Gas Knudsen Diffusion Research Articles

Modelling Diffusion as a Guide to the Rational Design of Porous Materials

Porous materials are extensively used as catalysts, sorbents, and matrices for the controlled release or uptake of, e.g., pharmaceutics, all of which are either influenced by or rely on diffusion. Diffusion plays a role at two levels. A first level is that of the smallest pores, the nanopores; a second that of the broader mesoand macropores, i.e., the Autobahn network of transport channels that bring molecules in and out of the porous material. In the nanopores, the first level, diffusing molecules constantly feel the walls, and the geometry and chemical composition of the wall considerably influence their motion. Modelling diffusion in nanopores remains an important research topic, since the behaviour is so versatile, while overall continuum descriptions of diffusion in nanoporous materials are lacking. Because the interpretation of measurements is not easy either, molecular simulation is the ideal tool to study diffusion in nanopores. We have studied diffusion in a variety of nanoporous materials: Knudsen diffusion of gases in mesopores, activated diffusion in zeolites, water and solutes in protein crystals and in the ion and water channels that traverse cell membranes. Interestingly, unifyingmodels describing the overall behavior useful to chemical engineers could be derived in each case. At the second level, the network of transport channels can be optimized to minimize diffusion limitations, say, in heterogeneous catalysis. Optimal control theory, multi-scale simulation methods, continuum and network theory can be applied to find the network that, e.g., maximizes chemical yield. Progress in nano-structuring porous materials should allow synthesizing materials with the optimized pore channel network, and a desired structure at the nanoscale. One example is the synthesis of zeolite composites. A fascinating example is the prospect to imitate the remarkably high-flux, highly selective protein channels found in cell membranes: molecular simulations could guide us in selecting which chemical and geometrical structure leads to the desired separation behavior.

Modeling gas-phase flow in porous media

In this communication, the equations and methodology for modeling convection and both ordinary and Knudsen diffusion of gases in a porous medium are described. Parallels between our development and that of the dusty-gas model are made. Our derivation results in a self-consistent description of the various transport mechanisms and is more robust for numerical solutions, especially for conditions involving different flow regimes or where the regime is not known a priori. Along with the equation development, some limiting cases are examined and discussed with respect to the benefits and differences of our methodology versus that of the dusty-gas model.

Modeling the Cathode Compartment of Polymer Electrolyte Fuel Cells: Dead and Active Reaction Zones

A two‐dimensional model of the cathode compartment of a polymer electrolyte fuel cell has been developed. The existence of gas channels in the current collector is taken into account. The model is based on continuity equations for concentrations of the gases and Poisson's equations for potentials of membrane and carbon phase, coupled by Tafel relation for reaction kinetics. Stefan‐Maxwell and Knudsen diffusion of gases are taken into account. The simulations were performed for high and low values of carbon phase conductivity. The results revealed (i) for a low value of carbon phase conductivity, a “dead zone” in the active layer in front of the gas channel is formed, where the reaction rate is small. One may remove catalyst from this zone without significant loss in cell performance. (ii) For a high carbon phase conductivity value, such a zone is absent, but removal of the catalyst from the same part of the active layer forces the reaction to proceed more rapidly in the remaining parts, with only marginal losses in performance. This conclusion is valid for high diffusivity of oxygen. For low diffusivity, dead zones are formed in front of the current collector, so that catalyst can be removed from these zones. The results, thus, show the possibilities for a considerable reduction of the amount of catalyst. © 1999 The Electrochemical Society. All rights reserved.

Dipolar Energy Transfer and Knudsen Diffusion Inside Disordered Porous Media: Interfacial Geometry and Chord Distributions.

AbstractThe interfacial geometry of a disordered porous medium strongly influences Knudsen diffusion of gases and interfacial dipolar energy transfer. Some interesting comparison can be made between these two transport processes, involving statistical properties of chords belonging either to the solid matrix or to the pore network. A quantitative analysis of these two mechanisms is proposed, based on a chord distribution model. In a first part, we discuss how chord distribution functions contribute to the stastistical characterization of a porous medium. We show that a direct connection between imaging techniques and small angle scattering provides, in many cases, a reliable description of theses functions. In a second part, interfacial direct energy transfer is analyzed. This one step excitation transfer strongly relies on the interfacial autocorrelation function φ2s(r). An analytic expression of φ2s(r) is given and theoretical predictions compared with available experiments. In a third part and following the seminal work of Derjaguin on the Knudsen diffusion, we critically examine how the self diffusion coefficient can be related to the two first moments of the pore chord distribution. A direct comparison with experimental results and numerical simulations is presented in the case of a model porous medium: the random packing of hard spheres. Finally, we analyze a trapping reaction where an excited gas molecule, diffusing in the Knudsen regime, relaxes primarily by wall effects. We show how the chord distribution of the pore network permits to compute the survival probability of the tagged molecules. Two situations are more closely analyzed: the strong and the very weak wall quenching efficiency.

COLLISION FREQUENCIES OF GAS MOLECULES WITH PORE WALLS

In previous papers, Monte Carlo simulations of the Knudsen diffusion of gases in porous solids having convex or concave pore walls have been performed. In the present paper, molecular trajectories inside pores are computed in the Knudsen region to obtain both collision density and collision numbers. It was found that these parameters were strongly dependent on the pore structure. The results obtained here will have applications to reactive flow and heterogenous catalysis.