Sedimentation Analysis - Stokes Law (2023)

Sedimentation Analysis - Stokes Law (1)Small particles of particular size range in liquid suspension have a tendency to settle down due to multiple type of forces acting on them. This behaviour of particles is known as sedimentation.

In soil mechanics we use this property of small particles to analyze the particle size distribution. Particle size distribution is the method of separation of soil sample into different fractions based on their particles sizes.

Soils with particle size greater than 75 micron are analyzed by Sieve analysis method using sieves of different sizes.

Particles of size smaller than 75 micron cannot be sieved because smaller particles carry charges on their surface and have tendency to stick to each other and other particles, even to the sieves or to the experimenter’s hand. So handling such kind of soils would be very difficult.

So to analyze soils containing these particles we use the method sedimentation analysis.

This method is based on the Stokes law.

According to this law a small particle in a liquid suspension tries to settle down due to its own weight under the action of gravity. And because of acceleration due to gravity its downward velocity keeps on increasing.

Sedimentation Analysis - Stokes Law (2)

But two forces,

One is Buoyant force, which acts upwards and acts due to the pressure difference on the body inside the liquid.

Sedimentation Analysis - Stokes Law (3)

second is drag force, which is a resistive force and acts opposite to the direction of motion of the body.

These two forces starts acting on the particle in the opposite direction of particle’s motion and start retarding the particle until it acquires the equilibrium condition. And because of which particle’s velocity becomes constant. That is, now particle falls with a constant velocity, which is called its terminal velocity.

Sedimentation Analysis - Stokes Law (4)

The expression for terminal velocity can be obtained by writing equation of equilibrium for this falling particle in fluid.

(Video) Sedimentation Analysis - Stokes Law

Particle’s weight W downward, buoyant force B and drag force D upwards.

So equilibrium equation will be W equal to B plus D.

W = B + D

Weight can be written as volume of particle multiplied by its unit weight gamma s.

Buoyant force will be weight of liquid, in our case that liquid is water, this particle has displaced which is volume of particle multiplied by the unit weight of water it displaces.

Drag force on a small spherical particle moving through a viscous fluid is given by 6 pie eta are wee.

Sedimentation Analysis - Stokes Law (5)

Eta is the dynamic viscosity of soil suspension

Dynamic viscosity is also represented as letter mu.

Ys is unit weight of soil particle

And Yw is unit weight of water

Solving this equation and after a little rearrangement we get the terminal velocity as this.

Sedimentation Analysis - Stokes Law (6)

Remember this equation as equation number 1.

In this equation these quantities are constant for a particular soil and water and viscosity is constant for a particular temperature.

(Video) Sedimentation Analysis | Stoke's Law | Mechanical Analysis of Soil

Sedimentation Analysis - Stokes Law (7)

So we can see the relationship between settling terminal velocity of the particle and its diameter.

Sedimentation Analysis - Stokes Law (8)

We can see that larger the diameter of a particle, higher its speed will be and smaller the particle slower it will settle to the bottom.

Now by simple equation of motion we know that velocity of any particle which falls through a height of He centimeter in time t mins, would be He upon t. Here substitute the value of velocity from the equation number 1 and we get this equation.

Sedimentation Analysis - Stokes Law (9)

remeber this as equation number 2. Here these quantities are constant,

Sedimentation Analysis - Stokes Law (10)

So we observe a relationship between diameter of a soil particle and its time of settlement to the depth He. By this we can calculate the time required t by any soil particle of diameter D to settle down to a depth of He.

Sedimentation Analysis - Stokes Law (11)

Sedimentation Analysis - Stokes Law (12)That’s ok, but how do we carry out particle size analysis with this method?

To start with let’s first prepare the soil suspension for sedimentation analysis.

We take about 50 gm of oven dried soil sample which passed through 75 micron sieve. Put it into a vessel and mix about 100 ml of a dispersing agent.

Sedimentation Analysis - Stokes Law (13)We need to mix dispersing agent because fine soil particles tends to stick to each other and in the liquid suspension they form bigger flocs. These flocs behave like a single particle and according to above established equation number 1, they settle with greater speed than the individual particles should settle. Hence true sedimentation results cannot be obtained.

Sedimentation Analysis - Stokes Law (14)

(Video) Sedimentation analysis - Stokes law

There is also a method given for the preparation of dispersing agent. We prepare it by mixing 33 gm of sodium hexameta-phosphate and 7 gm of sodium carbonate to one litre of distilled water.

