Apr 11, 2011 i am trying to simulate the electroosmotic flow in a nanochannel using the poisson nernst planck and navierstokes equations coupling them from the electrostatics,transport of dilute species and laminar flow modules respectively using stationary solver in comsol 4. Utilizing the unparalleled capabilities in comsol multiphysics, this interface can be seamlessly coupled to other interfaces that describe fluid flow and heat transfer. Aug 30, 2009 is it possible to solve timedependent schroedinger equation using comsol multiphysics. How to model ionexchange membranes and donnan potentials. In ion transport, i used electrostatic and dilute material transport interfaces, as well as nernstplankposson, but i cant find an interface for nernst equation. The nernstplanck equation is often used to describe the diffusion, convection, and migration of charged particles. It includes the nernstplanck np equations for each charged species in the electrolytic solution in addition to a charge conservation equation which relates the species concentration to each other. The poissonnernstplanck pnp system for ion transport.
The migration, diffusion and convection mass transfer mechanisms were solved using the nernstplanck equation coupled to the navierstokes equation. I assumed that there is no chemical reaction at the interface, so it means that the current density is zero. I am new to the software and want to set up a 2d electromechanical model with pde modules not the batteries and fuel cells module. The electrochemistry module provides an interface for tertiary current distributions that utilizes the nernstplanck equation to describe the transport of chemical species in the electrolyte. Also this interface is available for fixed and moving boundaries. The electrostatic poisson equation was defined in the biomolecules and in the solvent, while the nernstplanck equation. Solving poisson, nernstplanck and navierstokes for a nanopore in. An introduction to fluid flow, heat transfer, and mass transport the subject of transport phenomena describes the transport of momentum, energy, and mass in the form of mathematical relations 1. Numerical simulation of electricallydriven flows using.
I want to model the electric double layer using the nernst planck equation, also coupled with poisson equation. I have a problem in coupling poissons equation and nernst planck equation. Poissonboltzmann equation 4 2 0 1 f i i i h h \ f z c nernstplanck equation. I hope this derivation of the pervasive nernst equation helps give you a feel for the thinking behind its development as well as some inroad into practically applying the equation to problems in neuroscience. A corrosion model based on the mixed potential theory was used to provide kinetics parameters for oxygen reduction, water reduction and iron oxidation reactions. Also, your interval is 1 m long, which makes no sense, i. The poissonnernstplanck pnp system for ion transport taichia lin national taiwan university 3rd ocamitims workshop in japan, osaka, march 16, 2011. In nernst plank equation, we must enter the mobility of one ion for the migration in electric field. Whereas the theory of the poisson equation is mainly rooted in electrostatics, the nernstplanck equation is an incarnation of a conservation law, as will be shown later. Note that while comsol employees may participate in the discussion forum, comsol software users who are onsubscription should submit their questions via the support center for a more comprehensive response from the technical support team. The stressaffected diffusion equation i have used is. But i am confused as to what equations to include in my multiphysics. I want to model the electric double layer using the nernstplanck equation, also coupled with poisson equation. You will need an onsubscription comsol license attached to your comsol access account or a software trial provided by your sales representative.
This may sound completely wrong to anyone who has seen, for instance, a nafion membrane, one of the most common polymer electrolyte materials. Electroneutrality is inherently included in the current balance. The time dependent form of the nernstplanck equation is a conservation of mass equation used to describe the motion of a charged chemical species in a fluid medium. However i need the nernst planck without electroneutrality and comsol does not seem to offer that.
