Discussion Examples for Particle Sedimentation Experiments | Effects of Settling Velocity, Particle Size, and Viscosity

What Is a Particle Sedimentation Experiment?

A particle sedimentation experiment is an experiment that investigates the phenomenon in which solid particles dispersed in a liquid move downward over time because of gravity.
The rate at which particles settle changes depending on particle size, particle density, liquid density, liquid viscosity, particle shape, dispersion state, and other factors.
By observing sedimentation behavior, the dispersion stability of the particles and the presence or absence of aggregation can be discussed.

Sedimentation experiments are related to colloids, suspensions, muddy water, pigment dispersions, powder materials, wastewater treatment, and other systems.
If particles settle immediately, the dispersion stability can be considered low, while if they remain suspended for a long time, possible reasons include small particle size, a small density difference, high viscosity, or stable dispersion caused by surface charge.

Main Items to Include in the Results

In the results of a particle sedimentation experiment, organize the particle type, particle size, particle concentration, dispersion medium, density, viscosity, temperature, sedimentation distance, sedimentation time, sedimentation velocity, change in the sedimentation interface, clarity of the supernatant, height of the sediment layer, and other information.
When recording changes over time, presenting sedimentation distance or turbidity changes at fixed time intervals in a table or graph makes the discussion easier.

Main Items to Include in the Results

• Type of particle
• Particle size or particle-size distribution
• Particle concentration
• Particle density
• Type of dispersion medium
• Density of the dispersion medium
• Viscosity of the dispersion medium
• Measurement temperature
• Sedimentation distance
• Sedimentation time
• Sedimentation velocity
• Clarity of the supernatant
• Position of the sedimentation interface
• Height of the sediment layer
• Presence or absence of aggregation or floc formation
• Stirring conditions
• Causes of error and points for improvement

Reference Experimental Values and Calculation Examples for Particle Sedimentation Experiments

Here, the sedimentation velocity of particles settling through a liquid is calculated from the sedimentation distance and sedimentation time, and the effects of particle size, liquid viscosity, and the density difference between the particles and liquid on sedimentation are organized.

In a particle sedimentation experiment, the time required for a particle to settle a certain distance is measured and the sedimentation velocity is calculated.
Sedimentation tends to become faster as particle size increases and as the density difference between the particle and liquid increases, while it tends to become slower as the viscosity of the liquid increases.

Reference Experimental Conditions

Basic Equation for Sedimentation Velocity

Sedimentation velocity is calculated by dividing the distance a particle settles by the time required to move that distance.

Sedimentation velocity = Sedimentation distance ÷ Sedimentation time

For example, if a particle takes 40.0 seconds to settle 20.0 cm, the sedimentation velocity is calculated as follows.

20.0 cm ÷ 40.0 s = 0.500 cm/s

The shorter the sedimentation time, the greater the sedimentation velocity, and the longer the sedimentation time, the smaller the sedimentation velocity.

Example of Sedimentation Time with Different Particle Sizes

First, the sedimentation times are compared when the particle size is varied in the same liquid.
Here, water is used as the liquid and the sedimentation distance is fixed at 20.0 cm.

Example Calculation of Average Sedimentation Time and Sedimentation Velocity

For Sample B, suppose the sedimentation times were 43.8 seconds, 44.6 seconds, and 44.1 seconds.
The average sedimentation time is calculated as follows.

Average sedimentation time = (43.8 + 44.6 + 44.1) ÷ 3 = 44.2 s

Because the sedimentation distance is 20.0 cm, the average sedimentation velocity is calculated as follows.

Average sedimentation velocity = 20.0 cm ÷ 44.2 s = 0.452 cm/s

In this way, when the same sedimentation distance is used for comparison, samples with shorter sedimentation times have greater sedimentation velocities.

Relationship Between Particle Size and Sedimentation Velocity

Organizing the above results shows that the average sedimentation velocity increases as the particle size increases.

For particles with larger particle sizes, the effect of gravity on sedimentation becomes greater and the sedimentation velocity increases.
On the other hand, for particles with smaller particle sizes, the effect of resistance from the liquid becomes relatively greater and the sedimentation velocity becomes smaller.