Back to our sample, after mixing the dispersing agent the sample is stirred with a mechanical stirrer for few minutes.

Then sample is transferred to a measuring jar and distilled water is added to it to make the suspension volume 1000 ml.

By placing a hand over the jar make the jar upside down a few times so as to ensure complete mixing.

Sedimentation Analysis - Stokes Law (15)Here we assume that our suspension is completely mixed and is homogeneous. That means we assume that all the soil particles of different sizes are uniformly distributed throughout the suspension and concentration of particles of different sizes is the same at all depths. This means the number of different sized particles at any depth is the same.

For clarity let’s take fewer particles and show all the particles of different sizes separated.

As per the equation number 1 we can know particles of larger diameter will have higher settling velocity and will settle earlier then small sized particles.

At the beginning of the sedimentation, amount of particles at any layer of the suspension will be same. But as time proceeds, particles start settling down and amount of particles of different layers become different.

Sedimentation Analysis - Stokes Law (16)

By equation number 2 we know that in time t a particle of diameter D would have settled for He depth, which means above this depth He, only particles of size smaller than D will be present, because He is the depth from the surface and we are considering the particle of size D which has traveled the maximum distance so we can be sure that no particle of this size will be present above this layer.

Sedimentation Analysis - Stokes Law (17)

So if we take a sample from the depth He all particles smaller than D will be present in this sample and in the same concentration as were in the beginning because of being the same settling velocity of similar sized particles. That is, two particles will leave the layer and two particles will arrive in the layer at the same time. So number of particles of particular size on the layer will remain the same.

As we know percentage finer is weight of sample with particles of size smaller than D divided by weight of the total soil sample with all the particles present in it.

Sedimentation Analysis - Stokes Law (18)

By taking weight of highlighted layer at the beginning and after time t we can simply calculate percentage finer.

(Video) Sediment deposition and Stokes' Law

To determine the weight of soil particles on this layer we employ two methods

1. pipette method

2. hydrometer method.

In the pipette method the weight of solids is determined directly by collecting sample of soil suspension from a specified sampling depth using pipette.

In hydrometer method the weight of solids is calculated indirectly by reading the density of soil suspension on hydrometer.

There are some limitations of the Stokes law, and hence sedimentation analysis does not give correct values of the particle size analysis and the percentage finer. These limitations are eventually also the limitations of both pipette and hydrometer method.

1. Stokes law is based on the assumption that all the soil particles are spherical. But fine soils particles are never spherical and actually are flaky or needle shaped in reality.

Sedimentation Analysis - Stokes Law (19)

2.specific gravity of solids for different particles is different, but we use its average value.

Sedimentation Analysis - Stokes Law (20)

3. Stokes law is applicable when fall of particle is in the liquid which has infinite extent, that is no boundary is present. But our suspension is in the jar and its walls affect the results to some extent as falling particles may collide with the wall.

4. we have also assumed that there is no interference on the movement of a particle by other surrounding particles. But practically there is a lot of interference. Particles may collide and may change their course and velocity.

However it has been shown that for suspension of 50 gm per litre or less particle to particle influence is negligible.

5. Sedimentation analysis cannot be used for particles of size larger than 0.2 mm because they may cause to generate turbulent conditions and stokes law is not applicable for that.

6. Sedimentation analysis is also not applicable for particles smaller than 0.2 micron because such small particles may set Brownian motion in the suspension and these particles do not settle as per stokes law.

(Video) Sediment deposition and Stokes’ Law


What is sedimentation analysis? ›

Sediment analysis is primarily based on the recognition of the main sedimentary components, including the identification of heavy minerals and clay minerals for provenance studies (Weltje and Von Eynatten, 2004). Textural and structural analyses are based on standard routines and techniques used in sedimentology.

What is the law for sedimentation? ›

According to Stokes' law, the particle sedimentation velocity is proportional to the density difference between the solid phase and the liquid phase, inversely proportional to the viscosity of the liquid, and proportional to the square of particle diameter.

What is the process of sedimentation in Brownian motion? ›

Sedimentation is the phenomenon that Brownian particles attain a certain velocity under the action of an external field. This translational velocity is referred to as the sedimentation or settling velocity. The most common example of an external field is the earth's gravitational field.

What is Stokes law used for? ›

Knowing the terminal velocity, the size and density of the sphere, and the density of the liquid, Stokes' law can be used to calculate the viscosity of the fluid. A series of steel ball bearings of different diameters are normally used in the classic experiment to improve the accuracy of the calculation.

