A Modelling Approach to Determine Gas and Temperature Profiles during Catalytic Reactions in Environmental Transmission Electron Microscopy
A scheme has been developed for finding the gas and temperature profiles in an environmental transmission electron microscope (ETEM), using COMSOL Multiphysics and the finite element method (FEM). This model should permit better correlation between catalyst structure and activity, by providing a more accurate understanding of gas composition than the assumption of homogeneity typically used. While more data is needed to complete the model, current progress has identified several details about the system and its ideal modeling approach.
It is found that at the low pressures and flowrates of catalysis in ETEM, natural and forced convection are negligible forms of heat transfer. Up to 250 °C, radiation is also negligible. Gas conduction, being enhanced at low pressures, dominates.
Similarly, mass transport is dominated by diffusion, which is most accurately described by the Maxwell-Stefan model. Bulk fluid flow is highly laminar, and in fact borders the line between continuum and molecular flow. The no-slip boundary condition does not apply here, and both viscous slip and thermal creep must be considered. In the porous catalyst pellet considered in this work, Knudsen diffusion dominates, with bulk flow being best described by the Darcy-Brinkman equation.
With these physics modelled, it appears as though the gas homogeneity assumption is not completely accurate, breaking down in the porous pellet where reactions occur. While these results are not yet quantitative, this trend is likely to remain in future model iterations. It is not yet clear how significant this deviation is, though methods are proposed to minimize it if necessary.
Some model-experiment mismatch has been found which must be further explored. Experimental data shows a pressure dependence on the furnace temperature at constant power, a trend as-yet unresolvable by the model. It is proposed that this relates to the breakdown of the assumption of fluid continuity at low pressures and small dimensions, though no compelling mathematical formulation has been found. This issue may have significant ramifications on ETEM and ETEM experiment design.