Flow through brushborders and similar protuberant wall structures

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Abstract
Longitudinal flow through channels with protuberant wall structures such as brushborders were studied both experimentally and theoretically. The experiments were performed using tubes with synthetic internal brushborders, scaled to resemble the geometry and flow in proximal tubules of the kidney. Fractional flow rates in the brushborder were deduced from transit times of dye traces through the central core and total flow rate. The measured ratios of brushborder to core flowQ B /Q C were found to be independent of Reynolds number over the rangeRe=0.01–0.2. They agreed reasonably well with theoretical predictions based on the Kozeny-Carman equation for flow through arrays of parallel cylinders. The predictions can be extended to arbitrary geometries and turbulent flow conditions by appropriate modifications. Extrapolation of the results to the proximal tubule of the kidney indicate that brushborder flowrates there vary from 0.003 to 0.09% of total flow. Any axial transport in these structures would be predominantly diffusive in nature, and would be highly unlikely to affect radial brushborder gradients and transmural flux.

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