A theoretical model is developed for predicting both conduction and diffusion in thin-film ionic conductors or cables. With the linearized Poisson-Nernst-Planck(PNP)theory, the two-dimensional(2D) equations for thin i...A theoretical model is developed for predicting both conduction and diffusion in thin-film ionic conductors or cables. With the linearized Poisson-Nernst-Planck(PNP)theory, the two-dimensional(2D) equations for thin ionic conductor films are obtained from the three-dimensional(3D) equations by power series expansions in the film thickness coordinate, retaining the lower-order equations. The thin-film equations for ionic conductors are combined with similar equations for one thin dielectric film to derive the 2D equations of thin sandwich films composed of a dielectric layer and two ionic conductor layers. A sandwich film in the literature, as an ionic cable, is analyzed as an example of the equations obtained in this paper. The numerical results show the effect of diffusion in addition to the conduction treated in the literature. The obtained theoretical model including both conduction and diffusion phenomena can be used to investigate the performance of ionic-conductor devices with any frequency.展开更多
Poisson-Nernst-Planck equations are a coupled system of nonlinear partial differential equations consisting of the Nernst-Planck equation and the electrostatic Poisson equation with delta distribution sources,which de...Poisson-Nernst-Planck equations are a coupled system of nonlinear partial differential equations consisting of the Nernst-Planck equation and the electrostatic Poisson equation with delta distribution sources,which describe the electrodiffusion of ions in a solvated biomolecular system.In this paper,some error bounds for a piecewise finite element approximation to this problem are derived.Several numerical examples including biomolecular problems are shown to support our analysis.展开更多
Poisson-Nernst-Planck equations are widely used to describe the electrodiffusion of ions in a solvated biomolecular system. Two kinds of two-grid finite element algorithms are proposed to decouple the steady-state Poi...Poisson-Nernst-Planck equations are widely used to describe the electrodiffusion of ions in a solvated biomolecular system. Two kinds of two-grid finite element algorithms are proposed to decouple the steady-state Poisson-Nernst-Planck equations by coarse grid finite element approximations. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the two-grid algorithms for solving Poisson-Nernst-Planck equations.展开更多
We have developed efficient numerical algorithms for solving 3D steadystate Poisson-Nernst-Planck(PNP)equations with excess chemical potentials described by the classical density functional theory(cDFT).The coupled PN...We have developed efficient numerical algorithms for solving 3D steadystate 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.展开更多
In this article,we derive the a posteriori error estimators for a class of steadystate Poisson-Nernst-Planck equations.Using the gradient recovery operator,the upper and lower bounds of the a posteriori error estimato...In this article,we derive the a posteriori error estimators for a class of steadystate Poisson-Nernst-Planck equations.Using the gradient recovery operator,the upper and lower bounds of the a posteriori error estimators are established both for the electrostatic potential and concentrations.It is shown by theory and numerical experiments that the error estimators are reliable and the associated adaptive computation is efficient for the steady-state PNP systems.展开更多
In this paper, a coordinate transformation method (CTM) is employed to numerically solve the Poisson–Nernst–Planck (PNP) equation and Navier–Stokes (NS) equations for studying the traveling-wave electroosmotic flow...In this paper, a coordinate transformation method (CTM) is employed to numerically solve the Poisson–Nernst–Planck (PNP) equation and Navier–Stokes (NS) equations for studying the traveling-wave electroosmotic flow (TWEF) in a two-dimensional microchannel. Numerical solutions indicate that the numerical solutions of TWEF with and without the coordinate transformation are in good agreement, while CTM effectively improves stability and convergence rate of the numerical solution, and saves computational cost. It is found that the averaged flow velocity of TWEF in a micro-channel strongly depends on frequency of the electric field. Flow rate achieves a maximum around the charge frequency of the electric double layer. The approximate solutions of TWEF with slip boundary conditions are also presented for comparison. It is shown that the NS solution with slip boundary conditions agree well with those of complete PNP-NS equations in the cases of small ratios of Electric double layer(EDL) thickness to channel depth(λD/H). The NS solution with slip boundary conditions over-estimates the electroosmotic flow velocity as this ratio(λD/H) is large.展开更多
