This is the maxwellstefan equation, an equation that forms the basis for. This apparatus have been modeled with comsol multiphysics software. Using maxwell stefan equation for diffusion, i want to set anisotrpic values for the diffusion coefficients. The maxwellstefan formulation describes diffusion from first principles. Figure 4 shows the oxygen isoconcentration surfaces in a gas diffusion cathode for a fuel cell. Parametric study will be conducted to analyze the effects of various parameters on the performance of pem fuel cells.
A 1d steady state model for a spherical catalyst shape is developed in comsol multiphysics software using transport of dilute species and heat conduction interfaces. The maxwell stefan ms equations maxwell 1866, stefan 1871 describe the process of diffusion, where diffusive fluxes, j i, of species through a plane, across which no net transfer of moles occurs, depend on all n1 independent driving forces in a mixture of n species. Modeling the chemical, diffusional, and thermal processes of. This is the measure of the rate of the diffusion process.
It will be really great if someone can help me with the primary syntaxes and function. The maxwell stefan diffusion or stefan maxwell diffusion is a model for describing diffusion in multicomponent systems. For multicomponent gas diffusion, the maxwell stefan diffusion model was used. The concentration isosurfaces reveal mass transfer through diffusion. The general form of the maxwell stefan equation is shown below. Comsol multiphysics is a modeling package that solves. Maxwellstefan theory for diffusion through zeolite membrane. Oct 27, 2004 in the bottom of a stefan tube there is a quiescent liquid with a mixture of acetone component 1 and methanol component 2. Modeling of single cell solid oxide fuel cells using comsol. On the help menu, click about comsol multiphysics to check your version. Solution of a system of odes with polymath and matlab. This work proposes a 3d multiphysics model to predict and optimize the gde cell behavior, specifically for the cl and the gdl. The real problem of a proton exchange membrane pem fuel cell modeling involves different scales, multiple variables and processes, coupling of solvers. Comsol multiphysics is a generalpurpose simulation software for modeling designs, devices, and processes in all fields of engineering, manufacturing, and scientific research.
However, because this ideal model faced convergence issues due to the complexity of the maxwell stefan diffusion equations, a simpler model is presented. When modeling diffusion, it is often a good idea to begin with the assumption that all diffusion coefficients are equal and independent of temperature, pressure, etc. Solution of a maxwell stefan diffusion problem in matlab. This paper will present the model developed in comsol of an electrolytesupported planar button sofc and a summary of the parametric study done for the same model. Excerpt from the proceedings of the comsol conference 2007, boston. The friction between the solute species and the soil skeleton wall, which is proportional to the relative velocity between the solute species and the soil skeleton, is introduced. The pdes used to model diffusion problems might include ficks laws, the convection diffusion equation, or more complex methods for concentrated mixtures, like maxwell stefan diffusion. But somehow i am not able to code it using ode45, more likely i am not able to write the system to solve using ode45. This application mode models concentrated solutions where the species in solution interact with each other as well as the solvent.
The necessary equations are formulated as the maxwellstefan description of diffusion. Modelling of multicomponent diffusion and swelling in. The model incorporates stokesbrinkman, maxwellstefan, and nonlinear butlervolmer equations, computed and solved with comsol multiphysics software v4. Comsol is promoted to be a very good tool to solve multiphysics problems. Diffusion equation comsol multiphysics modeling software. Warning your internet explorer is in compatibility mode and may not be displaying the website correctly.
Diffusion coefficient understanding the diffusion coefficient. Modeling the chemical, diffusional, and thermal processes of a microreactor by. This matlab function simulates the 1962 bulb diffusion experiment of duncan and toor, an experiment that validated the accuracy of maxwell stefan diffusion. This example illustrates the use of the maxwellstefan diffusion model available with the transport of concentrated species interface.
