Abstract
Roughness induces the complex transport of fluid on interfacial flow. The intrinsic asperities of surfaces involve fractal trait. A fractal roughness model for the transport of fractional non-Newtonian fluid is proposed in this work. In the present analysis, the effective local radius is characterized by means of the algebraic superposition of the measuring radius as well as the roughness in the angular and the longitudinal directions. A novel Poiseuille number is put forward that combines the non-locality of non-Newtonian fluid and the fractal attribute of the surface within a microtube. The effects of the relative roughness, the fractal dimension, and the fractional derivative order on frictional resistance are investigated and discussed. In addition, the accuracy and feasibility of the present model are verified by comparing with the conventional model with regard to the experimental data of polyacrylamide (PAM). The present model may serve as a potential approach to quantify and manipulate the transport of complex fluid in microfluidic field.
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