particle settling velocity put particle in a still fluid… what happens? speed at which particle...
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Particle Settling Velocity
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
Fg
Fd
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STOKES Settling Velocity
Assumes: spherical particle
laminar settling
Gravity:
Drag:
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At terminal velocity,
Fg = Fd
Solve for Ws,
Stokes settling velocity:
Remember Assumptions!
Stokes Region: WsD/ < 1 Laminar
spherical
non-flocculated
18
2 gDWs
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Assumptions:
Shape close to a sphere
Laminar –
What if turbulent?
Cd = f (ν, D, ρ) - turbulent
Cd = 24/Re - laminar
D (nominal)
Ws SF = 1
SF < 1
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Turbulent part of the curve:
Gibbs formulation –
(cgs units)
use for spheres 0.0063 cm < D < 1.0 cm
D
DgD
Ws
s
07440.0011607.0
02480.0003869.0)(932
1
22
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Laminar (Stokes) vs. Turbulent (Gibbs) settling
Comparison of Stokes and Gibbs
0
50
100
150
0 0.05 0.1 0.15
Diameter, cm
Set
tlin
g V
elo
city
, cm
/s
Stokes
Gibbs
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For a 0.01 mm particle:
How long to settle through 10 m of water column?
Size (D) Ws (Stokes) Time(S) Time(G)Very coarse sand 1 mm 64 cm/s 16 sec 1.1 min
Fine to 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
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What we see:
“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
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Particles have a tendency to form aggregates:
Larger particles (settle faster)
Lower density (settle slower)
Settling Camera :
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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.
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Aggregation of particles:
• physio-chemical processes
• biological processes
Physio-chemical processes
Electrostatic forces – All particles are charged..
Van der Waals force – attraction of one molecules nuclei with another’s electrons.
Born Repulsion – once close enough, electrons of one repulse electrons of another.
++
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All these forces require particles to be close together
How do they get together and cause collisions?
• Brownian motion
• Shearing mechanisms
• Differential settling
Smaller grain sizes – of similar size Brownian motion
of different size Shear
Larger grain sizes of similar size Differential settling
of different size Shear
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Flocculation - less common in rivers (ionic strength)
- reversible process
Limits to size
Biological Processes
• fecal pellets – settle at high rates
• mucous “stringers”
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When aggregation occurs,
• Aggregates can grow O(102) larger than compound particles.
• “card-house” structure with much water in interstices.
• Floc density typically ranges 1.27 – 1.07 g/cm3
primary aggregates – 1.16-1.27 g/cm3
secondary aggregates – 1.06 – 1.07 g/cm3
• Floc settling velocity is substantially higher than the settling velocity of the component grains.
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Hindered SettlingAt increasing concentrations, flocs interact
hydrodynamically
• Particles cause an upward flow of the fluid they displace
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At ~ 10 – 20 g/l (10 - 20 ppm of flocculated sediment) hindered settling occurs