An Energetic Variational Approach for ion transport

Keywords

Physics, Classical mechanics, Electrokinetic phenomena, Boundary value problem, Poisson's equation

References

• Thermodynamics : an advanced course with problems and solutions亮五 久保 — 1968
• New Poisson–Boltzmann type equations: one-dimensional solutionsChiun‐Chang Lee, Hijin Lee, YunKyong Hyon — 2011
• Some General Theorems relating to VibrationsJohn William Strutt — 1871
• Derivation of Poisson and Nernst-Planck equations in a bath and channel from a molecular model.Z. Schuss, Boaz Nadler, Bob Eisenberg — 2001
• Energy variational analysis of ions in water and channels: Field theory for primitive models of complex ionic fluids.Bob Eisenberg, YunKyong Hyon, Chun Liu — 2010
• Reciprocal Relations in Irreversible Processes. II.Lars Onsager — 1931
• Induced electrokinetic transport in micro-nanofluidic interconnect devices.Xiaozhong Jin, Sony Joseph, Enid N. Gatimu — 2007
• Nonlinear Smoluchowski slip velocity and micro-vortex generationYuxing Ben, Hsueh‐Chia Chang — 2002
• Diffuse-charge dynamics in electrochemical systems.Martin Z. Bazant, Katsuyo Thornton, Armand Ajdari — 2004
• Adiabatic Relaxation of Convective-Diffusive Gas Transport in a Porous Fuel Cell ElectrodeKeith Promislow, John M. Stockie — 2001
• Energetic variational approach in complex fluids: Maximum dissipation principleYunKyong Hyon, Do Y. Kwak, Chun Liu — 2009
• LI. A contribution to the theory of electrocapillarityDavid Leonard Chapman — 1913
• Fundamentals of interface and colloid science, volume II. Solid-liquid interfacesRoger Parsons — 1997
• Digital flow control of electroosmotic pump: Onsager coefficients and interfacial parameters determinationZuli Xu, Jianying Miao, Ning Wang — 2011
• A variational approach to moving contact line hydrodynamicsTiezheng Qian, Xiaoping Wang, Ping Sheng — 2006
• Mathematical Methods of Classical MechanicsV. I. Arnold — 1974
• Onsager Principle and Electrorheological Fluid DynamicsPing Sheng, Jianwei Zhang, Chun Liu — 2008
• Progress and Prospects in PermeationWolfgang Nonner, Duan P. Chen, Bob Eisenberg — 1999
• Energy variational approach to study charge inversion (layering) near charged wallsYunKyong Hyon, James Fonseca, Bob Eisenberg — 2012
• Semiconductor equationsP. Markowich, C. Ringhofer, C. Schmeiser — 1990

Cited by

• Can we make biochemistry an exact scienceBob Eisenberg — 2014
• A Wasserstein gradient flow approach to Poisson−Nernst−Planck equationsDavid Kinderlehrer, Léonard Monsaingeon, Xiang Xu — 2015
• Mass Action and Conservation of CurrentBob Eisenberg — 2015
• Diffusion Limit of Kinetic Equations for Multiple Species Charged ParticlesHao Wu, Tai‐Chia Lin, Chun Liu — 2013
• Transport of Charged Particles: Entropy Production and Maximum Dissipation PrincipleChia-Yu Hsieh, YunKyong Hyon, Hijin Lee — 2014
• Conservation of Charge and Conservation of CurrentBob Eisenberg — 2016
• Well-posedness on a new hydrodynamic model of the fluid with the dilute charged particlesYong Wang, Chun Liu, Zhong Tan — 2017
• Modified Poisson-Nernst-Planck Model with Accurate Coulomb Correlation in Variable MediaPei Liu, Xia Ji, Zhenli Xu — 2016
• A novel linear second order unconditionally energy stable scheme for a hydrodynamic Q-tensor model of liquid crystalsJia Zhao, Xiaofeng Yang, Yuezheng Gong — 2017
• A Review of Mathematical Modeling, Simulation and Analysis of Membrane Channel Charge TransportDuan Chen, Guo‐Wei Wei — 2016
• Q-tensor model for electrokinetics in nematic liquid crystalsO. M. Tovkach, Christopher Conklin, M. Carme Calderer — 2016
• Analysis of the Mean Field Free Energy Functional of Electrolyte Solution with Nonhomogenous Boundary Conditions and the Generalized PB/PNP Equations with Inhomogeneous Dielectric PermittivityXuejiao Liu, Yu Qiao, Benzhuo Lu — 2018
• Modeling and Computations of Cellular Dynamics Using Complex-fluid ModelsJia Zhao — 2015
• Analysis of a degenerate parabolic cross-diffusion system for ion transportAnita Gerstenmayer, Ansgar Jüngel — 2017
• Dynamics of Current, Charge and MassBob Eisenberg, Xavier Oriols, D. K. Ferry — 2017
• Fractional Poisson–Nernst–Planck Model for Ion Channels I: Basic Formulations and AlgorithmsDuan Chen — 2017
• An Energetic Variational Approach for the Cahn-Hilliard Equation with Dynamic Boundary Conditions: Derivation and AnalysisChun Liu, Hao Wu — 2017
• Green's function and pointwise estimate for a generalized Poisson‐Nernst‐Planck‐Navier‐Stokes model in dimension threeZhigang Wu, Weike Wang — 2018
• Do Bistable Steric Poisson-Nernst-Planck Models Describe Single-Channel Gating?Nir Gavish, Chun Liu, Bob Eisenberg — 2018
• On transport of ionic solutions: from kinetic laws to continuum descriptionsHao Wu, Tai‐Chia Lin, Chun Liu — 2013

Related papers

• Electrokinetic transport of charged solutes in micro‐ and nanochannels: The influence of transverse electromigrationXiangchun Xuan, Dongqing Li — 2006
• Physical origins of apparently enhanced viscosity of interfacial fluids in electrokinetic transportPeng Wu, Rui Qiao — 2011
• Notes on the electrokinetic potential of cellulose and on electrokinetic equationsA. S. Buchanan, E. Heymann — 1948
• Electrokinetic Measurements on Stainless Steel CapillariesB. Levy, Alain Fritsch — 1959
• Electrokinetic energy conversion in microchannels using polymer solutions.Claudio L. A. Berli — 2010
• Research on the electrokinetic method for studying charging properties of biological cellsLin Cheng, Zhong Lisheng, Yue Zhang — 2011
• Influence of Gel Layers on Electrokinetic Phenomena: 2. Effect of Ions Interaction with the Gel LayerVíctor M. Starov, Yuri Solomentsev — 1993