What are the methods used in sedimentation analysis? ›

Pipette method is one of the methods of taking observation of liquid soil suspension for the purpose of sedimentation analysis of soils containing fine particles. Theory of sedimentation, its limitations and the method of preparation of soil suspension have already been discussed, read them here.

What are the 4 types of sedimentation? ›

Type 1 – Dilutes, non-flocculent, free-settling (every particle settles independently.) Type 2 – Dilute, flocculent (particles can flocculate as they settle). Type 3 – Concentrated suspensions, zone settling, hindered settling (sludge thickening). Type 4 – Concentrated suspensions, compression (sludge thickening).

How is Stokes law used in soil science? ›

The amounts of silt and clay (+/- sand) are usually determined by a sedimentation procedure, which uses a basic principle of sedimentation called "Stoke's Law": because soil particles are denser than water, they tend to sink, settling at a velocity that is proportional to their size.

Which law is used for particle size determination in sedimentation method? ›

Particle size analysis by gravitational sedimentation analysis. Gravitational sedimentation (originally the pipette method) measures the settling rate of particles in liquid medium and relates this rate to the particle mass by use of the Stokes law.

How is Stokes law applied in soil particle analysis? ›

This method is based on the Stokes law. According to this law a small particle in a liquid suspension tries to settle down due to its own weight under the action of gravity. And because of acceleration due to gravity its downward velocity keeps on increasing.

What is the role of Brownian movement in sedimentation of particle? ›

Brownian motion is in part responsible for facilitating movement in bacteria that do not encode or express motility appendages, such as Streptococcus and Klebsiella species. Brownian motion can also affect “deliberate” movement exhibited by inherently motile bacteria that harbor pili or flagella.

What are the two processes of sedimentation? ›

There are two main processes operating: compaction: by overlying sediments, involving the close-packing of the individual grains by eliminating the pore space and expulsion of entrapped water. cementation: development of secondary material in the former pore spaces which then binds the sedimentary particles together.

What are the three types of sedimentation? ›

The chapter discusses the three distinct types of sedimentation—namely, discrete settling, flocculent settling, and zone settling.

What factors affect Stokes law? ›

Stoke's Law Derivation

The viscous force acting on a sphere is directly proportional to the following factors: Coefficient of viscosity (η). The radius of the sphere (r). The velocity of the object (v).

What are the limitations in the use of Stokes law in sedimentation analysis? ›

When the solid content of a suspension is high, Stokes' equation may not show the real sedimentation rate. High solid content imparts additional viscosity to the system, which must be taken into consideration if the correct rate of settling is to be determined. The equation contains only the viscosity of the medium.

What is Stokes law write its formula? ›

Statement of Stoke's law: Stokes law states that the force of viscosity on a small sphere moving through a viscous fluid is given by: F=6πμrv. Where, F is the frictional force acting on the interface between the fluid and the particle.

How is sedimentation measured? ›

How is sedimentation measured? Attension® Sigma 700/701 force tensiometers can be used to evaluate the amount of sedimentation of a suspension due to gravity. The suspension liquid is kept still and the balance of the tensiometer measures the mass change of the sedimentation probe within a time period.

How is sedimentation value measured? ›

The sedimentation value according to Zeleny (Zeleny value) describes the degree of sedimen- tation of flour suspended in a lactic acid solution during a standard time interval and this is taken as a measure of the baking quality.

What is the purpose of sedimentation test? ›

Purpose: Measure the relative amounts of sand, silt and clay in a soil sample based on the fact that large, heavy particles will settle most rapidly in water; while small, light particles will settle most slowly.

What are 5 types of sediment? ›

Sediments are classified according to their size. In order to define them from the smallest size to the largest size: clay, silt, sand, pebble, cobble, and boulder.

What are two sedimentation examples? ›

Sand and water separation (sand settlement). Oil and vinegar separation, Settled chalk powder, and water separation.

What is the application of sedimentation? ›

The sedimentation process is used to reduce particle concentration in the water. The advantage of sedimentation is that it minimizes the need for coagulation and flocculation. Typically, chemicals are needed for coagulation and flocculation, but improved sedimentation controls the need for additional chemicals.

What are the four conditions of Stokes law? ›

Assumption of Stokes' Law

Particles must be solid, smooth, and spherical. Particles must be of uniform density. Particles must be sufficiently large (>0.001mm) as compared to molecules of fluid so that the thermal (Brownian) motion of the fluid molecules does not affect the particles.