Example of Sedimentation Time with Different Liquid Viscosities

Next, the sedimentation times are compared when the viscosity of the liquid is changed using the same particles.
Here, particles with a particle size of 0.50 mm are used and the sedimentation distance is 20.0 cm.

The higher the viscosity of the liquid, the longer it takes for the particles to settle and the smaller the sedimentation velocity becomes.
This is because the viscous resistance of the liquid becomes greater and inhibits the movement of the particles.

Example of Sedimentation Velocity with Different Density Differences

The density difference between the particles and the liquid is also related to sedimentation.
The greater the particle density relative to the liquid, the easier the particles settle, while the smaller the density difference, the smaller the sedimentation velocity becomes.

In this reference example, even when the particle size is fixed at 0.50 mm and the liquid is water, the sedimentation velocity increases as the particle density increases.
This is because the difference between the gravitational force and buoyancy acting on the particles becomes larger, increasing the downward force that causes sedimentation.

Example of How to Write the Results

When particle sedimentation in water was measured, the sample with a particle size of 0.30 mm had an average sedimentation time of 79.2 s and an average sedimentation velocity of 0.253 cm/s.
On the other hand, the sample with a particle size of 1.00 mm had an average sedimentation time of 19.1 s and an average sedimentation velocity of 1.05 cm/s.
These results confirmed a tendency for sedimentation velocity to increase as particle size increased.

In addition, when the viscosity of the liquid was changed using particles with a particle size of 0.50 mm, the average sedimentation velocity in water was 0.452 cm/s, whereas it decreased to 0.167 cm/s in a 40% aqueous glycerin solution.
Therefore, it was found that sedimentation velocity decreases as the viscosity of the liquid increases.

Points for Connecting the Results to the Discussion

In a discussion of a particle sedimentation experiment, it is important not only to describe whether the sedimentation velocity was large or small, but also to organize which of the factors of particle size, viscosity, and density difference affected the sedimentation velocity.

• Did the sedimentation velocity increase as particle size increased?
• Did the sedimentation velocity decrease as the viscosity of the liquid increased?
• Did the particles settle more readily as the density difference between the particles and liquid increased?
• Was the variation in the measured values not too large?
• Did the particles approach the container wall or have bubbles attached to them?
• If the particles were not perfectly spherical, could their shape have affected the sedimentation velocity?
• Can the velocity be considered to have become constant during sedimentation?

Example Discussion

In this experiment, the sedimentation time became shorter and the sedimentation velocity increased as the particle size increased.
The sample with a particle size of 0.30 mm had an average sedimentation velocity of 0.253 cm/s, whereas the sample with a particle size of 1.00 mm had a velocity of 1.05 cm/s.
This was considered to result from the increased effect of gravity on the particles as the particle size increased, causing them to settle more rapidly through the liquid.

In addition, the sedimentation velocity decreased when the viscosity of the liquid was increased.
For particles with a particle size of 0.50 mm, the average sedimentation velocity in water was 0.452 cm/s, whereas it was 0.167 cm/s in a 40% aqueous glycerin solution.
This was considered to result from the greater resistance to particle motion in a more viscous liquid, making sedimentation more difficult.

Furthermore, the sedimentation velocity increased when the density difference between the particles and liquid was larger.
This is because a larger density difference increases the downward force resulting from the difference between gravity and buoyancy.
These results confirm that particle sedimentation velocity is strongly affected by particle size, liquid viscosity, and the density difference between the particles and liquid.

However, in actual measurements, particle shape not being perfectly spherical, the effect of the container wall, attachment of bubbles, and the acceleration process immediately after sedimentation begins may become sources of error.
Therefore, it is necessary to perform multiple measurements and calculate the average value, while also ensuring that particles settle sufficiently far from the container wall.

Summary

In a particle sedimentation experiment, calculating sedimentation velocity from sedimentation distance and sedimentation time makes it possible to compare the effects of particle size and liquid properties on sedimentation behavior.