Control of ion transport and fluid flow through nanofluidic devices is of primary importance for energy storage and conversion, drug delivery and a wide range of biological processes. Recent development of nanotechnol...Control of ion transport and fluid flow through nanofluidic devices is of primary importance for energy storage and conversion, drug delivery and a wide range of biological processes. Recent development of nanotechnology, synthesis techniques, purification technologies, and experiment have led to rapid advances in simulation and modeling studies on ion transport properties. In this review, the applications of Poisson-Nernst-Plank （PNP） equations in analyzing transport properties are presented. The molecular dynamics （MD） studies of transport properties of ion and fluidic flow through nanofluidic devices are reported as well.展开更多
Modeling of biomolecular systems plays an essential role in understanding biological processes, such as ionic flow across channels, protein modification or interaction, and cell signaling. The continuum model describe...Modeling of biomolecular systems plays an essential role in understanding biological processes, such as ionic flow across channels, protein modification or interaction, and cell signaling. The continuum model described by the Poisson- Boltzmann （PB）/Poisson-Nernst-Planck （PNP） equations has made great contributions towards simulation of these pro- cesses. However, the model has shortcomings in its commonly used form and cannot capture （or cannot accurately capture） some important physical properties of the biological systems. Considerable efforts have been made to improve the con- tinuum model to account for discrete particle interactions and to make progress in numerical methods to provide accurate and efficient simulations. This review will summarize recent main improvements in continuum modeling for biomolecu- lar systems, with focus on the size-modified models, the coupling of the classical density functional theory and the PNP equations, the coupling of polar and nonpolar interactions, and numerical progress.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11672265,11202182,and 11621062)the Fundamental Research Funds for the Central Universities(Nos.2016QNA4026 and2016XZZX001-05)the Open Foundation of Zhejiang Provincial Top Key Discipline of Mechanical Engineering
文摘A theoretical model is developed for predicting both conduction and diffusion in thin-film ionic conductors or cables. With the linearized Poisson-Nernst-Planck(PNP)theory, the two-dimensional(2D) equations for thin ionic conductor films are obtained from the three-dimensional(3D) equations by power series expansions in the film thickness coordinate, retaining the lower-order equations. The thin-film equations for ionic conductors are combined with similar equations for one thin dielectric film to derive the 2D equations of thin sandwich films composed of a dielectric layer and two ionic conductor layers. A sandwich film in the literature, as an ionic cable, is analyzed as an example of the equations obtained in this paper. The numerical results show the effect of diffusion in addition to the conduction treated in the literature. The obtained theoretical model including both conduction and diffusion phenomena can be used to investigate the performance of ionic-conductor devices with any frequency.
基金supported by the China NSF(NSFC 11001062,NSFC 11161014)the fund from Education Department of Guangxi Province under grant 201012MS094B.Z.Lu was supported by the National Center for Mathematics and Interdisciplinary Sciences,Chinese Academy of Sciences and the China NSF(NSFC10971218).
文摘Poisson-Nernst-Planck equations are a coupled system of nonlinear partial differential equations consisting of the Nernst-Planck equation and the electrostatic Poisson equation with delta distribution sources,which describe the electrodiffusion of ions in a solvated biomolecular system.In this paper,some error bounds for a piecewise finite element approximation to this problem are derived.Several numerical examples including biomolecular problems are shown to support our analysis.
文摘Poisson-Nernst-Planck equations are widely used to describe the electrodiffusion of ions in a solvated biomolecular system. Two kinds of two-grid finite element algorithms are proposed to decouple the steady-state Poisson-Nernst-Planck equations by coarse grid finite element approximations. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the two-grid algorithms for solving Poisson-Nernst-Planck equations.
