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

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.

Automated summary

The present work investigates the flow rate/pressure gradient relationship for yield stress fluids through non-circular capillaries, proposing empirical relationships for both Bingham and Herschel-Bulkley fluids. Numerical simulations show good agreement between the predicted empirical relationships and results from literature, allowing for easy prediction of total flow rate in bundles of non-circular capillaries. This has implications for processing experimental data based on capillaries with non-circular cross-sections in yield stress fluid porosimetry method.