Related Experiment Video
Updated: May 4, 2026
08:51
Monitoring Protein Adsorption with Solid-state Nanopores
Published on: December 2, 2011
13.1K
A Stabilized Finite Element Method for Modified Poisson-Nernst-Planck Equations to Determine Ion Flow Through a
Jehanzeb Hameed Chaudhry1, Jeffrey Comer2, Aleksei Aksimentiev2
1Department for Mathematics, Colorado State University, Fort Collins, CO 80523, USA.
Communications in Computational Physics
|December 24, 2013
Summary
Finite ion size effects are crucial for accurate modeling of ion transport. This study introduces a robust finite element solver for modified Poisson-Nernst-Planck equations, yielding realistic ion concentrations near charged surfaces.
Area of Science:
- Computational physics
- Physical chemistry
- Nanotechnology
Background:
- Conventional Poisson-Nernst-Planck equations neglect finite ion size, leading to unrealistic high concentrations near charged surfaces.
- Modified Poisson-Nernst-Planck equations incorporating steric effects provide more accurate ionic concentration profiles.
Purpose of the Study:
- To evaluate numerical methods for solving modified Poisson-Nernst-Planck equations.
- To model electric field-driven ion transport through nanopores using a novel finite element solver.
Main Methods:
- Developed a robust finite element solver combining Newton's method with a nonlinear Galerkin form.
- Incorporated stabilization terms to handle drift-diffusion processes effectively.
- Designed the solver for periodic boundary conditions and ion number conservation for comparison with particle-based simulations.
Main Results:
- The finite element solver accurately models ion distribution and transport under various conditions.
- Demonstrated the solver's capability in simulating ion concentration near charged plates and ionic current through nanopores.
- Successfully modeled the influence of DNA on ion concentration and nanopore current.
Conclusions:
- The developed finite element solver offers a robust and accurate approach for solving modified Poisson-Nernst-Planck equations.
- This method provides realistic ion concentration profiles, crucial for understanding ion transport phenomena in nanoscale systems.
- The solver facilitates direct comparison with particle-based simulations, advancing the study of complex ionic systems.
Related Concept Videos
01:17Controlled-Potential Coulometry: Electrolytic Methods
916
Controlled-potential coulometry, also known as potentiostatic coulometry, employs a three-electrode system in which the working electrode's potential is precisely regulated using a potentiostat. Platinum working electrodes are utilized for positive potentials, while mercury pool electrodes are favored for extremely negative potentials. The platinum counter electrode is separated from the analyte using a membrane or salt bridge to avoid interference in the analysis.
The chosen potential...
The chosen potential...
916
01:17Pore Transport and Ion-Pair Transport
1.6K
Pore transport and ion-pair formation are critical mechanisms for the absorption and distribution of drugs in the body.
Pore transport, also known as convective transport, is a process where small molecules like urea, water, and sugars rapidly cross cell membranes as though there were channels or pores in the membrane. Although direct microscopic evidence is limited but the concept of pores or channels is widely accepted based on physiological evidence. Despite the lack of direct...
Pore transport, also known as convective transport, is a process where small molecules like urea, water, and sugars rapidly cross cell membranes as though there were channels or pores in the membrane. Although direct microscopic evidence is limited but the concept of pores or channels is widely accepted based on physiological evidence. Despite the lack of direct...
1.6K
01:28Debye–Huckel–Onsager Conductance Equation
291
The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect.
291
01:25Poisson's And Laplace's Equation
4.3K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
4.3K
01:31Transport Number
230
The transport number is the fraction of the total current carried by an ion in an electrolyte solution. It is defined as the ratio of the current carried by a specific ion to the total current flowing through the solution. The transport number, t, is central to understanding ionic mobility, which describes how fast an ion moves under the influence of an electric field. This link connects the physical behavior of ions in solution to the chemical processes that occur during electrochemical...
230