Modeling rate-limited processes along non-uniform surfaces via the method of volume averaging Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/vm40xt96z

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  • Quantification of macroscale transport phenomenon in microfluidic systems is important to many science and engineering disciplines. In part, this is because fully resolved solutions to microscale balance laws over large domains are out of reach with current computational technology. Additionally, engineers are most often interested in some upscaled quantity and would filter or average a fully resolved data set for this desired result. If the balance laws themselves can be upscaled prior to computation, not only can larger, more interesting problems be solved, but the solutions to these problems will provide engineers with the specific information desired rather than data which must be processed. While many upscaled models are basically empirically fitted equations based on measured macroscale data, it is our belief that the interaction of macro and microscale processes are embedded in the continuum scale balance laws. With proper perspective, equations governing this interaction can be isolated and solved, leading to physics-based closures for upscaled problems. We will examine the method of volume averaging as it applies to partial differential equations. The goal will be to construct a new, continuous, balance law which describes the volume-averaged concentration of a chemical species and fully accounts for the influence of microscale processes on the macroscale variables, focusing on microscale rate-limited reactions.
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