The following model/experiment comparisons aid in predicting the maximum performance of a normalH2∕oxygen proton exchange membrane fuel cell (PEMFC) for a cathode catalyst with known oxygen reduction reaction (ORR) kinetics in the absence of gas transport resistances. Specific focus was on modeling the voltage loss within the cathode catalyst layer, which results from a balance between slow ORR kinetics and resistance to proton transport. A unique plot of proton resistance correction vs the ratio of ohmic (expressed by the proton conduction sheet resistance, Rsheet ) to charge transfer resistance (expressed by the ratio of the Tafel slope of the ORR over the current density, b∕i ) in a PEMFC cathode (iRsheet∕b) was developed, based on an analytical solution to effective proton resistance in the porous cathode electrode of a proton exchange membrane fuel cell. Additionally, a plot of catalyst utilization (u) vs iRsheet∕b was developed to serve as a guideline of experimental design parameters such that catalyst utilization is kept above 90%, which is a prerequisite for measuring the ORR kinetics. The model is applicable as long as the ORR follow simple Tafel kinetics.
This paper deals with the theoretical analysis of the unloading of oxygen from a red cell. A scale analysis of the governing transport equations shows that the solutions have a boundary layer structure near the red-cell membrane. The boundary layer is a region of chemical nonequilibrium, and it owes its existence to the fact that the kinetic time scales are shorter than the diffusion time scales in the red cell. The presence of the boundary layer allows an analytical solution to be obtained by the method of matched asymptotic expansions. A very useful result from the analysis is a simple, lumped-parameter description of the oxygen delivery from a red cell. The accuracy of the lumped-parameter description has been verified by comparing its predictions with results obtained by numerical integration of the full equations for a one-dimensional slab. As an application, we calculate minimum oxygen unloading times for red cells.
Diffusion based separations are essential for laboratory and clinical dialysis processes. New molecularly thin nanoporous membranes may improve the rate and quality of separations achievable by these processes. In this work we have performed protein and small molecule separations with 15 nm thick porous nanocrystalline silicon (pnc-Si) membranes and compared the results to 1- and 3- dimensional models of diffusion through ultrathin membranes. The models predict the amount of resistance contributed by the membrane by using pore characteristics obtained by direct inspection of pnc-Si membranes in transmission electron micrographs. The theoretical results indicate that molecularly thin membranes are expected to enable higher resolution separations at times before equilibrium compared to thicker membranes with the same pore diameters and porosities. We also explored the impact of experimental parameters such as porosity, pore distribution, diffusion time, and chamber size on the sieving characteristics. Experimental results are found to be in good agreement with the theory, and ultrathin membranes are shown to impart little overall resistance to the diffusion of molecules smaller than the physical pore size cutoff. The largest molecules tested experience more hindrance than expected from simulations indicating that factors not incorporated in the models, such as molecule shape, electrostatic repulsion, and adsorption to pore walls, are likely important.
Microfluidic systems are powerful tools for cell biology studies because they enable the precise addition and removal of solutes in small volumes. However, the fluid forces inherent in the use of microfluidics for cell cultures are sometimes undesirable. An important example is chemotaxis systems where fluid flow creates well-defined and steady chemotactic gradients but also pushes cells downstream. Here we demonstrate a chemotaxis system in which two chambers are separated by a molecularly thin (15 nm), transparent, and nanoporous silicon membrane. One chamber is a microfluidic channel that carries a flow-generated gradient while the other chamber is a shear-free environment for cell observation. The molecularly thin membranes provide effectively no resistance to molecular diffusion between the two chambers, making them ideal elements for creating flow-free chambers in microfluidic systems. Analytical and computational flow models that account for membrane and chamber geometry, predict shear reduction of more than five orders of magnitude. This prediction is confirmed by observing the pure diffusion of nanoparticles in the cell-hosting chamber despite high input flow (Q = 10 µL min−1; vavg ~45 mm min−1) in the flow chamber only 15 nm away. Using total internal reflection fluorescence (TIRF) microscopy, we show that a flow-generated molecular gradient will pass through the membrane into the quiescent cell chamber. Finally we demonstrate that our device allows us to expose migrating neutrophils to a chemotactic gradient or fluorescent label without any influence from flow.
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