Overview of fluid flow, heat transfer, and mass transport. I am trying to simulate the electroosmotic flow in a nanochannel using the poisson nernst planck and navierstokes equations coupling them from the electrostatics,transport of dilute species and laminar flow modules respectively using stationary solver in comsol 4. This includes electrolyte mass transport explicitly in the analysis, which is a computationally much more demanding problem since. In this paper we developed accurate finite element methods for solving 3d poissonnernstplanck pnp equations with singular permanent charges for electrodiffusion in solvated biomolecular systems. Now, with one species leaving, the concentration changes and therfore the space charge density, which over the poissonequation and and the defined space charge density should have influence on the migrationterm in the nernstplanck equation as far as i understand. The chemical reaction engineering module is useful for engineers and scientists working for example within the chemical, process, electric power, pharmaceutical, polymer, and food industries where material transport and chemical reaction are integral to the process you are working with. The new nernstplanckpoisson equations multiphysics interface can be used to investigate charge and ion distributions within an electrochemical double layer. The comsol discussion forum covers a wide variety of simulation topics. The nernstplanck equation is used to describe the mass transport of species.
Equation 638 is defined by the electrokinetic flow application mode in the chemical engineering module and does not solve the electroneutrality condition as in the nernst planck application mode for this type of transport. Noting the increased use of this product in analytical electrochemistry, the authors. Equation 638 is defined by the electrokinetic flow application mode in the chemical engineering module and does not solve the electroneutrality condition as in the nernstplanck application mode for this type of transport. Blog best posters from the comsol conference 2016 shanghai. This enables you to couple the physics describing your electrodeposition or etching process to other modules, such as the heat transfer module for studying thermal.
Nernstplanck equation system hermes examples guide. The existence and stability for the solutions of the steady pnp equations are established by jerome in studying the steady van roostbroeck model for electron flows in semiconductors, via a delicate construction of a schauder fixed point. Nernstplanck equation with excel which turns out to be interesting. It allows you to solve these equations in two ways. Browse the threads and share your ideas with the comsol community. The use of the nernstplanck and poisson npp equations allows. The basis for these descriptions is found in the laws for conservation of momentum, energy, and mass in combination with. A pore network modeling pnm framework 1 for the simulation of transport of charged species, such as ions, in porous media is presented. In what concerns available software packages, comsol multiphysics. I want to model ionic behavior in a conical nanopore and need to solve the nernst planck, poisson and navier stokes equations. A simple derivation of the nernst equation the goal of this handout is to help you avoid taking notes during the lecture.
The subject of transport phenomena describes the transport of momentum, energy, and mass in the form of mathematical relations. Nonlinear poissonnernst planck equations for ion flux through con. The new nernstplanckpoisson equations multiphysics interface can be used to investigate charge and ion distributions within an electrochemical double layer, where charge neutrality cannot be assumed. Multiphysics moduleheat transferconduction and convection steady state analysis. If you do not yet have a comsol access account, please create one now.
Using this application mode, we have obtained the concentration fields of the ionic species as well as the charge distribution as a function of time. Our group uses comsol multiphysics for numerical simulation to. Definition of species within the nernstplanck application in chem. The nernstplanckpoisson equations an ionexchange material is typically modeled as a porous medium consisting of a fixed matrix with the pores filled up with water and additional mobile ions. Modeling transport of charged species in pore networks. Poissonnernstplanck equations for simulating biomolecular. In this paper we developed accurate finite element methods for solving 3d poisson nernst planck pnp equations with singular permanent charges for electrodiffusion in solvated biomolecular systems. Comsol white paper series modeling corrosion and corrosion protection 6 the model equations in the electrolyte domain are as follows. Planck formulation of conservative and reactive transport equations 14, allowing the description of physical displacement, coulombic interactions, and a wide range of geochemical reactions in multidimensional saturated porous media. A corrosion model based on the mixed potential theory was used to provide kinetics parameters for oxygen reduction, water.
