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

STOKES Settling Velocity

Assumes: spherical particle

laminar settling

Gravity:

Drag:

At terminal velocity,

Fg = Fd

Solve for Ws,

Stokes settling velocity:

Remember Assumptions!

Stokes Region: WsD/ < 1 Laminar

spherical

non-flocculated

18

2 gDWs

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

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

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

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

Particles have a tendency to form aggregates:

Larger particles (settle faster)

Lower density (settle slower)

Settling Camera :

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 Brownian motion

of different size Shear

Larger grain sizes 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 SettlingAt 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