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Empirical Flow Rate/Pressure Drop Relationships for Capillaries of Triangular and Rectangular Cross-Sections to be Used in Yield Stress Fluid Porosimetry

Article dans une revue avec comité de lecture
Author
MACKAYA, Terence Emery
1002421 Institut de Mécanique et d'Ingénierie [I2M]
AHMADI-SENICHAULT, Azita
1002421 Institut de Mécanique et d'Ingénierie [I2M]
OMARI, Abdelaziz
1002421 Institut de Mécanique et d'Ingénierie [I2M]
RODRÍGUEZ DE CASTRO, Antonio
211915 Mechanics surfaces and materials processing [MSMP]

URI
http://hdl.handle.net/10985/20695
DOI
10.1007/s11242-020-01531-9
Date
2021
Journal
Transport in Porous Media

Abstract

The aim of the present work is to investigate the flow rate/pressure gradient relationship for the flow of yield stress fluids through rectilinear capillaries of non-circular cross-sections. These capillaries very often serve as basic elements in the modeling of porous media as bundles of capillaries or pore-network models. Based on the notions of shape coefficient and critical Bingham number, empirical flow rate/pressure gradient relationships have been proposed for both Bingham and Herschel–Bulkley fluids. The reliability of these relationships has been assessed by performing numerical simulations with the open-source Computational Fluid Dynamics (CFD) package OpenFOAM. For the considered cross-sectional shapes (equilateral triangle and square), and for a wide range of Bingham numbers, the predictions of the proposed empirical relationships have shown to be in very good agreement with the results of the current numerical simulations, as well as with previous results from the literature. An interesting feature of the proposed empirical relationships is the possibility to easily predict the total flow rate under a given imposed pressure gradient in a bundle of non-circular capillaries having any random distribution of inscribed circle radii. Furthermore, in the context of the yield stress fluid porosimetry method (YSM), experimental data may now be processed based upon bundles of capillaries with non-circular cross-sections.

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  • Institut de Mécanique et d’Ingénierie de Bordeaux (I2M)
  • Laboratoire Mechanics, Surfaces and Materials Processing (MSMP)

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