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Mesoscale filtering and protective layers are replete throughout the naturalworld. Within the body, arrays of extracellular proteins, microvilli, and ciliacan act as both protective layers and mechanosensors. For example, blood flowprofiles through the endothelial surface layer determine the amount of shearstress felt by the endothelial cells and may alter the rates at which moleculesenter and exit the cells. Characterizing the flow profiles through such layersis therefore critical towards understanding the function of such arrays in cellsignaling and molecular filtering. External filtering layers are also importantto many animals and plants. Trichomes (the hairs or fine outgrowths on plants)can drastically alter both the average wind speed and profile near the leaf'ssurface, affecting the rates of nutrient and heat exchange. In this paper,dynamically scaled physical models are used to study the flow profiles outsideof arrays of cylinders that represent such filtering and protective layers. Inaddition, numerical simulations using the Immersed Boundary Method are used toresolve the 3D flows within the layers. The experimental and computationalresults are compared to analytical results obtained by modeling the layer as ahomogeneous porous medium with free flow above the layer. The experimentalresults show that the bulk flow is well described by simple analytical models.The numerical results show that the spatially averaged flow within the layer iswell described by the Brinkman model. The numerical results also demonstratethat the flow can be highly 3D with fluid moving into and out of the layer.These effects are not described by the Brinkman model and may be significantfor biologically relevant volume fractions. The results of this paper can beused to understand how variations in density and height of such structures canalter shear stresses and bulk flows.

Three-dimensional low Reynolds number flows near biological filtering and protective layers