The following matlab project contains the source code and matlab examples used for solution of a maxwell stefan diffusion problem. H gas channel inlet o 2 gas channel inlet pvim membrane at. A onedimensional transport model for multicomponent solute in. The model uses current balances, mass transport equations maxwellstefan diffusion for reactants, water and nitrogen gas, and momentum transport darcys. Comsol multiphysics is a finite element method fem based software that facilitates such analysis. The maxwellstefan diffusion or stefanmaxwell diffusion is a model for describing diffusion in multicomponent systems. Maxwell stefan s diffusion and convection equations explained the material transport, solved for both anode and cathode flow channel by using a transport of concentrated species interface. Solution of a maxwell stefan diffusion problem file. This example illustrates the use of the maxwell stefan diffusion model available with the transport of concentrated species interface. Simultaneous multicomponent diffusion of gases the parameters n a and n b the molar fluxes of components a and b respectively are unknown. Browse the threads and share your ideas with the comsol community.
Which is the most suitable software comsol vs ansys maxwell for femm. This is the maxwell stefan equation, an equation that forms the basis for the mathematical description of mass transfer of chemical species in a mixture 2. In addition to using multiphysics modeling for your own projects, you can also turn your models into simulation applications and. Transport of the heavy species is determined by solving a modified form of maxwell stefan equations using the heavy. Twodimensional pem fuel cells modeling using comsol. The comsol multiphysics geometry and cad environment 320. In the absence of chemical reactions source terms and convective contributions, the maxwellstefan formulation results in zero net mass flux. For characterizing the thermal profile, convective, conductive, and radiataive heat transfer modes were all included. A onedimensional transport model for multicomponent solute in saturated soil was developed based on the maxwell stefan diffusion theory and the mcl equation.
Which is the most suitable software comsol vs ansys maxwell. They can be calculated using the boundary conditions. Ns equation and the pure diffusion equation in pem fuel cell modeling. Modelling of multicomponent diffusion and swelling in protein. A onedimensional transport model for multicomponent solute. Comparison of diffusion flux models for fischertropsch. It solves for the fluxes in terms of mass fraction. It models multicomponent gasphase diffusion in a stefan tube in 1d. Pdf twodimensional pem fuel cells modeling using comsol. A onedimensional transport model for multicomponent. Ode45 in maxwellstefan equation matlab answers matlab. Estimates of na and nb can be obtained from application of the ficks law assuming simple binary diffusion. The mass flux is zero at the walls of the gas channel and gde, this boundary condition is usually taken as insulating.
When defining and solving these problems, the fluid is modeled as incompressible by default but can. Comsol multiphysics software was applied to analyze the steam methane reforming in the chemical reactor investigated. A significant advantage with the maxwellstefan diffusion formulation, in comparison with ficks law, is the inclusion of a conservation of mass. Fick diffusion coefficient d ij maxwell stefan diffusion coefficient between species i and j e charge on a proton e youngs modulus f net force force acting per unit mass of component i f i body force g gibbs free energy gex excess gibbs free energy. Simplifications of these equations for diluted mixtures give, for example, ficks first law of diffusion and the nernstplanck equations for diffusion. Species transport in the gas diffusion layers of a pem comsol. Comparison of darcys law, the brinkman equation, the. Modeling of htpem fuel cell startup process by using comsol multiphysics y. To try to reduce this mass transport limitation, operation at high pressure, increase co2 solubility by adding chemical compounds or the use of gas diffusion electrodes 5. When i read the users guide, i found that all introductions are referred to. For a comprehensive analysis, use the comsol multiphysics software and the acdc module to see how multiple physics affect your design. In the bottom of a stefan tube there is a quiescent liquid with a mixture of acetone component 1 and methanol component 2. Fick diffusion coefficient d ij maxwellstefan diffusion coefficient between species i and j e charge on a proton e youngs modulus f net force force acting per unit mass of component i f i body force g gibbs free energy gex excess gibbs free energy. It is easy to download the latest version of the comsol software if you have a comsol access account with your license number linked to it.
Thus, unlike fick diffusion, maxwell stefan diffusion can describe multicomponent mixtures. Modeling and simulation of planar sofc to study the. The gas chosen to insert in the retentate gas chamber is co2 and the inert gas is argon. Anisotropic diffusion coefficients in maxwellstefan equation. Temperature based correlations for diffusivities of ft products in wax are widely used and a comparison of diffusion flux models wilke, wilkebosanquet, maxwell stefan, and dusty gas to describe species transportkinetic interactions for fts has not been reported in literature.
