in Wiley InterScience (www.interscience.wiley.com).A multiscale modeling approach was developed to capture concentration variations in the fluid in two dimensions for catalytic flow reactors. The methodology couples continuum descriptions of the fluid phase and kinetic Monte Carlo simulations of the catalyst domain. A number of catalytic domains, placed as patches along the length of the reactor, were solved using kinetic Monte Carlo (kMC) and linked with a finite difference (FD) solver for the fluid phase. Patch dynamics concepts, such as lifting, restriction and interpolation, were employed to provide the complete set of boundary conditions to the continuum solver. A simple kinetic mechanism involving adsorption, desorption and a single-step surface reaction was used to validate the approach by comparing the solution obtained using the multiscale scheme with a model solved using a wholly implicit solution. Solutions from a mean-field model and the multiscale scheme for a system in which surface diffusion was low were then contrasted.

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Molecular squares" are novel self-assembling structures, typically containing metal-ion corners and porphyrin sides and centers, that have exciting promise as stereoselective catalysts that mimic enzymes. Recently, films of molecular squares have been fashioned on membrane supports, and their efficacy for oxidation of styrene has been demonstrated. To aid in the design of these materials, continuum models were developed that allow the effects of the film thickness, pore size, and reactant ratios to be explored. The coupled set of nonlinear partial differential equations describing transient reaction and diffusion was solved numerically using three different classes of methods: a split-step method using finite difference (FD); domain decomposition in two different forms, one involving three overlapping subdomains and the other involving a gaptooth scheme; and the multiple-time-step method. The first two classes of methods were implemented based on literature methods, and some modifications, particularly to the gaptooth scheme, were made to handle the problem at hand. The multiple-time-step method was developed in this work and was shown to be about 250 times faster than the split-step method and a factor of 60 faster than domain decomposition using the gap-tooth scheme.

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