Transcript Particle Settling Velocity Put particle in a still fluid… what happens? Fd Fg Speed at which particle settles depends on: particle properties: D, ρs, shape fluid.

Particle Settling Velocity
Put particle in a still fluid… what happens?
Fd
Fg
Speed at which particle settles depends on:
particle properties: D, ρs, shape
fluid properties: ρf, μ, Re
STOKES Settling Velocity
Assumes:
spherical particle
laminar settling
Gravity:
Drag:
At terminal velocity,
Fg = Fd
Solve for Ws,
D g
Ws 
18
2
Stokes settling velocity:
Remember Assumptions!
Stokes Region: WsD/ < 1
Laminar
spherical
non-flocculated
Assumptions:
SF = 1
Ws
Shape close to a sphere
SF < 1
D (nominal)
Laminar –
What if turbulent?
Cd = f (ν, D, ρ)
- turbulent
Cd = 24/Re
- laminar
Turbulent part of the curve:
Gibbs formulation –


 
 3  9 2  gD2 ( s
)0.003869 0.02480 D 



Ws 
0.011607 0.07440 D 
(cgs units)
use for spheres 0.0063 cm < D < 1.0 cm
1
2
Settling Velocity, cm/s
Laminar (Stokes) vs. Turbulent (Gibbs) settling
Comparison of Stokes and Gibbs
150
100
Stokes
50
Gibbs
0
0
0.05
0.1
Diameter, cm
0.15
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
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
Settling Camera :
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.
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.
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
of different size
Larger grain sizes
Brownian motion
Shear
of similar size Differential settling
of different size
Shear
Flocculation - less common in rivers (ionic strength)
- reversible process
Limits to size
Biological Processes
• fecal pellets – settle at high rates
• mucous “stringers”
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.
Hindered Settling
At increasing concentrations, flocs interact
hydrodynamically
• Particles cause an
upward flow of the
fluid they displace
At ~ 10 – 20 g/l (10 - 20 ppm of flocculated sediment)
hindered settling occurs