In this reference example, sedimentation velocity increased as particle size increased and decreased as the viscosity of the liquid increased.
In addition, sedimentation velocity increased as the density difference between the particles and liquid increased.
In a report, relating these changes to gravity, buoyancy, and viscous resistance acting on the particles makes it easier to provide a convincing discussion.

Why Particles Settle

Particles settle in a liquid because gravity acts on them.
When the particle density is greater than the liquid density, the particles experience a downward force and sink.
However, because particles also experience buoyancy from the liquid, the force that actually drives sedimentation is determined by the density difference between the particles and the liquid.

When a particle sinks, it experiences viscous resistance from the liquid.
As the sedimentation velocity increases, the resistance also increases, and eventually the gravitational force and resistance balance.
At this point, the particle settles at a constant velocity, called the terminal velocity.

What Is Sedimentation Velocity?

Sedimentation velocity is the distance that a particle or sedimentation interface moves per unit time.
In an experiment, the position of the sedimentation interface is read at fixed time intervals, and the sedimentation velocity is calculated by dividing the sedimentation distance by time.
A larger sedimentation velocity means that the particles settle faster.

Sedimentation velocity increases as particle size increases and decreases as liquid viscosity increases.
It also becomes easier for particles to settle as the density difference between the particles and liquid increases.
If particles aggregate and form large flocs, their apparent particle size increases and the sedimentation velocity may increase.

Sedimentation velocity v = Sedimentation distance / Time

What Is Stokes’ Law?

Stokes’ law is an equation that represents the terminal velocity of a small spherical particle settling slowly through a viscous fluid.
It applies when the particle is sufficiently small, the flow is not turbulent, and the interactions among particles are small.
In particle sedimentation experiments, it is often used to consider the relationships among sedimentation velocity, particle size, density difference, and viscosity.

v = d²(ρp – ρf)g / 18η

v: sedimentation velocity, d: particle diameter, ρp: particle density, ρf: fluid density, g: gravitational acceleration, η: viscosity

From this equation, it can be seen that sedimentation velocity is proportional to the square of the particle diameter, proportional to the density difference between the particle and liquid, and inversely proportional to the liquid viscosity.
In other words, even a small increase in particle size can greatly change the sedimentation velocity.
Considering the experimental results in light of Stokes’ law makes it easier to organize the factors that affected the sedimentation velocity.

Effect of Particle Size

Particle size is one of the factors that most strongly affects sedimentation velocity.
According to Stokes’ law, sedimentation velocity is proportional to the square of the particle diameter.
Therefore, if the particle diameter doubles, the sedimentation velocity becomes approximately four times greater under ideal conditions.
Even a small difference in particle size may produce a large difference in sedimentation velocity.

Particles with smaller particle sizes have lower sedimentation velocities and tend to remain dispersed for longer periods.
In extremely small particles such as colloidal particles, Brownian motion and repulsion caused by surface charge also have an effect, making sedimentation more difficult.
On the other hand, when particles aggregate and the apparent particle size increases, sedimentation may suddenly become easier.

Effect of Density Difference

Whether particles settle is related to the difference between the particle density and the density of the dispersion medium.
When the particle density is greater than the density of the dispersion medium, the particles settle.
The larger the density difference, the greater the effective downward force and the greater the sedimentation velocity.

Conversely, when the density difference between the particles and dispersion medium is small, the particles become more difficult to settle.
If the particle density is lower than that of the dispersion medium, flotation rather than sedimentation may occur.
When comparing sedimentation velocities, not only particle size but also density difference must be considered.

Effect of Viscosity

Viscosity represents how difficult it is for a liquid to flow.
In a highly viscous liquid, particles experience greater resistance when they move.
Therefore, even for the same particles, the sedimentation velocity becomes smaller in a liquid with higher viscosity.

According to Stokes’ law, sedimentation velocity is inversely proportional to viscosity.
In other words, the greater the viscosity, the slower the sedimentation.
In dispersion media with high viscosity, such as aqueous glycerin solutions or polymer solutions, particles tend to remain suspended for longer periods.
Differences in viscosity are also related to dispersion stability.

