Under certain conditions, during binary mixture adsorption in nanoporous hosts, the concentration of one component may temporarily exceed its equilibrium value. This implies that, in contrast to Fick's Law, molecules must diffuse in the direction of increasing rather than decreasing concentration. Although this phenomenon of ‘overshooting' has been observed previously, it is only recently, using microimaging techniques, that diffusive fluxes in the interior of nanoporous materials have become accessible to direct observation. Here we report the application of interference microscopy to monitor ‘uphill' fluxes, covering the entire period of overshooting from initiation until final equilibration. It is shown that the evolution of the profiles can be adequately predicted from the single-component diffusivities together with the binary adsorption equilibrium data. The guest molecules studied (carbon dioxide, ethane and propene) and the host material (ZSM-58 or DDR) are of practical interest in relation to the development of kinetically selective adsorption separation processes.

Microimaging by IR microscopy is applied to the recording of the evolution of the concentration profiles of reactant and product molecules during catalytic reaction, notably during the hydrogenation of benzene to cyclohexane by nickel dispersed within a nanoporous glass. Being defined as the ratio between the reaction rate in the presence of and without diffusion limitation, the effectiveness factors of catalytic reactions were previously determined by deliberately varying the extent of transport limitation by changing a suitably chosen system parameter, such as the particle size and by comparison of the respective reaction rates. With the novel options of microimaging, effectiveness factors become accessible in a single measurement by simply monitoring the distribution of the reactant molecules over the catalyst particles.

Mass transfer in hierarchically porous materials is a function of various parameters, notably including the diffusivities in the various pore spaces, their relative populations and the exchange rates. Their interplay is shown to be quantified in the two‐region model of diffusion which in magnetic resonance imaging is in common use under the name Kärger equations. After manifold applications in NMR diffusometry with compartmented systems, the underlying formalism is now demonstrated to offer an excellent tool for assessing mass transfer in hierarchically porous materials. The potentials include a comprehensive description of mass transfer, in parallel with the specification of the various limiting cases and their reflection by experimental measurement. Information provided by application of microscopic techniques of measurement such as microimaging and pulsed field gradient NMR is shown to notably exceed the message of, e.g., macroscopic uptake measurement of diffusion in hierarchically porous media. This includes, in particular, experimental insight into the dominating mechanisms of mass transfer, which is crucial for the development of optimal strategies of performance enhancement for the technological exploitation of such materials. Depending on the microstructural and microdynamic situation, elucidated in such studies, very different and even mutually opposing strategies for performance enhancement are shown to result.

HitrodnetionLet Qc W , as%, be a bounded connected domain with D piecewise smooth and LIPSCHITZ continuous boundary an. Using the summation convention, we consider the DUUCRLET problem 8Xt (1.1) a ai(z, ec, uz) +b(x, a, uz) =O in B , et-@ on M ,where th= (uzl, ..., %=) and @ is a given sufficiently regular function defined on B. We assume that d(z, z, p) and b(z, 8, p) are regular enough on C x R x Rn. W e suppose that for a even m>O and LwO there exists 8 constant v=v(m, L) > O such that for ulf =the inequality ad *j (1.2)is satisfied for all cc Rn, ~€ 6 , z < R rand pE R* with 1 2 1 s;nr and Ip1 sL.Instead of (1.1) me consider the associated meek equation to (1.1).(1-3)a, uz) y,,,+b(z, u, uz) 9. 31 dz=O R for all ~E C~( Q ) , u=@ on &?. We mume that the conicai point in consideration is the origin x = O . Let QP= D n B,(O), e>.O smdl enough, where B&) denotes B bail with radius , O -0 and the centre at z. We suppose that u~Ca.l(~m)nCa(D,),powO, is a soluhn of (1.3) for a12 q