EMERGENCE OF TAPERED DUCTS IN VASCULAR DESIGNS WITH LAMINAR AND TURBULENT FLOWS

Abstract

Here we show that tapered ducts emerge in volumetrically bathed porous materials to decrease the resistance to the flow in laminar and turbulent flow regimes. The fluid enters the volume from one point and it is distributed to the entire volume. After bathing the volume, it is collected and leaves the volume from another point, i.e., two trees matched canopy to canopy. This paper shows that the flow architecture (i.e., design of the void spaces in a porous material) should be changed to obtain the minimum resistance to the flow as its size increases. Tapering the ducts decreases the order of the transition size, i.e., the size for changing from one construct to another to obtain the minimum pressure drop. The decrease in the pressure drop is 16% and 38% with the tapered ducts when the flow is laminar and turbulent, respectively. In addition, the volume ratios and the shape of the tapered ducts are documented. There is no design existing in nature with diameters of constant size in order to distribute and/or collect heat, fluid, and/or stress such as bones, rivers, veins, and tree branches. The emergence of the tapered ducts in designed porous materials is natural.