| Mathematical models are important to analyze anomalous phenomena and the behavior of systems in science and engineering. They are the building stones for process design, control and performance optimization. When it comes to modeling schemes in chemical engineering, there are two schools of thoughts; continuum models and molecular level approaches. While the former require certain conditions and criteria pertinent to macro-scale processes, the latter involve a higher level of complexity and thus are considered more powerful at atomistic scale. However, for systems in the rarefied regime (microchemical systems) neither continuum nor molecular models are believed to be adequate [70].; This dissertation addresses the problem of modeling microchemical systems in which selective permeation and chemical reactions take place. Starting with the microfluidic modeling, it was found that velocity-slip, when not accounted for, predicts flow reversal on the walls that are parallel to the permeable membrane, and leads to errors in over-estimating the pressure gradient in rectangular microchannels. For higher Knudsen numbers (Kn), relative errors as high as 50% are possible.; When the analytic pressure formulae derived in this work for slipping flow in rectangular microchemical systems are used to generate concentration profiles, which in turn are based on constitutive laws, simulation results revealed that a 4-cm long microchannel was capable of completely removing the permeate and totally consuming the unwanted species. The mathematically derived expressions for species and microfluidic flows offer influential modeling alternatives that are complicated enough to capture the physics of microchemical systems while maintaining a decent level of mathematical solvability.; The last part of this dissertation illustrates a rigorous derivation and an analytical solution to the energy problem applicable to membrane microreactors incorporating velocity slip and temperature jump boundary conditions. Criteria under which several terms of the energy equation can be ignored will be highlighted. Investigation of the dimensionless viscous dissipation shows that it decreases with increasing Kn and with decreasing permeation. For rectangular microchannels with aspect ratios less than 1.0, the dimensionless cross-sectional-averaged viscous dissipation was found to become nearly independent of the aspect ratio when the value of Kn exceeds 0.3. |