Chemical engineering modulemass transport nernst planck, transient analysis. Nonlinear poissonnernst planck equations for ion flux. Please login with a confirmed email address before reporting spam. Sep 20, 2010 mathematical analyses of the poisson nernst planck equations have been developed long after the introduction of the equation by nernst and planck 41, 42. And you have not given the units of the global parameters. The standardized comsol desktop user interface, which is the basis for the electrodeposition module, is also used for all the other addon products in the comsol product suite. Nernstplanckpoisson equations interface u u u electrophoretic transport interface u u u primary and secondary current distribution based on the boundary element method bem u a builtin thermodynamic properties library u u u link between reaction engineering interface and thermodynamic property packages u u u. For users of the electrochemistry module, comsol multiphysics version 5. The flux of an ion species is given by the nernstplanck equation, which. Solving poisson, nernstplanck and navierstokes for a nanopore in comsol i think i have all the settings in terms of boundary conditions right and i get a converged solution with reasonable. An integral part of optimizing your chemical reaction processes. Equilibrium potential calculation using the nernst equation in the electrode reaction and porous electrode reaction features, the equilibrium potential of electrode reactions can be defined using the new nernst equation option, making it easier to set up thermodynamically consistent models. This tutorial example shows how to couple the nernstplanck equations to the. This discussion is about an older version of the comsol multiphysics software.
Discussion closed this discussion was created more than 6 months ago and has been closed. Solving the nernstplanck equations for all species concentrations with concentration of current and electroneutrality makes the equation set nonlinear and very complicated for the tertiary current distribution, which results in more time and memory storage requirements for the simulation. It should be noted that each differential equation is an expression of the governing equation, so selection of the appropriate governing equation is a critical step. Planck formulation of conservative and reactive transport equations 14, allowing the description of physical displacement, coulombic interactions, and a wide range of geochemical reactions in. Warning your internet explorer is in compatibility mode and may not be displaying the website correctly.
Electrodeposition module application gallery examples comsol. Electrodeposition, tertiary nernstplanck interface for transport of species through diffusion, migration, and convection and with kinetics expressions that account for both activation and concentration overpotential. Energy dissipation law as for fokkerplanck equation, the energy law of pnp is given by. Solving the nernst planck equations for all species concentrations with concentration of current and electroneutrality makes the equation set nonlinear and very complicated for the tertiary current distribution, which results in more time and memory storage requirements for the simulation. Outside the approximations defined above, the tertiary current distribution, nernstplanck interface can be used to solve the nernstplanck equations subject to the approximation of electroneutrality eqs. Solving poisson, nernstplanck and navierstokes for a nanopore in comsol. Chemical engineering modulemass transportnernst planck, transient analysis.
First, in what we refer to as pde modes, you enter the equations from scratch at the keyboard. Nu multiion charge regulation equation 2 2 n a b s total a s b s k k h f k h k h v comsol multiphysics p02 p u \u e u 0 stokes equation continuity equation highly coupled equations nonlinear partial. I am interested by the potential and the concentration profiles of the edl. Please login with a confirmed email address before. You have a problem with the units both in the poissonboltzmann and nernst planck equation.
The poissonnernstplanck pnp system for ion transport taichia lin. Equilibrium potential calculation using the nernst equation. It extends ficks law of diffusion for the case where the diffusing particles are also moved with respect to the fluid by electrostatic forces. Trial licenses are automatically associated with your account. The nernst planck equation is often used to describe the diffusion, convection, and migration of charged particles. Solving poisson, nernstplanck and navierstokes for a. Comsol multiphysics is a modeling package that solves arbitrary systems of partial differential equations pdes. No external field or voltage is applied, my goal is to check whether these concentration gradients reach the electrode next to the tubes by migration in the presence of convection by the fluid. The chemical engineering module university of michigan. The basis for these descriptions is found in the laws for conservation of momentum, energy, and mass in combination with the constitutive. Citeseerx document details isaac councill, lee giles, pradeep teregowda. White paper modeling corrosion and corrosion protection.
In fembased computational study for transport phenomena in electrochemical and corrosion systems, there are two prevailing modeling approaches. Comsol is the developer of comsol multiphysics software, an interactive environment for modeling and simulating scientific and engineering problems. This example shows how to couple the nernstplanck equations to poissons equation, in order to consider this deviation from electroneutrality. You will experience speedup by a factor of up to ten in software responsiveness, as well as new and improved features for solving, meshing, and the physicsbased addon modules. Blog how to model ionexchange membranes and donnan potentials. In the scientific articles, they use the mobility with unit m2vs. Numerical simulation of carbon steel corrosion exposed to.
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