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Fluids 2017, 2(4), 62;

Three-Dimensional Low Reynolds Number Flows near Biological Filtering and Protective Layers

Department of Mathematics, University of Tennessee Knoxville, 1403 Circle Drive, Knoxville, TN 37996, USA
Department of Mathematics, CB 3250, University of North Carolina, Chapel Hill, NC 27599, USA
Department of Biology, CB 3280, University of North Carolina, Chapel Hill, NC 27599, USA
School of Mechanical and Aerospace Engineering, Oklahoma State University, 218 Engineering North, Stillwater, OK 74078, USA
Department of Mathematics, Bucknell University, Lewisburg, PA 17837, USA
Department of Mathematics and Statistics, The College of New Jersey, 2000 Pennington Rd., Ewing, NJ 08628, USA
Army Research Office, 4300 S Miami Blvd, Durham, NC 27703, USA
Author to whom correspondence should be addressed.
Received: 5 September 2017 / Revised: 30 October 2017 / Accepted: 6 November 2017 / Published: 13 November 2017
(This article belongs to the Special Issue Mechanics of Fluid-Particles Systems and Fluid-Solid Interactions)
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Mesoscale filtering and protective layers are replete throughout the natural world. Within the body, arrays of extracellular proteins, microvilli, and cilia can act as both protective layers and mechanosensors. For example, blood flow profiles through the endothelial surface layer determine the amount of shear stress felt by the endothelial cells and may alter the rates at which molecules enter and exit the cells. Characterizing the flow profiles through such layers is therefore critical towards understanding the function of such arrays in cell signaling and molecular filtering. External filtering layers are also important to 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’s surface, affecting the rates of nutrient and heat exchange. In this paper, dynamically scaled physical models are used to study the flow profiles outside of arrays of cylinders that represent such filtering and protective layers. In addition, numerical simulations using the Immersed Boundary Method are used to resolve the three-dimensional flows within the layers. The experimental and computational results are compared to analytical results obtained by modeling the layer as a homogeneous porous medium with free flow above the layer. The experimental results show that the bulk flow is well described by simple analytical models. The numerical results show that the spatially averaged flow within the layer is well described by the Brinkman model. The numerical results also demonstrate, however, that the flow can be highly three-dimensional with fluid moving into and out of the layer. These effects are not described by the Brinkman model and may be significant for biologically relevant volume fractions. The results of this paper can be used to understand how variations in density and height of such structures can alter shear stresses and bulk flows. View Full-Text
Keywords: immersed boundary method; porous flow; trichomes; glycocalyx; leakiness; filtering layers immersed boundary method; porous flow; trichomes; glycocalyx; leakiness; filtering layers

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Strickland, C.; Miller, L.; Santhanakrishnan, A.; Hamlet, C.; Battista, N.A.; Pasour, V. Three-Dimensional Low Reynolds Number Flows near Biological Filtering and Protective Layers. Fluids 2017, 2, 62.

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