effects on electrophoresis of a colloidal particle." Journal of Fluid Mechanics 640 (November 13, 2009): 343–56. http://dx.doi.org/10.1017/s0022112009991728.

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We calculate the electrophoretic mobility Me of a spherical colloidal particle, using modified Poisson–Nernst–Planck (PNP) equations that account for steric repulsion between finite sized ions, through Bikerman's mean-field model (Bikerman, Phil. Mag., vol. 33, 1942, p. 384). Ion steric effects are controlled by the bulk volume fraction of ions ν, and for ν = 0 the standard PNP equations are recovered. An asymptotic analysis in the thin-double-layer limit reveals at small zeta potentials (ζ < kBT/e ≈ 25 mV) Me to increase linearly with ζ for all ν, as expected from the Helmholtz–Smoluchowski (HS) formula. For larger ζ, however, it is well known that surface conduction of ions within the double layer reduces Me below the HS result. Crucially, however, in the PNP equations surface conduction becomes significant precisely because of the aphysically large and unbounded counter-ion densities predicted at large ζ. In contrast, ion steric effects impose a limit on the counter-ion density, thereby mitigating surface conduction. Hence, Me does not fall as far below HS for finite sized ions (ν ≠ 0). Indeed, at sufficiently large ν, ion steric effects are so dramatic that a maximum in Me is not observed for physically reasonable values of ζ(≤ 10 kBT/e), in stark contrast to the PNP-based calculations of O'Brien & White (J. Chem. Soc. Faraday Trans. II, vol. 74, 1978, p. 1607) and O'Brien (J. Colloid Interface Sci., vol. 92, 1983, p. 204). Finally, by calculating a Dukhin–Bikerman number characterizing the relative importance of surface conduction, we collapse Me versus ζ data for different ν onto a single master curve.
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Zhang, Kai, Lengjun Jiang, Zhihan Gao, Changxiu Zhai, Weiwei Yan, and Shuxing Wu. "Design and Numerical Study of Micropump Based on Induced Electroosmotic Flow." Journal of Nanotechnology 2018 (2018): 1–6. http://dx.doi.org/10.1155/2018/4018503.

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Induced charge electroosmotic flow is a new electric driving mode. Based on the Navier–Stokes equations and the Poisson–Nernst–Planck (PNP) ion transport equations, the finite volume method is adopted to calculate the equations and boundary conditions of the induced charge electroosmotic flow. In this paper, the formula of the induced zeta potential of the polarized solid surface is proposed, and a UDF program suitable for the simulation of the induced charge electroosmotic is prepared according to this theory. At the same time, on the basis of this theory, a cross micropump driven by induced charge electroosmotic flow is designed, and the voltage, electric potential, charge density, and streamline of the induced electroosmotic micropump are obtained. Studies have shown that when the cross-shaped micropump is energized, in the center of the induction electrode near the formation of a dense electric double layer, there exist four symmetrical vortices at the four corners, and they push the solution towards both outlets; it can be found that the average velocity of the solution in the cross-flow microfluidic pump is nonlinear with the applied electric field, which maybe helpful for the practical application of induced electroosmotic flow in the field of micropump.
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Ma, Pengfei, Jianxiang Zheng, Danting Zhao, Wenjie Zhang, Gonghao Lu, Lingxin Lin, Zeyuan Zhao, Zijing Huang, and Liuxuan Cao. "The Selective Transport of Ions in Charged Nanopore with Combined Multi-Physics Fields." Materials 14, no. 22 (November 19, 2021): 7012. http://dx.doi.org/10.3390/ma14227012.

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The selective transport of ions in nanopores attracts broad interest due to their potential applications in chemical separation, ion filtration, seawater desalination, and energy conversion. The ion selectivity based on the ion dehydration and steric hindrance is still limited by the very similar diameter between different hydrated ions. The selectivity can only separate specific ion species, lacking a general separation effect. Herein, we report the highly ionic selective transport in charged nanopore through the combination of hydraulic pressure and electric field. Based on the coupled Poisson–Nernst–Planck (PNP) and Navier–Stokes (NS) equations, the calculation results suggest that the coupling of hydraulic pressure and electric field can significantly enhance the ion selectivity compared to the results under the single driven force of hydraulic pressure or electric field. Different from the material-property-based ion selective transport, this method endows the general separation effect between different kinds of ions. Through the appropriate combination of hydraulic pressure and electric field, an extremely high selectivity ratio can be achieved. Further in-depth analysis reveals the influence of nanopore diameter, surface charge density and ionic strength on the selectivity ratio. These findings provide a potential route for high-performance ionic selective transport and separation in nanofluidic systems.
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Xu, Shixin, Minxin Chen, Sheereen Majd, Xingye Yue, and Chun Liu. "Modeling and Simulating Asymmetrical Conductance Changes in Gramicidin Pores." Computational and Mathematical Biophysics 2, no. 1 (January 1, 2014). http://dx.doi.org/10.2478/mlbmb-2014-0003.