Discussion of Terminal Velocity

When a particle begins to settle, it is initially accelerated by gravity.
However, as the velocity increases, the viscous resistance from the liquid also increases.
Eventually, the gravitational settling force, buoyancy, and viscous resistance balance, and the particle settles at a constant velocity.
This constant velocity is called the terminal velocity.

For small particles, the time required to reach terminal velocity is extremely short, so in experiments they are often treated as settling at an almost constant velocity.
If the relationship between sedimentation distance and time is linear, the particles can be considered to be settling at a constant terminal velocity.
On the other hand, if the velocity changes during sedimentation, aggregation, concentration changes, wall effects, and other factors must be considered.

Effect of Brownian Motion

Very small particles are moved irregularly by the thermal motion of liquid molecules.
This is called Brownian motion.
Brownian motion may act in a direction that interferes with particle sedimentation and is one reason why colloidal particles can remain dispersed for a long time.

For large particles, the effect of gravity becomes greater and the effect of Brownian motion becomes relatively small.
On the other hand, for small particles, the sedimentation velocity becomes extremely low, making sedimentation more difficult because of Brownian motion and electrostatic repulsion.
When considering sedimentation of fine particles, thermal motion must be considered in addition to gravity.

Dispersion Stability and Sedimentation

Particles with high dispersion stability remain difficult to aggregate in the liquid and maintain a state in which sedimentation is difficult.
When particle surfaces have charges of the same sign, the particles electrostatically repel one another and the dispersion remains stable.
In addition, when particle surfaces are protected by polymers or surfactants, aggregation may be suppressed.

When dispersion stability is low, particles aggregate with one another to form large aggregates.
Because aggregates have a larger apparent particle size, they settle faster than individual particles.
Therefore, an increase in sedimentation velocity may indicate that particle aggregation occurred.

Discussion of Aggregation and Floc Formation

Aggregation is the process in which particles gather together to form larger assemblies.
In water treatment and other fields, loose particle aggregates are sometimes called flocs.
Because flocs are larger than individual particles, they settle more readily.
Therefore, adding a coagulant may accelerate sedimentation.

However, because flocs contain water internally, their density may be lower than that of simple solid particles.
Therefore, even if the particle size becomes larger, the sedimentation velocity changes depending on shape and density.
When discussing sedimentation promotion by aggregation, not only the apparent particle size but also the density and structure of the flocs must be considered.

Effect of Particle Concentration

When particle concentration is low, interactions among particles are relatively small and individual particles can settle independently.
This type of sedimentation is sometimes called free settling.
On the other hand, when particle concentration is high, particles interact with one another and the sedimentation velocity changes.

In a highly concentrated suspension, sedimentation may be hindered because the particles settle while displacing the surrounding liquid.
Collisions and aggregation among particles also become more likely.
Therefore, when the particle concentration is changed, it is necessary to consider whether the behavior corresponds to free settling or hindered settling.

Discussion of the Sedimentation Interface

When a suspension is allowed to stand, a clear supernatant may appear in the upper portion while a turbid layer containing particles remains in the lower portion.
The boundary between this clear layer and the turbid layer can be observed as the sedimentation interface.
By recording the position of the sedimentation interface over time, the sedimentation velocity can be calculated.

When the sedimentation interface is clear, it is easier to consider the particles to be settling at relatively similar velocities.
On the other hand, when the interface is unclear, possible causes include a broad particle-size distribution, particle aggregation, low concentration, or inappropriate lighting.
Errors in reading the interface lead to errors in sedimentation velocity.

Discussion of Sediment-Layer Height

As sedimentation proceeds, a sediment layer forms at the bottom of the container.
The height of the sediment layer is affected by the amount of particles, packing state, aggregation state, particle shape, floc structure, and other factors.
Even with the same amount of particles, the sediment layer becomes lower if the particles pack densely, while it may become higher if they settle as loose flocs.

If the height of the sediment layer decreases over time, the particles or flocs may be consolidating and water may be leaving the layer.
Observing the height of the sediment layer makes it possible to discuss the aggregation state of the particles after sedimentation.
However, because it is difficult to accurately evaluate particle amount from sediment-layer height alone, it should be considered together with concentration and mass information.

