PNP models with an arbitrary number of positively charged ion species and one negatively charged ion species are studied in this paper under the assumption that positively charged ion species have the same valence and...PNP models with an arbitrary number of positively charged ion species and one negatively charged ion species are studied in this paper under the assumption that positively charged ion species have the same valence and the permanent charge is a piecewise constant function. The permanent charge plays the key role in many functions of an ion channel, such as selectivity and gating. In this paper, using the geometric singular perturbation theory, a flux ratio independent of the permanent charge is proved.展开更多
In this paper, a stationary one-dimensional Poisson-Nernst-Planck model with permanent charge is studied under the assumption that <em>n</em> - 1 positively charged ion species have the same valence and th...In this paper, a stationary one-dimensional Poisson-Nernst-Planck model with permanent charge is studied under the assumption that <em>n</em> - 1 positively charged ion species have the same valence and the permanent charge is small. By expanding the singular solutions of Poisson-Nernst-Planck model with respect to small permanent charge, the explicit formulae for the zeroth order approximation and the first order approximation of individual flux can be obtained. Based on these explicit formulae, the effects of small permanent charges on individual flux are investigated.展开更多
A steady-state Poisson-Nernst-Planck model with n ion species is studied under the assumption that <em>n</em> - 1 positively charged ion species have the same valence and there is only one negatively charg...A steady-state Poisson-Nernst-Planck model with n ion species is studied under the assumption that <em>n</em> - 1 positively charged ion species have the same valence and there is only one negatively charged ion species. By re-scaling, this model can be viewed as a standard singularly perturbed system. Based on the explicit formulae for the solutions of its limit slow system and singular perturbation methods, the existence of the solutions is analyzed.展开更多
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
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
Poisson-Nernst-Planck systems are basic models for electrodiffusion process,particularly,for ionic flows through ion channels embedded in cell membranes.In this article,we present a brief review on a geometric singula...Poisson-Nernst-Planck systems are basic models for electrodiffusion process,particularly,for ionic flows through ion channels embedded in cell membranes.In this article,we present a brief review on a geometric singular perturbation framework for analyzing the steady-state of a quasi-one-dimensional Poisson-Nernst-Planck model.The framework is based on the general geometric singular perturbed theory from nonlinear dynamical system theory and,most crucially,on the reveal of two specific structures of Poisson-Nernst-Planck systems.As a result of the geometric framework,one obtains a governing system-an algebraic system of equations that involves all physical quantities such as protein structures of membrane channels as well as boundary conditions,and hence,provides a complete platform for studying the interplay between protein structure and boundary conditions and effects on ionic flow properties.As an illustration,we will present concrete applications of the theory to several topics of biologically significant based on collaboration works with many excellent researchers.展开更多
文摘PNP models with an arbitrary number of positively charged ion species and one negatively charged ion species are studied in this paper under the assumption that positively charged ion species have the same valence and the permanent charge is a piecewise constant function. The permanent charge plays the key role in many functions of an ion channel, such as selectivity and gating. In this paper, using the geometric singular perturbation theory, a flux ratio independent of the permanent charge is proved.
文摘In this paper, a stationary one-dimensional Poisson-Nernst-Planck model with permanent charge is studied under the assumption that <em>n</em> - 1 positively charged ion species have the same valence and the permanent charge is small. By expanding the singular solutions of Poisson-Nernst-Planck model with respect to small permanent charge, the explicit formulae for the zeroth order approximation and the first order approximation of individual flux can be obtained. Based on these explicit formulae, the effects of small permanent charges on individual flux are investigated.
文摘A steady-state Poisson-Nernst-Planck model with n ion species is studied under the assumption that <em>n</em> - 1 positively charged ion species have the same valence and there is only one negatively charged ion species. By re-scaling, this model can be viewed as a standard singularly perturbed system. Based on the explicit formulae for the solutions of its limit slow system and singular perturbation methods, the existence of the solutions is analyzed.
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.
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supported by Simons Foundation Mathematics and Physical Sciences-Collaboration Grants for Mathematicians 581822。
文摘Poisson-Nernst-Planck systems are basic models for electrodiffusion process,particularly,for ionic flows through ion channels embedded in cell membranes.In this article,we present a brief review on a geometric singular perturbation framework for analyzing the steady-state of a quasi-one-dimensional Poisson-Nernst-Planck model.The framework is based on the general geometric singular perturbed theory from nonlinear dynamical system theory and,most crucially,on the reveal of two specific structures of Poisson-Nernst-Planck systems.As a result of the geometric framework,one obtains a governing system-an algebraic system of equations that involves all physical quantities such as protein structures of membrane channels as well as boundary conditions,and hence,provides a complete platform for studying the interplay between protein structure and boundary conditions and effects on ionic flow properties.As an illustration,we will present concrete applications of the theory to several topics of biologically significant based on collaboration works with many excellent researchers.