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Abstract Gramicidin A is a small and well characterized peptide that forms an ion channel in lipid membranes. An important feature of gramicidin A (gA) pore is that its conductance is affected by the electric charges near the its entrance. This property has led to the application of gramicidin A as a biochemical sensor for monitoring and quantifying a number of chemical and enzymatic reactions. Here, a mathematical model of conductance changes of gramicidin A pores in response to the presence of electrical charges near its entrance, either on membrane surface or attached to gramicidin A itself, is presented. In this numerical simulation, a two dimensional computational domain is set to mimic the structure of a gramicidin A channel in the bilayer surrounded by electrolyte. The transport of ions through the channel is modeled by the Poisson-Nernst-Planck (PNP) equations that are solved by Finite Element Method (FEM). Preliminary numerical simulations of this mathematical model are in qualitative agreement with the experimental results in the literature. In addition to the model and simulations, we also present the analysis of the stability of the solution to the boundary conditions and the convergence of FEM method for the two dimensional PNP equations in our model.
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Conference papers on the topic "Poisson-Nernst-Planck (PNP) equations"

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Mathur, Sanjay R., and Jayathi Y. Murthy. "A Multigrid Method for the Solution of Ion Transport Using the Poisson Nernst Planck Equations." In ASME 2007 InterPACK Conference collocated with the ASME/JSME 2007 Thermal Engineering Heat Transfer Summer Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/ipack2007-33410.

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Recently there has been much interest in simulating ion transport in biological and synthetic ion channels using the Poisson-Nernst-Planck (PNP) equations. However, many published methods exhibit poor convergence rates, particularly at high driving voltages, and for long-aspect ratio channels. The paper addresses the development of a fast and efficient coupled multigrid method for the solution of the PNP equations. An unstructured cell-centered finite volume method is used to discretize the governing equations. An iterative procedure, based on a Newton-Raphson linearization accounting for the non-linear coupling between the Poisson and charge transport equations, is employed. The resulting linear system of equations is solved using an algebraic multigrid method, with coarse level systems being created by agglomerating finer-level equations based on the largest coefficients of the Poisson equation. A block Gauss-Seidel update is used as the relaxation method. The method is shown to perform well for ion transport in a synthetic channel for aspect ratios ranging from 16.67 to 1667 for a range of operating parameters.
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Fernandes, Dolfred Vijay, Sangmo Kang, and Yong Kweon Suh. "Numerical Analysis of Electrokinetic Interaction Between a Colloidal Particle and a Planar Wall." In ASME 2009 Second International Conference on Micro/Nanoscale Heat and Mass Transfer. ASMEDC, 2009. http://dx.doi.org/10.1115/mnhmt2009-18426.

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At present electrokinetics is widely used in biotechnology for the manipulation of biomolecules, such as separation of proteins, sequencing of polypeptide chains etc. Thus it is important to study the interaction forces between the molecules and the surfaces they come in contact. In the present study we numerically solve Poisson-Nernst-Planck (PNP) model to obtain electric double layer (EDL) and its interaction when a cylindrical particle is in proximity of a planar charged wall. The axial flow field induced by the external electric field applied parallel to the planar wall is obtained from the solution of Stokes equations. The electrophoretic motion of the particle is then obtained by balancing the forces acting on the particle such as hydrodynamic, electrostatic etc. The EDL interaction force calculated using Maxwell tensor in conjunction with PNP model is validated by comparing with the one obtained from surface-element-integration method.
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Sprague, Isaac B., and Prashanta Dutta. "The Electrode-Electrolyte Interface in Acidic and Alkaline Fuel Cells." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-63833.