Effect of Temperature

Temperature affects the viscosity of the dispersion medium.
In general, as temperature increases, the viscosity of a liquid decreases and the viscous resistance experienced by particles becomes smaller.
Therefore, sedimentation velocity may increase under higher-temperature conditions.

Temperature also affects Brownian motion and dispersion stability.
Molecular motion becomes more active at higher temperatures, but at the same time sedimentation may become easier because viscosity decreases.
When comparing sedimentation velocities, it is important to keep the temperature constant.

Effect of Particle Shape

Stokes’ law assumes spherical particles.
However, actual particles are not necessarily spherical and may be plate-like, needle-like, or irregularly shaped.
Nonspherical particles experience different resistance in the liquid and their sedimentation velocity may deviate from the ideal equation.

Irregularly shaped particles may change orientation or rotate during sedimentation.
In addition, even for the same volume, resistance differs depending on shape, so the sedimentation velocity also differs.
When experimental results deviate from Stokes’ law, the effect of particle shape can be discussed.

Discussion of Wall Effects

When the container used in a sedimentation experiment is narrow, particles may be affected by the container wall as they settle.
When a particle is close to the wall, the flow of the surrounding liquid is restricted and the resistance becomes greater.
As a result, the sedimentation velocity may become smaller than when the particle settles in a wide container.

Wall effects become larger when the particle diameter is large relative to the container diameter or when the container is narrow.
To accurately measure sedimentation velocity, it is desirable to use a container sufficiently wide relative to the particle size.
If the experimental sedimentation velocity is smaller than expected, wall effects can be discussed as a source of error.

Cases in Which Stokes’ Law Is Difficult to Apply

Stokes’ law is most applicable when the particles are spherical, the particle concentration is low, the flow is laminar, and interactions among particles are small.
However, if the particles are too large, the sedimentation velocity is too high, the particles are aggregated, or the particle concentration is high, the conditions deviate from the ideal assumptions.

In addition, irregular particle shape, a non-Newtonian dispersion medium, or strong container-wall effects also cause deviations from Stokes’ law.
When discussing experimental results, it is important to confirm the assumptions of the equation and explain the applicability range.

Causes of Error in Particle Sedimentation Experiments

Causes of error in particle sedimentation experiments include variation in particle size, differences in particle concentration, insufficient stirring, differences in the start time of settling, errors in reading the sedimentation interface, temperature changes, tilting of the container, wall effects, differences in aggregation state, and entrained bubbles.
Because sedimentation velocity is affected by multiple factors, comparison becomes difficult unless the conditions are standardized.

In particular, when the sedimentation interface is read visually, an unclear interface can cause large errors.
In addition, if the time between sample mixing and the start of measurement differs among samples, initial sedimentation may already have progressed and the velocity may deviate.
Causes of error are easier to organize when divided into sample preparation, settling operation, measurement operation, and analysis.

When the Results Can Be Considered Good

A particle sedimentation experiment can be considered to have produced good results when trends corresponding to Stokes’ law are observed, such as larger particles having greater sedimentation velocities and higher-viscosity liquids producing smaller sedimentation velocities.
In addition, if the relationship between sedimentation distance and time is linear, the particles can be considered to have settled at a constant terminal velocity.

If sedimentation becomes faster under conditions with a coagulant or electrolyte added, this can be explained by particles aggregating and increasing their apparent particle size.
If sedimentation becomes slower under conditions with a dispersant added, the dispersion can be considered to have been stabilized by repulsion among particles or a protective effect.
It is important to relate trends in the results to particle size, viscosity, density difference, and dispersion stability.

Example Discussions When the Experiment Did Not Go Well

When a particle sedimentation experiment does not go well, possible causes should be considered from results such as a sedimentation interface that is difficult to see, a sedimentation velocity that is not constant, failure of the relationship between particle size and sedimentation velocity to match expectations, variation in results for the same sample, or sedimentation that is slower or faster than expected.
Organizing the causes according to particle-size distribution, aggregation, viscosity, temperature, container, and measurement method makes the discussion easier.

