Particle Settling Velocity

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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, ?s, shape fluid properties ?f,
µ, Re
Fd
Fg
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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/? lt 1
Laminar spherical non-flocculated
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Assumptions Shape close to a sphere
Laminar What if turbulent? Cd f (?,
D, ?) - turbulent Cd 24/Re -
laminar
SF 1
SF lt 1
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Turbulent part of the curve Gibbs formulation
(cgs units) use for spheres 0.0063
cm lt D lt 1.0 cm
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Laminar (Stokes) vs. Turbulent (Gibbs) settling
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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Settling Camera
Particles have a tendency to form
aggregates Larger particles (settle
faster) Lower density (settle slower)
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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 anothers 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