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Results for “Poisson-Nernst-Planck equations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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7 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Integral Kernel Methods for Nonlinear Parabolic-Elliptic Systems

Nonlinear parabolic-elliptic systems arise in many physical, biological, and chemical phenomena such as chemotaxis, ion transport, self-gravitating particles, and Brownian vortices. Existing methods struggle with the strong coupling and high nonlinearity and nonlocality of some of these systems, especially the ill-conditioned, convection-dominated problems. To overcome numerical difficulties, current approaches rely on initial guesses, preconditioning, or iterative techniques with no convergence guarantees. They might suffer from poor scalability, large memory usage, and difficulty to parallelize. Inspired by the connection of parabolic-elliptic systems to stochastic processes, we introduce a novel meshless, monolithic, and fully explicit method that naturally encapsulates the elliptic and parabolic operators into a single step which updates each node deterministically with global information. By being fully quadrature-based, it avoids solving systems of discretized equations and does not utilize initial guesses or preconditioning, while requiring little memory and being easy to parallelize. We first derive the method in an integral kernel formulation with quadratic complexity in the number of integration nodes and then leverage kernel-independent fast multipole methods (FMM) to present a scalable algorithm with linear complexity. We provide numerical examples for the Poisson-Nernst-Planck equations in one, two, and three dimensions, together with the derivation of the integral kernel for each case. Furthermore, the examples demonstrate the fast convergence and scalability of the FMM-accelerated algorithm, as well as its suitability for convection-dominated problems, making it competitive against traditional PDE solvers.

PDE systems↗
DOE OSTI2021

Microstructural changes and mass transport in cement-based materials: A modeling approach

Highlights: • Concept to relate microstructural changes, mass transport, and chemical reactions in cement-based materials is presented. • Multi-physics modeling approach utilizing an extended version of the PNP equation and the geochemical code IPHREEQC. • Case studies indicate significant changes in mass transport properties due to alterations in the microstructure. • Microstructural changes depend on exposure and interactions between chemical reactions, pore structure, and mass transport. A generic modeling framework is presented to relate microstructural changes, i.e. changes in the pore volume distribution and phase assemblage, and mass transport in cement-based materials. The modeling framework accounts for mass transport and chemical equilibrium between ions in the pore solution and solid hydrates by means of an extended version of the Poisson-Nernst-Planck equation, in which the chemical equilibrium is solved by the external geochemical code IPHREEQC. Results of numerical studies concerning carbonation and leaching of a cement-based material indicate significant changes in mass transport properties due to chemical reactions leading to alterations in the microstructure. The resulting highly non-linear (both spatial and temporal) microstructural changes are thereby depending on the exposure and indicate that interactions between chemical reactions, pore structure changes, and mass transport have to be accounted for as a whole.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Ion Transport in Charged Membranes: Linking Electric-Field-Driven Mechanisms to Pore Size via Perturbation Analysis

Ion-exchange membranes are a critical component in electrochemical systems. Nevertheless, the understanding and modeling of ion transport within these porous structures have been limited by particular complexity reductions, either ignoring the dimensionality of their porous network architecture or imposing geometric assumptions (i.e., overlapping double layers). Before addressing this morphology-transport gap, a framework that relates the driving forces of transport to the geometry of a single pore is required. In this work, our modeling domain consists of a two-dimensional single pore with charged walls, connecting two identical electrolyte reservoirs. Using the Poisson-Nernst-Planck equations and regular perturbation theory, we decouple the electric fields and analyze the driving forces of ion transport, specifically electromigration and induced electroosmosis within the pore. These processes are described as analytical functions of the interaction aspect ratio, ?, defined as the ratio of the pore radius to the Debye length. Using this parameter, our study (i) describes the interplay between electromigrative and electroosmotic mechanisms that set ionic conductivity, (ii) identifies a dimensionless group of intrinsic electrolyte properties that indicates the predominant driving force, and (iii) provides a qualitative, confinement-dependent perspective on selectivity in ion-conducting membranes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