How to Write Points for Improvement

In a discussion of a particle sedimentation experiment, writing not only the causes of error but also points for improvement makes the report easier to organize.
Points for improvement can be organized according to sample preparation, measurement conditions, sedimentation observation, and data analysis.

Improvements to Sample Preparation

• Accurately standardize the particle concentration
• Use samples with a uniform particle-size distribution
• Disperse the particles sufficiently before measurement
• Check for aggregation
• Avoid introducing bubbles
• Confirm the viscosity and density of the dispersion medium

Improvements to Measurement Conditions

• Keep the temperature constant
• Use the same container
• Place the container vertically
• Standardize the measurement start time
• Read the sedimentation distance accurately
• Observe under the same lighting conditions

Improvements to Analysis

• Create a graph of sedimentation distance versus time
• Calculate the sedimentation velocity from the linear portion
• Perform multiple measurements and calculate the average value
• Compare the relationships with particle size, viscosity, and density difference
• Confirm the applicability conditions of Stokes’ law
• Discuss deviations caused by aggregation or wall effects

Difference Between a Superficial Discussion and a Good Discussion

In a discussion of a particle sedimentation experiment, simply writing that “larger particles settled faster” or “sedimentation was slower at higher viscosity” results in a superficial discussion.
A good discussion relates Stokes’ law, the square of particle size, density difference, viscosity, aggregation, and dispersion stability.

Examples of Expressions That Can Be Used in Reports

The following expressions can be used when writing the results and discussion of particle sedimentation experiments.
Adjust the necessary parts according to your own experimental results.

• Particle sedimentation is determined by the balance among gravity, buoyancy, and viscous resistance.
• When the particle density is greater than the dispersion-medium density, the particle settles.
• Sedimentation velocity can be calculated by dividing sedimentation distance by time.
• According to Stokes’ law, sedimentation velocity is proportional to the square of particle diameter.
• The higher the viscosity of the dispersion medium, the greater the resistance experienced by the particle and the lower the sedimentation velocity.
• The greater the density difference between the particle and dispersion medium, the greater the sedimentation velocity.
• Small particles may be difficult to settle because of the influence of Brownian motion.
• When aggregation increases the apparent particle size, sedimentation becomes faster.
• At high particle concentrations, interactions among particles may cause deviation from free settling.
• Stokes’ law assumes spherical particles, low concentration, and laminar-flow conditions.

Points to Check When Discussing Particle Sedimentation Experiments

Checking the following points before writing the report makes the discussion easier to write.

• Is the reason why particles settle explained?
• Is the method for calculating sedimentation velocity written?
• Is Stokes’ law used in the discussion?
• Is the relationship between particle size and sedimentation velocity explained?
• Is density difference related to sedimentation velocity?
• Is the effect of viscosity on sedimentation velocity described?
• Is the concept of terminal velocity explained?
• Are Brownian motion and the difficulty of fine-particle sedimentation considered?
• Are the effects of aggregation and floc formation explained?
• Are the effects of particle concentration and wall effects considered?
• Are errors in reading the sedimentation interface considered?
• Do the points for improvement correspond to the causes of error?

Summary

A particle sedimentation experiment is an experiment that investigates the rate at which particles dispersed in a liquid settle because of gravity.
Gravity, buoyancy, and viscous resistance act on the particles, and when these forces balance, the particles settle at a constant terminal velocity.
Sedimentation velocity is greatly affected by particle size, the density difference between the particles and dispersion medium, and the viscosity of the dispersion medium.

According to Stokes’ law, sedimentation velocity is proportional to the square of particle diameter and inversely proportional to viscosity.
Therefore, larger particles settle faster, while sedimentation becomes slower in liquids with higher viscosity.
In addition, when particles aggregate and the apparent particle size increases, the sedimentation velocity increases, while stable dispersions are more difficult to settle.

In a report, rather than simply writing that “the particles settled” or “the particles did not settle,” organize and discuss sedimentation velocity, particle size, density difference, viscosity, Stokes’ law, terminal velocity, aggregation, