Flow of non-Newtonian fluids in self-similar networks across different scales

Abstract

Several natural and manufactured flow systems exhibit scale-invariance or selfsimilarity, despite appearing to be disordered. This study focuses on the laminar flow of non-Newtonian fluids through self-similar systems of tubes with porous walls (intrinsic permeability much less than 10-4 m2). Two arrangements of tubes are discussed: a dendritic flow structure and a bundle of tubes. The size of these arrangements is described as a function of structural parameters for both straight and tortuous tubes, and the flow resistance is obtained as a function of structural parameters and fluid properties. Among other findings, it is shown that the prefractal dimension of dendritic networks for maximum flow access is dependent on the size constraint chosen to design the network. Results also show that as the prefractal dimensions of diameters and lengths rise, so does the overall size of the dendritic network and tube bundle system. In contrast, it is observed that the flow resistance diminishes as the prefractal dimension for diameters increases, whereas for tortuous tubes the flow resistance increases as the prefractal dimension for lengths increases. The approaches presented in this paper have numerous potential applications, including fluxes in biological systems, microfluidic media, and hydrology.