How Stokes law equation is useful for determining soil texture? ›

As we can see, Stokes Law can be used to determine when a volume of a soil-water suspension will be devoid of soil particles larger than a given size. Then we can measure the concentration of soil remaining in that volume.

What are the 4 methods of determining the particle size? ›

The most common techniques to determine particle size distribution are dynamic image analysis (DIA), static laser light scattering (SLS, also called laser diffraction), dynamic light scattering (DLS) and sieve analysis.

What are the 2 types of particle size analysis? ›

Two of the main types of particle size analyzers dynamic light scattering and laser particle analyzers. Dynamic light scattering analyzers measure particles in solutions in the 0.6 nm to 6 um range. Laser diffraction analyzers are used for particles in a material within the range of 10 nm to 3 mm.

What are the limitations of Stokes law? ›

The lower limit of particle size for the validity of Stoke's Law is 0.0002 mm. However, the upper limit for the same is 0.2 mm. For particles of size less than 0.0002 mm, Brownian movement affects their settlement and in the case of particles larger than 0.2 mm, turbulence affects the settlement.

How does Brownian movement prevent sedimentation of suspension? ›

➢ Brownian movement of particle prevents sedimentation by keeping the dispersed material in random motion.

What is the separation technique of sedimentation? ›

Sedimentation can be used to separate particles based on their size by applying a centrifugal force to the required solution. In the process of Centrifugation, a centrifugal force is applied to a heterogeneous mixture which will separate the mixture according to its density.

How many types of sedimentation are there? ›

There are two types of sedimentation process, the first one is plain sedimentation and the second one is sedimentation with coagulation( clarification).

What is the difference between sedimentation and sedimentation? ›

Difference Between Decantation and Sedimentation

Decantation is the act of separating two immiscible substances by pouring off one component, whereas sedimentation is the process of settling or being deposited as sediment. This is the primary distinction.

What is the common sedimentation process? ›

Sedimentation is the separation of suspended solids from a liquid by gravity. As solids and particles fall out of liquid suspension and settle, they become sediment. This process, often referenced as settling, is regularly used in water and wastewater treatment.

What is another name for sedimentation? ›

Definitions of sedimentation. the phenomenon of sediment or gravel accumulating. synonyms: alluviation, deposit.

What are the agents of sedimentation? ›

4 agents move sediment: Water, Wind, Glaciers, and Mass Wasting (gravity).

Why is sediment analysis important? ›

Analysis of sediments provides environmentally significant information. Their chemical characterization is needed to understand the natural and anthropogenic influence on the bodies of water.

What is the simple definition of sedimentation? ›

: the action or process of depositing sediment. : the depositing especially by mechanical means of matter suspended in a liquid.

What is sedimentation in analytical chemistry? ›

Sedimentation can be used to separate particles based on their size by applying a centrifugal force to the required solution. In the process of Centrifugation, a centrifugal force is applied to a heterogeneous mixture which will separate the mixture according to its density.

What is a good sedimentation rate? ›

0 to 15 mm/hour in men younger than 50. 0 to 20 mm/hour in men older than 50. 0 to 20 mm/hour in women younger than 50. 0 to 30 mm/hour for women older than 50.

What are limitations of sedimentation analysis? ›

Sedimentation analysis cannot be used for particles of size larger than 0.2 mm because they may cause to generate turbulent conditions and stokes law is not applicable for that.

What is the conclusion of sedimentation? ›

Conclusion and RecommendationsSedimentation practices are designed to be effective at retaining suspended solids thattypically adsorb to solids. In every after the experiment, the retained solids must need to beremoved.

How is sedimentation analysis used for size determination? ›

Particle size analysis by gravitational sedimentation analysis. Gravitational sedimentation (originally the pipette method) measures the settling rate of particles in liquid medium and relates this rate to the particle mass by use of the Stokes law. The particle mass is determined by density and particle size.

What are the two types of sedimentation? ›

The theory reflects two basic forms of sedimentation: unhindered and hindered settling. When the particle concentration in the suspension is about 18% v/v then there is a transition in how the suspension appears.

What is another name of sedimentation? ›

Definitions of sedimentation. the phenomenon of sediment or gravel accumulating. synonyms: alluviation, deposit.

What process is called sedimentation? ›

Sedimentation is the deposition of sediments. It takes place when particles in suspension settle out of the fluid in which they are entrained and come to rest against a barrier.

What are the factors affecting sedimentation? ›

Factors that affect the sedimentation process include the shape and size of particles, the density of particles, water temperature, particle charge, dissolved substances in the water, environmental effects, and characteristics of the basin.


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