Particle Size Distributions

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 =-4 sieve would collect material larger than 16 mm.

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

• direct observation, aided by microscope
• sieving through standard sieves (generally applied to very fine sands and above, >=0.6 mm)
• sedimentation rate through a fluid (generally applied to silts and clays, <=0.6 mm)

• laser diffraction
• acoustic diffraction
• field flow fractionation
• microscopy coupled with computerized image analysis

Figure 32-1

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

Figure 32-2, (35)

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:

Analyzing dimensionally:

Eq 32-2:

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

Eq 32-3:

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

Eq 32-4:

At terminal velocity, these two forces are balanced:

Eq 32-5:

Solving for w:

Eq 32-6:

Typically is 1.5 g cm and for seawater µ is .01 g-cmsec 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.

Figure 32-3

Figure 32-4