Dynamic behaviors of sedimenting colloidal gel materials: hydrodynamic interactions
It is a highly nonlinear poromechanics phenomenon that colloidal gel materials that are exposed to a gravitational stress greater than their yield stress undergo elastic compression. Here, we resolve theoretically the dynamic behaviors of colloidal gel settling in a closed cylindrical tube of finite height. We develop an extended phenomenological model by considering the hydrodynamic interactions between the backflow of the interstitial fluid and the sedimenting gel columns. We address the hydrodynamic signature by assembling a cylindrical streamer channel into pure Darcy's flow regime, and therefore our continuous model enables us to explore how geometric confinement exerted by the wall affects the colloidal gel sedimentation in a closed tube, which extends beyond the conventional poroelastic model. The results suggest a dynamically propagating strain rate from the gel bottom towards the settling gel front, which demonstrates the duality characteristics of fluidity and solidity for all gel types in our calculations. Our results confirm the vital role that geometric confinement has in association with hydrodynamic interactions in speeding up the sedimentation in gels because the average velocity of the settling front and the bulk sedimentation velocity of the gel particle (cluster) increase significantly under confinement. Furthermore, an analytical model we derive identifies the functional correlation of the velocity ratio to concentration in the compressive sedimentation regime of the gel. The numerical and analytical results collaboratively elucidate a signature that the compressive regime in the settling gel can be suppressed by the confinement, but strengthened again as the confinement increases to exceed a threshold. This threshold is shown to highly depend on the gel softness and initial particle loadings. Our systematic investigations benefit desirable strategies to manage the sedimentation dynamics of colloidal gel materials for application in various fields.