MOSCATO Development and Integration in Fiscal Year 2022

During FY21, we conducted ongoing development work for the MOSCATO (Molten Salt Chemistry and Transport) solver. The code development work primarily consisted of transitioning capabilities from the original version of the solver, which was written in OpenFOAM, into Nek5000. In doing so, a fast, highly parallelizable solver was created that is capable of complex chemistry and corrosion simulations for engineering-scale molten salt systems. The Nek5000 version of MOSCATO is now fully featured and capable of higher-fidelity simulations than were previously possible. Demonstration cases including a thermal convection loop have been simulated to test these new capabilities. We built upon the work for FY22 and improved the code from several different perspectives. First, we improved the user interface by adding a new component to the official Nek5000 input file (.par). This new part contains documents parameters like, salt properties (density, viscosity, Cp, thermal conductivity), diffusion coefficients, standard potential, etc. Second, we built a conversion script to extract salt properties from the MSTDB-TP salt database and write to MOSCATO input file. Third, we migrated the code to NekRS, which is the GPU branch of Nek5000 and suitable for next generation supercomputers. Verification and Validation (V&V) work was also continued in FY22. Two tasks were performed. The first V&V task involved the validation of the Poisson-Nernst-Planck equation solver and Butler-Volmer electrode kinetics, by comparing with numerical and experimental data about thermoelectric cells. The second task involved the comparisons to corrosion results from a thermal convection loop run during the MSRE era. Satisfactory agreement was obtained from both tasks.

Yuan, Haomin↗
DOE OSTI2025

Physics-based stabilized finite element approximations of the Poisson–Nernst–Planck equations

We present and analyze two stabilized finite element methods for solving numerically the Poisson–Nernst–Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for the ion equations, whereas the discrete equation for the electric potential need not be stabilized. Discrete solutions stemmed from the first algorithm preserve both maximum and minimum discrete principles. For the second algorithm, its discrete solutions are conceived so that they hold discrete principles and obey an entropy law provided that an acuteness condition is imposed for meshes. Remarkably the latter is found to be unconditionally stable. We validate our methodology through transient numerical experiments that show convergence toward steady-state solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Breakdown of electroneutrality in nanopores

Ion transport in extremely narrow nanochannels has gained increasing interest in recent years due to unique physical properties at the nanoscale and the technological advances that allow us to study them. It is tempting to approach this confined regime with the theoretical tools and knowledge developed for membranes and microfluidic devices, and naively apply continuum models, such as the Poisson-Nernst-Planck and Navier-Stokes equations. However, it turns out that some of the most basic principles we take for granted in larger systems, such as the complete screening of surface charge by counter-ions, can break down under extreme confinement. Additionally, we show that in a truly one-dimensional system of ions interacting with three-dimensional electrostatic interactions, the screening length is exponentially large, and can easily exceed the macroscopic length of a nanotube. Without screening, electroneutrality breaks down within the nanotube, with fundamental consequences for ion transport and electrokinetic phenomena. In this work, we build a general theoretical framework for electroneutrality breakdown in nanopores, focusing on the most interesting case of a one-dimensional nanotube, and show how it provides an elegant interpretation for the peculiar scaling observed in experimental measurements of ionic conductance in carbon nanotubes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

A Poisson–Nernst–Planck Model of Ion Transport and Interface Segregation in Metal–Insulator–Semiconductor Structures and Solar Cells

A numerical model that describes the transport of mobile ionic species in metal–insulator–semiconductor (MIS) and photovoltaic (PV) devices subject to temperature and voltage stress is presented. The finite element method (FEM) is used to solve the Nernst–Planck equation while imposing Poisson's equation self-consistently as a restriction for the electrostatic potential. This allows the contribution of the ionic species to the potential to be taken into account. Using a variational formulation eases the implementation of diverse boundary conditions, including the incorporation of segregation kinetics at the device interfaces. Segregation across the dielectric–semiconductor interface is relevant to modeling the electronic device degradation in systems where contamination reaches the semiconductor. The model in closed systems with no-flux boundary conditions is validated first. In the limiting case of low contamination levels with respect to the gate bias, the FEM solution matches analytically derived approximations. Then, the implementation is broadened to include an open boundary at the dielectric–semiconductor interface to account for leakage of ions. The predicted time dependence of the flatband voltage in Na-contaminated MIS test structures agrees well with measurements. This model successfully captures the role of long-range ion transport at concentrations of relevance to electronic and PV device instability and neuromorphic computing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