Soil Science

Particle size theory

In 1850, G.G. Stokes identified three factors that influence the terminal velocity of particles as they fall through a fluid.

The factor of Particle Diameter:

The terminal velocity of a particle falling through a fluid is influenced by its diameter.

The terminal velocity is proportional to the square of the particle's diameter.

However, this relationship does not apply to particles larger than 200 µm in diameter due to excessive turbulence during their settlement, or to particles smaller than 0.2 µm in diameter, which are affected by Brownian motion and may never settle out.

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The factor of Density Difference:

The terminal velocity of a particle is influenced by the density difference between the particle and the fluid it is falling through. A greater difference in densities results in a faster settling rate. For instance, a particle with a density lower than that of the fluid will float.

As an illustration, consider the settling rate difference between a lead particle (density 11.4 g/cm³) and a glass particle (density 2.65 g/cm³).

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The factor of Fluid Viscosity:

The terminal velocity of a particle falling through a fluid is also influenced by the viscosity of the fluid.

A particle will fall more slowly through a fluid with higher viscosity. The velocity is inversely related to the viscosity. Water, for instance, exhibits increased viscosity as temperature drops. The example illustrates two identical glass particles in water at different temperatures, and consequently, different viscosities.

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These factors gave rise to:

Stokes' Law

Stokes' Law formula

 

 
 

Using Stokes' Law, what is the terminal velocity of a particle of 20 μm diameter falling through water? Assume the particle density is 2.65 g cm-3. The water is at 20 ° and hence has a density of 0.998 g cm-3 and a viscosity of 0.01 poise Acceleration due to gravity is 9.81 m sec-2

Correct!

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You have calculated the velocity of fall of particles 20 pm and 2 um diameter to be 0.0360 cm sec-1 and 0.0

00360 cm sec-1.

How long would it take these particles to fall 10 cm, assuring that terminal velocity is attained almost instantly?

?

Correct!

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