Particle Settling Velocity Put particle in a still fluid… what happens? Speed at which particle settles depends on: particle properties: D, ρ s , shape fluid properties: ρ f , μ, Re. F d. F g. STOKES Settling Velocity Assumes: spherical particle laminar settling Gravity:
Put particle in a still fluid… what happens?
Speed at which particle settles depends on:
particle properties: D, ρs, shape
fluid properties: ρf, μ, Re
Assumes: spherical particle
Fg = Fd
Solve for Ws,
Stokes settling velocity:
Stokes Region: WsD/ < 1 Laminar
Shape close to a sphere
What if turbulent?
Cd = f (ν, D, ρ) - turbulent
Cd = 24/Re - laminar
SF = 1
SF < 1
Gibbs formulation –
use for spheres 0.0063 cm < D < 1.0 cm
How long to settle through 10 m of water column?
Size (D) Ws (Stokes) Time(S) Time(G)
sand 1 mm 64 cm/s 16 sec 1.1 min
very fine sand 0.1 mm 0.64 cm/s 26 min 28.2 min
Silt 0.01 mm 0.0064 cm/s 43 hrs
Clay 0.001 mm 0.000064 cm/s 180 days
“Observations of suspended sediment concentration collected around the mouths of rivers around the globe provide clear support for the hypothesis that mud and sand both sink rapidly from discharge plumes” Hill et al, in press
“After a large flood, more than 80% of the flood sediment could be accounted for in water depths of less than 50 m at distances less than 20 km from the river mouths. Given that currents typically fall in the range of 10-20 cm/s, these observations suggest that particles must have been sinking at speeds of approximately 0.1 mm/s which is typical of medium silts and exceeds settling velocity of clay particles by an order of magnitude” Drake et al., 1972
Particles have a tendency to form aggregates:
Larger particles (settle faster)
Lower density (settle slower)
According to: Physio-chemical factors in particle aggregation, Johnson et al.
Aggregation applies to the general process of formation of larger particles from the collision of smaller particles.
Flocculation refers to aggregation when the bonding agent that holds particles together is a high molecular weight polymer that operates through inter-particle bridging.
Coagulation describes the process of aggregation in which primary particles are destabilized by charge neutralization through double layer compression.
But … in Oceanography the terms are used interchangeably to mean the formation of larger particles from smaller.
At ~ 10 – 20 g/l (10 - 20 ppm of flocculated sediment) hindered settling occurs