These are symmetric, so that an ncomponent system requires nn12 independent coefficients to parameterize the rate of diffusion of its components. 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. The transportkinetics interactions in the porous catalyst are analysed using various diffusion flux models such as wilke, wilkebosanquet, stefanmaxwell, and dusty gas models. Finally, maxwell stefan equations were implemented in order to capture the concentration and temperature. Excerpt from the proceedings of the comsol conference 2007, boston. Modeling the chemical, diffusional, and thermal processes. Transport of the heavy species is determined by solving a modified form of maxwell stefan equations using the heavy. A significant advantage with the maxwellstefan diffusion formulation, in comparison with ficks law, is the inclusion of a conservation of mass. Warning your internet explorer is in compatibility mode and may not be displaying the website correctly. Estimates of na and nb can be obtained from application of the ficks law assuming simple binary diffusion. Modelling of multicomponent diffusion and swelling in protein.
H gas channel inlet o 2 gas channel inlet pvim membrane at. The comsol discussion forum covers a wide variety of simulation topics. Modelling of multicomponent diffusion and swelling in protein gels 2011. About the maxwell stefan equation in comsol, can it be used for liquids. This application mode models concentrated solutions where the species in solution interact with each other as well as the solvent. A onedimensional transport model for multicomponent solute in. Diffusion of electrolyte solutions through protein gels was modelled using the generalised maxwell stefan gms equation. Ns equation and the pure diffusion equation in pem fuel cell modeling. Species transport in the gas diffusion layers of a pem comsol.
They can be calculated using the boundary conditions. Comsol is promoted to be a very good tool to solve multiphysics problems. Comparison of diffusion flux models for fischertropsch. On the maxwellstefan approach to multicomponent di. A onedimensional transport model for multicomponent solute in saturated soil was developed based on the maxwell stefan diffusion theory and the mcl equation. The gas chosen to insert in the retentate gas chamber is co2 and the inert gas is argon. Nov 26, 2014 dear experts, using maxwell stefan equation for diffusion, i want to set anisotrpic values for the diffusion coefficients. This work proposes a 3d multiphysics model to predict and optimize the gde cell behavior, specifically for the cl and the gdl. Comsol provides an ide and unified workflow for electrical, mechanical, fluid, acoustics and chemical applications.
Apr 30, 2014 the maxwell stefan formulation describes diffusion from first principles. Noting the increased use of this product in analytical electrochemistry, the authors aim to. The model incorporates stokesbrinkman, maxwellstefan, and nonlinear butlervolmer equations, computed and solved with comsol multiphysics software v4. Modeling of htpem fuel cell startup process by using comsol multiphysics y. Maxwellstefan theory for diffusion through zeolite membrane. Ansys maxwell is a software specializedoptimized for lf. This matlab function simulates the 1962 bulb diffusion experiment of duncan and toor, an experiment that validated the accuracy of maxwell stefan diffusion. The real problem of a proton exchange membrane pem fuel cell modeling involves different scales, multiple variables and processes, coupling of solvers. This can be easily done if i use ficks equation but it does not look straighforward if one uses maxwell stefan. The diffusion coefficient is most simply understood as the magnitude of the molar flux through a surface. The model is solved with commercial software comsol multiphysics 3. In the bottom of a stefan tube there is a quiescent liquid with a mixture of acetone component 1 and methanol component 2.
The paper reports the results of a heat transfer modeling of a membrane reactor for methane steam reforming, study developed in order to analyze the importance of temperature for methane conversion and hydrogen yield. Modelling of multicomponent diffusion and swelling in protein gels. Parametric study will be conducted to analyze the effects of various parameters on the performance of pem fuel cells. It models multicomponent gasphase diffusion in a stefan tube in 1d. Modeling the chemical, diffusional, and thermal processes of a microreactor by. Modeling of single cell solid oxide fuel cells using comsol. In addition to using multiphysics modeling for your own projects, you can also turn your models into simulation applications and. 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. For my master thesis i want to write a chapter to compare those 3 models and to justify my choice.
For a comprehensive analysis, use the comsol multiphysics software and the acdc module to see how multiple physics affect your design. Thus, unlike fick diffusion, maxwellstefan diffusion can describe multicomponent mixtures. Comsol multiphysics is a generalpurpose simulation software for modeling designs, devices, and processes in all fields of engineering, manufacturing, and scientific research. 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. Comsol multiphysics software was applied to analyze the steam methane reforming in the chemical reactor investigated. 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.
The concentration isosurfaces reveal mass transfer through diffusion. Simultaneous multicomponent diffusion of gases the parameters n a and n b the molar fluxes of components a and b respectively are unknown. Vapor that evaporates from this pool of liquid diffuses to the top of the tube. 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. Several different mathematical parameters had to be applied and solved. The general form of the maxwell stefan equation is shown below. In this module, the electron density and mean energy are computed by solving a pair of drift diffusion equations using a drift diffusion interface. 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. The comsol multiphysics geometry and cad environment 320. This is the measure of the rate of the diffusion process. Which is the most suitable software comsol vs ansys maxwell.
