Oceanography 540--Marine Geological Processes--Winter Quarter 2001

Particle Size Distributions

The physical behavior of particles is controlled principally by their size and density and to a lesser extent their shape. Because the density of many common minerals is similar, of order 2600-2700 m3kg-1, sediment and suspended particulates are first generaly characterized by a particle size distribution, expressing the number or mass of particles as a function of their size.

We begin with some common nomenclature. Particle size was first characterized by sieving material. As apparatus became standardized, particle size began to be expressed on a scale due to Wentworth (1922) called the phi-scale:

Class Name

Size Range (mm)

Size Range

(m m)

f Units

Boulders

Very Large

4096-2048

 

-11

Large

2048-1024

 

-10

Medium

1024-512

 

-9

Small

512-256

 

-8

Cobbles

Large

256-128

 

-7

Small

128-64

 

-6

Gravel

Very Coarse

64-32

 

-5

Coarse

32-16

 

-4

Medium

16-8

 

-3

Fine

8-4

 

-2

Very Fine

4-2

 

-1

Sand

Very Coarse

2-1

2000-1000

0

Coarse

1-0.5

1000-500

1

Medium

0.5-0.25

500-250

2

Fine

 

250-125

3

Very Fine

 

125-62

4

Silt

Coarse

 

62-31

5

Medium

 

31-16

6

Fine

 

16-8

7

Very Fine

 

8-4

8

Clay

Coarse

 

4-2

9

Medium

 

2-1

10

Fine

 

1-0.5

11

Very Fine

 

0.5-0.24

12

A standard sieve for a particular phi-value would collect all material larger than the smallest size in the class, e.g., a phi=-4 sieve would collect material larger than 16 mm.

There are now many techniques for determining particle size. Classical techniques include:

Instrumental methods are rapidly replacing manual techniques. These include: Results of these analyses are generally expressed either as a histogram showing weight or number in size class, or equivalently as a cumulative frequency versus size:

frequency and cumulative distribution

Figure 32-1


There are a number of statistical descriptors to quickly summarize the character of these distributions. Two keys ones are the width of the distribution and the skewness of the distribution. When the distribution is narrow the sediment is said to be well-sorted while when it is broad sediment is said to be poorly-sorted. Similarly the distribution may be skewed toward finer or coarse size fractions or may be symmetrical, all possible indicators of the origin of the sediment.

In the deep-sea, particles form a benthic boundary layer

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Particle Size Distributions Above Seafloor

Figure 32-2, (35)

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The parameter c is the light attenuation which is related to the particle density. Note the approximately 50 m thick layer of high particle concentration grading to background conditions approximately 100 m off the seafloor. Size distributions change considerably with small particles dominating the bottom mixed layer and large particles dominating the background ocean. What controls the distribution of sizes?

Sedimentation of Particles

Stokes developed a analysis of the settling of spherical particles involving the balance between the net gravity force acting on the particle and the viscous drag exerted by the fluid.

The viscous drag force will depend on the size, r, velocity, w, and viscosity, m, of the fluid medium:

Eq 32-2: terms of viscous drag

Analyzing dimensionally:

Eq 32-2: dimensional analysis

By inspection a=b=c=1. Without developing the hydrodynamics, the viscous drag force acting on a particle is:

Eq 32-3: viscous drag eqn

The net gravitational force (gravity less buoyancy) will be depend on the volume, density, r , and the acceleration of gravity, g:

Eq 32-4: grav force eqn

At terminal velocity, these two forces are balanced:

Eq 32-5: equating forces

Solving for w:

Eq 32-6: settling velocity

Typically Deltarho is 1.5 g cm^-3 and for seawater µ is .01 g-cm^-1sec^-1 so:

d

w

1000 meter descent

1 mm

87 cm s-1

1.15 x 103 s ~ 19 minutes

0.1 mm

0.87 cm s-1

1.15 x 105 s ~ 31 hours

0.01 mm

0.0087 cm s-1

1.15 x 107 s ~ 1/3 year

0.001 mm = 1 m m

0.000087 cm s-1

1.15 x 109 s ~ 35 years

If this were all that were happening, once in suspension small particles will be transported long distances and large ones small distances.

Settling of Aggregates

While discrete particles generally exhibit Stokes settling behavior, particles have attractive forces that cause them to form aggregates or flocs. These aggregates may be held together by relative weak forces (e.g., electrostatic forces) or by coatings of organic material. These aggregates will often have lower density than the constituent grains, due both to the inclusion of water in the interstices of the aggregates and to the lower density of associated organic material. Because many of the forces that lead to aggregation are weak, turbulence can cause disaggregation and the size distribution of flocs will represent some kind of balance between the rates of aggregation and disaggregation.

Figure 32-3 shows an example contrasting the size distribution of the discrete particles making up a collection of natural aggregates (as determined by Coulter sizing) and the size distribution of the aggregates themselves (as determined by image analysis of photographic images). The constituent grains are poorly sorted (spanning greater than 4 phi units) and a factor of 100-1000 smaller than the aggregates.

floc size distribution

Figure 32-3


These aggregates settle much more slowly than the Stokes settling velocity:

floc settling velocity

Figure 32-4


The Stokes settling velocity of a 1 mm grain is 870 mm/s. For these aggregates the settling velocity at 1 mm size is ~1.8 mm/s, ~480x lower. This could be expressed as an excess density; instead of 1600 kg m-3 about 3.3 kg m-3.


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