Reduced Sediment Settling in Turbulent Flows Due To Basset History and Virtual Mass Effects

The behavior of suspended particles in turbulent flows is a recalcitrant problem spanning wide-ranging fields including geomorphology, hydrology, and dispersion of particulate matter in the atmosphere. One key mechanism underlying particle suspension is the difference between particle settling velocity (ws) in turbulence and its still water counterpart (wso). This difference is explored here for a range of particle-to-fluid densities (1-10) and particle diameter to Kolmogorov micro-eddy sizes (0.1-10). Conventional models of particle fluxes that equate ws to wso result in eddy diffusivities and turbulent Schmidt numbers contradictory to laboratory experiments. Incorporating virtual mass and Basset history forces resolves these inconsistencies, providing clarity as to why ws/wso is sub-unity for the aforementioned conditions. The proposed formulation can be imminently used to model particle settling in turbulence, especially when sediment distribution outcomes over extended time scales far surpassing turbulence time scales are sought. In rivers and streams, mixed-up dirt called "suspended sediments" is known to influence water quality and its concomitant effects on many physical, chemical, and biological processes. Suspended sediments can be harmful to aquatic ecosystem productivity because they reduce light penetration. They can clog gills of fish and other aquatic organism, and they can impact reservoir operation and their capacity necessitating frequent dredging. There is debate about how these sediments interact with swirling motions ("turbulent flows") in moving water. Traditional mathematical models overlook how individual grains are affected by these swirls ("turbulent eddies") and how they displace water ("virtual mass") when sediments move in a fluid. For large grains, these overlooked details can generate new terms in the force balance that are associated with complex eddying motion lagging behind the grain motion ("Basset history term"). Including the Basset history and virtual mass factors reconciles controversies between recent laboratory experiments and traditional theories about how grains settle in turbulent flows. Settling velocity of suspended sediments is reduced by virtual mass and Basset history for grains larger than turbulent micro-scalesAn operational Rouse-like budget that models these two effects is derived and tested against experimentsTurbulent Schmidt number exceeding unity in the experiments can be linked to these two effects