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FRACTAL ANALYSIS OF FLOW RESISTANCE IN TREE-LIKE BRANCHING NETWORKS WITH ROUGHENED MICROCHANNELS

SHANSHAN YANG

School of Physics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China

College of Science, Three Gorges University, Yichang 443002, P. R. China

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HUAHUA FU

School of Physics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China

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BOMING YU

School of Physics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China

E-mail Address: yubm_2012@hust.edu.cn

Corresponding author.

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https://doi.org/10.1142/S0218348X17500086Cited by:93 (Source: Crossref)

Abstract

In this work, the effective average height of the roughness elements, the relative increase of the pressure gradients, the relative decrease of the permeability are derived based on the fractal geometry theory and technique for laminar flow through tree-like branching networks with roughened channels. The relationships among the effective average height, the structural parameters and pressure drops as well as permeability are studied. It is found that the total pressure drop across a tree-like branching network with roughened channels is increased by a factor of $1 / {(1 - ε)}^{4}$ , and the permeability for the network with roughened channels is decreased by a factor of ${(1 - ε)}^{2}$ , where $ε$ is the relative roughness of surfaces of channels, compared to those with smooth channels.

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