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This numerical study presents the role of diffuse region of the electric double layer in both acidic and alkaline fuel cells. The numerical model is based on the Poisson-Nernst-Planck (PNP) and generalized-Frumkin-Butler-Volmer (gFBV) equations. The Laminar Flow Fuel Cell (LFFC) is used as the model fuel cell architecture to allow for the appropriate and equivalent comparison of acidic and alkaline cells. In particular, we focus on how each device behaves to changing reactant supply at the electrodes, including the overall cell performance and individual electrode polarizations. It is found that the working ion concentration at the reaction plane contributes to differing performance behaviors in acidic and alkaline fuel cells, including activation losses and reactant transport overpotentials. This is due to the working ion, and the electrode where it’s consumed, being opposite for acidic and alkaline fuel cells.
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Cha, Youngsu, Matteo Aureli, and Maurizio Porfiri. "On a Physics-Based Model of the Electrical Impedance of Ionic Polymer Metal Composites." In ASME 2012 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/smasis2012-7982.

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In this paper, we analyze the chemoelectrical behavior of ionic polymer metal composites (IPMCs) in the small voltage range with a novel hypothesis on the charge dynamics in proximity of the electrodes. Specifically, this paper introduces a so-called composite layer which extends between the polymer membrane and the metal electrode. This homogeneous layer describes the charge distribution at the electrode via two species of charge carriers, that is, electrons and mobile counterions. Charge dynamics is described by adapting the multi-physics formulation based on the Poisson-Nernst-Planck (PNP) equations through the incorporation of the electron transport in the composite layer. Under the hypothesis of small voltage input, we use the linearized PNP model to derive an equivalent IPMC impedance model with lumped elements. The equivalent model is represented as a resistor connected in series with the parallel of a capacitor and a Warburg impedance element. These elements idealize the phenomena of charge build up in the double layer region and the faradaic impedance related to mass transfer, respectively. We validate the equivalent model through measurements on in-house fabricated samples addressing both IPMC step response and impedance.
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Fernandes, Dolfred Vijay, Sangmo Kang, and Yong Kweon Suh. "Numerical Study on Electrokinetic Interaction Between a Pair of Cylindrical Colloidal Particles." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-10582.

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Electrophoresis is the motion of dispersed particles relative to a fluid under the influence of an electric field. Presently this phenomenon of electrokinetics is widely used in biotechnology for the separation of proteins, sequencing of polypeptide chains etc. The separation efficiency of these biomolecules is affected by their aggregation. Thus it is important to study the interaction forces between the molecules. In this study we calculate the electrophoretic motion of a pair of colloidal particles under axial electric field. The hydrodynamic and electric double layer (EDL) interaction forces are calculated numerically. The EDL interaction force is calculated from electric field distribution around the particle using Maxwell stress tensor and the hydrodynamic force is calculated from the flow field obtained from the solution of Stokes equations. The continuous forcing approach of immersed boundary method is used to obtain flow field around the moving particles. The EDL distribution around the particles is obtained by solving Poisson-Nernst-Planck (PNP) equations on a hybrid grid system. The EDL interaction force calculated from numerical solution is compared with the one obtained from surface element integration (SEI) method.
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Hung, S. W., C. P. Chen, and C. C. Chieng. "Ionic Transport in Finite Length Nano-Sized Pores and Channels." In ASME 2008 First International Conference on Micro/Nanoscale Heat Transfer. ASMEDC, 2008. http://dx.doi.org/10.1115/mnht2008-52128.

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Surface-charge regulated ionic transport phenomena in nano-pores and nano-channels have important applications in bio molecular analyses and power conversion involving NEMS. In such devises, the surface-to-volume ratio increases significantly. In nanofluidics, one characteristic is the overlapping of the electrical double layer (EDL) and the disappearance of the electrically neutral zone. The configuration to be considered is a finite length nano pore/channel connected by two reservoirs. Multi-dimensional analyses based on solutions of the Poisson-Nernst-Planck (PNP) equation were performed for the configuration in this study. Numerical solutions show that the ionic transport process in such a configuration depends strongly on the liquid-solid interface models used. These interface models usually serve as wall boundary conditions in multi-dimensional numerical analyses. Most current models were derived based on 1-D fully developed analyses. Issues regarding the extension of the surface chemical equilibrium model to multi-dimensional nanofluidics simulations involving overlapping EDLs were investigated and discussed in this paper.
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