A theoretical study is presented of the flow of viscoplastic fluid through a Hele-Shaw cell that contains various kinds of obstructions. Circular and elliptical blockages of the cell are considered together with stepwise contractions or expansions in slot width, all within the simplifying approximation of a narrow gap. Specific attention is paid to the flow patterns that develop around the obstacles, particularly any stagnant plugged regions, and the asymptotic limits of relatively small or large yield stress. Periodic arrays of circular contractions or expansions are studied to explore the interference between obstructions. Finally, viscoplastic flow through a cell with randomly roughened walls is examined, and it is shown that constructive interference of local contractions and expansions leads to a pronounced channelization of the flow. An optimization algorithm based on minimization of the pressure drop is derived to construct the path of the channels in the limit of relatively large yield stress or, equivalently, relatively slow flow.

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Experiments are conducted exploring the flow of Carbopol past obstacles in a narrow slot and compared with predictions of a model based on the Herschel-Bulkley constitutive law and the conventional Hele-Shaw approximation. Although Carbopol is often assumed to be a relatively simple yield-stress fluid, the flow pattern around an obstacle markedly lacks the fore-aft symmetry expected theoretically. Such asymmetry has been observed previously for viscoplastic flows past obstacles in unconfined geometries, but the narrowness of the Hele-Shaw cell ensures that the stress state is very different, placing further constraints on the underlying origin. The asymmetry is robust, as demonstrated by varying the shape and number of the obstacles, the surfaces of the cell walls, and the steadiness of the flow rate. The results suggest that rheological hysteresis near the yield point may be the cause of the asymmetry.

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The endothelial glycocalyx is a dynamic structure integral to blood vessel hemodynamics and capable of tightly regulating a range of biological processes (ie, innate immunity, inflammation, and coagulation) through dynamic changes in its composition of the brush structure. Evaluating the specific roles of the endothelial glycocalyx under a range of pathophysiologic conditions has been a challenge in vitro as it is difficult to generate functional glycocalyces using commonly employed 2D cell culture models. We present a new multi-height microfluidic platform that promotes the growth of functional glycocalyces by eliciting unique shear stress forces over a continuous human umbilical vein endothelial cell monolayer at magnitudes that recapitulate the physical environment in arterial, capillary and venous regions of the vasculature. Following 72 hours of shear stress, unique glycocalyx structures formed within each region that were distinct from that observed in short (3 days) and long-term (21 days) static cell culture. The model demonstrated glycocalyx-specific properties that match the characteristics of the endothelium in arteries, capillaries and veins, with respect to surface protein expression, platelet adhesion, lymphocyte binding and nanoparticle uptake. With artery-to-capillary-to-vein transition on a 2 of 14 | SIREN Et al.