Simply log in and follow the onscreen product download directions. Simplifications of these equations for diluted mixtures give, for example, ficks first law of diffusion and the nernstplanck equations for diffusion. Comsol multiphysics is a crossplatform finite element analysis, solver and multiphysics simulation software. Learn more about these chemical reaction engineering features below. On the help menu, click about comsol multiphysics to check your version. Figure 4 shows the oxygen isoconcentration surfaces in a gas diffusion cathode for a fuel cell. Comsol multiphysics is a finite element method fem based software that facilitates such analysis. Pdf twodimensional pem fuel cells modeling using comsol. Comsol multiphysics is a modeling package that solves. A onedimensional transport model for multicomponent solute in saturated soil was developed based on the maxwellstefan diffusion theory and the mcl equation. When defining and solving these problems, the fluid is modeled as incompressible by default but can.
All of the features listed below are implemented through associated physics interfaces. It solves for the fluxes in terms of mass fraction. 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. Browse the threads and share your ideas with the comsol community. 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. As of update 2, the new rotordynamics module is available as an optional addon to the structural mechanics module. Twodimensional pem fuel cells modeling using comsol.
A modified multicomponent solute diffusion equation described with diffusion flux was derived in detail based on the classical maxwell stefan diffusion theory. A onedimensional transport model for multicomponent. 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. Ode45 in maxwellstefan equation matlab answers matlab. The maxwell stefan diffusion or stefan maxwell diffusion is a model for describing diffusion in multicomponent systems. This example illustrates the use of the maxwellstefan diffusion model available with the transport of concentrated species interface. 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. The mass flux is zero at the walls of the gas channel and gde, this boundary condition is usually taken as insulating. For multicomponent gas diffusion, the maxwell stefan diffusion model was used. These release notes provide information regarding new functionality in existing products.
Which is the most suitable software comsol vs ansys. It will be really great if someone can help me with the primary syntaxes and function. Modeling and simulation of planar sofc to study the. If you have an earlier build number, contact your comsol sales representative to get the official release of comsol 4.
These properties make mass transport systems described by ficks second law easy to simulate numerically. This is the maxwellstefan equation, an equation that forms the basis for. A complete mathematical model of protein gel swelling was established. A onedimensional transport model for multicomponent solute. When i read the users guide, i found that all introductions are referred to. 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. Comsol multiphysics modeling environment with customized user interfaces. This example illustrates the use of the maxwell stefan diffusion model available with the transport of concentrated species interface. Modeling the chemical, diffusional, and thermal processes of. 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. The following matlab project contains the source code and matlab examples used for solution of a maxwell stefan diffusion problem.
Simplifications of these equations for diluted mixtures give, for example, ficks first law of diffusion and the nernstplanck equations for diffusion and migration. This apparatus have been modeled with comsol multiphysics software. 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. In the absence of chemical reactions source terms and convective contributions, the maxwellstefan formulation results in zero net mass flux. Modelling of multicomponent diffusion and swelling in. Anisotropic diffusion coefficients in maxwellstefan equation. Comparison of darcys law, the brinkman equation, the. Diffusion equation comsol multiphysics modeling software. Using maxwell stefan equation for diffusion, i want to set anisotrpic values for the diffusion coefficients.
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. 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. 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. The necessary equations are formulated as the maxwellstefan description of diffusion. The maxwellstefan formulation describes diffusion from first principles. The model uses current balances, mass transport equations maxwellstefan diffusion for reactants, water and nitrogen gas, and momentum transport darcys. 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. While the maxwellstefan equations are successfully used in engineering applications, they seem much less known in the mathematical literature. Solution of a maxwell stefan diffusion problem in matlab. This matlab function simulates the 1962 bulb diffusion experiment of duncan and toor, an experiment that validated the accuracy of maxwellstefan diffusion.
For characterizing the thermal profile, convective, conductive, and radiataive heat transfer modes were all included. 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. However, because this ideal model faced convergence issues due to the complexity of the maxwell stefan diffusion equations, a simpler model is presented. Solution of a system of odes with polymath and matlab. In this case, it is a liquid mixture of acetone and methanol that evaporates into air. 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 model couples the maxwell stefan application mode to the navier. 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. Diffusion of each chemical species occurs independently. Thus, unlike fick diffusion, maxwell stefan diffusion can describe multicomponent mixtures. Diffusion coefficient understanding the diffusion coefficient.
Solution of a maxwell stefan diffusion problem file. 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. In the module transport of diluted and concentrated species one can model a diffusion. The swelling process of protein gels in this thesis involved multicomponent diffusion, chemical ionisation and mechanical deformation.
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