Particle Entrainment

Transport of sediment by fluid flow involves two fundamental steps: erosion and entrainment of sediment from the bed, followed by sustained downcurrent or downwind movement of sediment along or above the bed. ^[1] The term entrainment refers specifically to the processes involved in lifting resting grains from the bed or otherwise putting them into motion. ^[1] More energy is commonly required to initiate particle movement than to keep particles in motion after entrainment. ^[1] This distinction - between the threshold of motion and the threshold of sustained transport - is why rivers can carry coarse material far from source areas even after flood velocities subside; the grains were put in motion during the flood peak and continue rolling with less energy than was originally needed.

The Critical Threshold for Grain Movement

As the velocity and shear stress of a fluid moving over a sediment bed increase, a critical point is reached at which grains begin to move downcurrent. ^[1] Typically, the smaller and lighter grains move first; as shear stress increases, larger grains are put into motion until finally grain motion is common everywhere on the bed. ^[1] This critical threshold for grain movement is a direct function of several variables, including the boundary shear stress, fluid viscosity, and particle size, shape, and density. ^[1] Indirectly, it is also a function of the velocity of flow, which varies as the logarithm of the distance above the bottom. ^[1]

Forces Acting on a Grain

To understand particle entrainment, it is necessary to consider the opposing forces that come into play as a fluid moves across its bed.

Forces caused by gravity act downward to resist motion and hold particles against the bed. ^[1] The gravity forces result from the mass of the particles and are aided in resisting grain movement by frictional resistance between particles. ^[1] Fine, clay-size particles have added resistance to movement owing to cohesiveness that arises from electrochemical bonds between these small grains. ^[1] This explains the apparently counterintuitive observation that very fine particles can actually be harder to erode than medium sand: they are electrochemically bonded to their neighbours, and they sit within the viscous sublayer where turbulent lift forces are weakest.

The motive forces that fluid flow must generate to overcome these resisting factors include a drag force and a lift force. ^[1]

Drag Force

The drag force acts parallel to the bed and is related to the boundary shear stress. ^[1] It depends upon the boundary shear stress and the drag exerted on each grain exposed to that stress. ^[1]

Lift Force - The Bernoulli Effect

The hydraulic lift force known as the Bernoulli effect is caused by the convergence of fluid streamlines over a projecting grain. ^[1] The Bernoulli effect results from an increase in flow velocity in the zone where the streamlines converge over the grain - this velocity increase causes pressure to decrease above the grain, and hydrostatic pressure from below then tends to push the grain up off the bed into this low-pressure zone. ^[1] The mechanism is precisely the same as lift created when air flows over the curved wing of an airplane. ^[1]

The drag and lift forces combine to produce the total fluid force. For grain movement to occur, the fluid force must be large enough to overcome the gravity and frictional forces. ^[1]

Complicating Factors

Several factors complicate calculation of critical thresholds under natural conditions: variations in shape, size, and sorting of grains; bed roughness, which controls the presence or absence of a viscous sublayer; and cohesion of small particles. ^[1] Because of these complicating factors, the critical conditions for particle entrainment cannot be calculated and must be determined experimentally. ^[1] The Hjulström diagram and the Shields diagram are the two principal experimental tools used to express the critical conditions for grain movement as a function of grain size and flow conditions respectively.

Fine muds and silts may not erode to yield individual grains owing to the tendency of such cohesive materials to be removed as chunks or aggregates of grains. ^[1] This is a further reason why cohesive fine sediment behaves very differently from non-cohesive sand in its resistance to erosion - the relevant threshold is not for individual particles but for the tensile strength of the aggregate.

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