It allows conventional physicsbased user interfaces and coupled systems of partial differential equations pdes. Most electromagnetic components, devices, and products are affected by another branch of physics, whether it be heat transfer, structural mechanics, or acoustics, to name a few. The model is solved with commercial software comsol multiphysics 3. Diffusion of electrolyte solutions through protein gels was modelled using the generalised maxwell stefan gms equation.
This matlab function simulates the 1962 bulb diffusion experiment of duncan and toor, an experiment that validated the accuracy of maxwellstefan diffusion. Learn more about these chemical reaction engineering features below. Ansys maxwell is a software specializedoptimized for lf. This can be easily done if i use ficks equation but it does not look straighforward if one uses maxwell stefan.
On the maxwellstefan approach to multicomponent di. In this module, the electron density and mean energy are computed by solving a pair of drift diffusion equations using a drift diffusion interface. Numerical simulations were conducted with the finite element software comsol multiphysics, and the case of two heavy metal ion species was chosen as an example. As of update 2, the new rotordynamics module is available as an optional addon to the structural mechanics module. Sauer1,2,3 1 electrochemical energy conversion and storage systems group, institute for power electronics and electrical drives isea, rwth aachen university, germany 2 juelich aachen research alliance, jaraenergy, germany 3 institute for power generation and storage systems. Modelling of multicomponent diffusion and swelling in protein gels 2011. Modelling of multicomponent diffusion and swelling in protein gels. Finally, maxwellstefan equations were implemented in order to capture the concentration and temperature. A complete mathematical model of protein gel swelling was established. The comsol discussion forum covers a wide variety of simulation topics. Several different mathematical parameters had to be applied and solved.
About the maxwell stefan equation in comsol, can it be used for liquids. While the maxwellstefan equations are successfully used in engineering applications, they seem much less known in the mathematical literature. Vapor that evaporates from this pool of liquid diffuses to the top of the tube. Comsol provides an ide and unified workflow for electrical, mechanical, fluid, acoustics and chemical applications. The swelling process of protein gels in this thesis involved multicomponent diffusion, chemical ionisation and mechanical deformation. The transportkinetics interactions in the porous catalyst are analysed using various diffusion flux models such as wilke, wilkebosanquet, stefanmaxwell, and dusty gas models. Thus, unlike fick diffusion, maxwellstefan diffusion can describe multicomponent mixtures. In dilute species transport, the flux due to diffusion is given by ficks first law, which only depends on a single property of the solutes interaction with the solvent. Apr 30, 2014 the maxwell stefan formulation describes diffusion from first principles.
Finally, maxwell stefan equations were implemented in order to capture the concentration and temperature. This is the maxwellstefan equation, an equation that forms the basis for the mathematical description of mass transfer of chemical species in a mixture 2. These are symmetric, so that an ncomponent system requires nn12 independent coefficients to parameterize the rate of diffusion of its components. Modeling the chemical, diffusional, and thermal processes. Simply log in and follow the onscreen product download directions. Diffusion of each chemical species occurs independently. A onedimensional transport model for multicomponent solute in saturated soil was developed based on the maxwellstefan diffusion theory and the mcl equation. Simplifications of these equations for diluted mixtures give, for example, ficks first law of diffusion and the nernstplanck equations for diffusion and migration. If you have an earlier build number, contact your comsol sales representative to get the official release of comsol 4. All of the features listed below are implemented through associated physics interfaces.
The equations that describe these transport processes have been developed independently and in parallel by james clerk maxwell for dilute gases and josef stefan for fluids. Comsol multiphysics modeling environment with customized user interfaces. Comsol multiphysics is a crossplatform finite element analysis, solver and multiphysics simulation software. Nov 26, 2014 dear experts, using maxwell stefan equation for diffusion, i want to set anisotrpic values for the diffusion coefficients. In this case, it is a liquid mixture of acetone and methanol that evaporates into air. For my master thesis i want to write a chapter to compare those 3 models and to justify my choice.
1118 706 8 511 221 1180 863 279 941 382 1098 59 444 1152 189 488 1505 765 675 912 628 619 1453 817 90 575 196 1238 729 913 737 768 820 1024 1357 269 1232 331 1218 239 1137 173 1187 1162 1266 181 20 539