Linking pore flow propagation to pore size: correlations and underlying mechanisms

Flows through granular packings are critically important in various geotechnical and geoenvironmental systems. Special attention has been paid to the pore-scale hydrodynamics in previous research, while it is still unclear how the flow propagates among individual pores with different sizes. In this study, computational fluid dynamics (CFD) modelling is performed to resolve pore-scale flow through sphere packings with varying porosities and random fabrics. The flow rates through pore constrictions are quantified to characterise flow propagation. Results show that both the maximum and mean flow rates through constrictions of comparable areas are linearly proportional to the constriction area. Unified linear correlations are established between the normalised maximum\mean pore flow rate and the normalised constriction area for sphere packings with porosities below 0.5. The corresponding proportionality coefficients are approximately 2.75 for the maximum value and 1 for the mean value. Furthermore, a newly developed theoretical model demonstrates that these linear correlations arise from a sufficient number of parallel and serial constriction combinations within the pore networks. This study suggests that once the pore constriction size distribution is known, the maximum and mean flow rates through constrictions of comparable sizes can be readily estimated, which would be beneficial for a quantitative understanding of flow behaviour in granular packings.