Fluid effects on the dilatancy of two-phase gravity-driven granular flows

Volume fraction of solid grains plays a critical role in determining the dynamics of granular flows. The evolution of volume fraction is governed by flow dilatancy depending on the rheological behavior of solid–fluid mixtures and, hence, the pore fluid effects, which are dominated by apparent cohesion and viscous drag in unsaturated and saturated flows, respectively. Prevailing approaches for predicting volume fraction in wet granular flows using two-phase flow models have been proven valid for submerged granular flows or suspensions that conform to visco-inertial rheology. However, for unsaturated granular flows, widely accepted methods for volume fraction modeling remain lacking, due to the cohesive interaction mechanisms not yet being fully described. In this study, we conducted small-scale flume experiments using uniform pseudo-spherical ceramic beads, with initial water content progressively varied from dry to oversaturated states. The dynamics of the experimental flows were captured by sensor measurements and image processing techniques, with solid volume fraction evolution obtained by particle tracking velocimetry. We incorporated our experimental data into the μK (visco-inertial) and μIm (extended inertial) rheological frameworks constructed for two-phase flows and then contrasted the fitting performance of the two corresponding volume fraction scaling models, ΦK and ΦIm, through error analysis. We demonstrate here for the first time the excellent validity of ΦIm scaling for both unsaturated and saturated granular flows in which the dominated fluid effect ranges from apparent cohesion to viscous shear; by contrast, ΦK scaling shows significantly better applicability to saturated granular flows than to unsaturated flows.