基金the Materials Synthesis and Simulation across Scales(MS3)Initiative(Laboratory Directed Research and Development(LDRD)Program)at Pacific Northwest National Laboratory(PNNL).Work by GL was supported by the U.S.Department of Energy(DOE)Office of Science’s Advanced Scientific Computing Research Applied Mathematics program and work by BZ by Early Career Award Initiative(LDRD Program)at PNNL.PNNL is operated by Battelle for the DOE under Contract DE-AC05-76RL01830.
文摘We have developed efficient numerical algorithms for solving 3D steadystate 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.
基金supported by the China NSF(NSFC Nos.11971414,and 11571293).Y.Yang was supported by the China NSF(NSFC Nos.11561016,11701119 and 11771105)Guangxi Natural Science Foundation(Nos.2017GXNSFFA198012 and 2017GXNSFBA198056)the Hunan Key Laboratory for Computation and Simulation in Science and Engineering,Xiangtan University,Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation open fund.R.G.Shen was supported by Postgraduate Scientific Research and Innovation Fund of the Hunan Provincial Education Department(No.CX2017B268).
文摘In this article,we derive the a posteriori error estimators for a class of steadystate Poisson-Nernst-Planck equations.Using the gradient recovery operator,the upper and lower bounds of the a posteriori error estimators are established both for the electrostatic potential and concentrations.It is shown by theory and numerical experiments that the error estimators are reliable and the associated adaptive computation is efficient for the steady-state PNP systems.
文摘In this paper, a coordinate transformation method (CTM) is employed to numerically solve the Poisson–Nernst–Planck (PNP) equation and Navier–Stokes (NS) equations for studying the traveling-wave electroosmotic flow (TWEF) in a two-dimensional microchannel. Numerical solutions indicate that the numerical solutions of TWEF with and without the coordinate transformation are in good agreement, while CTM effectively improves stability and convergence rate of the numerical solution, and saves computational cost. It is found that the averaged flow velocity of TWEF in a micro-channel strongly depends on frequency of the electric field. Flow rate achieves a maximum around the charge frequency of the electric double layer. The approximate solutions of TWEF with slip boundary conditions are also presented for comparison. It is shown that the NS solution with slip boundary conditions agree well with those of complete PNP-NS equations in the cases of small ratios of Electric double layer(EDL) thickness to channel depth(λD/H). The NS solution with slip boundary conditions over-estimates the electroosmotic flow velocity as this ratio(λD/H) is large.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11374243 and 11574256)
文摘Control of ion transport and fluid flow through nanofluidic devices is of primary importance for energy storage and conversion, drug delivery and a wide range of biological processes. Recent development of nanotechnology, synthesis techniques, purification technologies, and experiment have led to rapid advances in simulation and modeling studies on ion transport properties. In this review, the applications of Poisson-Nernst-Plank （PNP） equations in analyzing transport properties are presented. The molecular dynamics （MD） studies of transport properties of ion and fluidic flow through nanofluidic devices are reported as well.
基金supported by the National Natural Science Foundation of China(Grant No.91230106)the Chinese Academy of Sciences Program for Cross&Cooperative Team of the Science&Technology Innovation
文摘Modeling of biomolecular systems plays an essential role in understanding biological processes, such as ionic flow across channels, protein modification or interaction, and cell signaling. The continuum model described by the Poisson- Boltzmann （PB）/Poisson-Nernst-Planck （PNP） equations has made great contributions towards simulation of these pro- cesses. However, the model has shortcomings in its commonly used form and cannot capture （or cannot accurately capture） some important physical properties of the biological systems. Considerable efforts have been made to improve the con- tinuum model to account for discrete particle interactions and to make progress in numerical methods to provide accurate and efficient simulations. This review will summarize recent main improvements in continuum modeling for biomolecu- lar systems, with focus on the size-modified models, the coupling of the classical density functional theory and the PNP equations, the coupling of polar and nonpolar interactions, and numerical progress.
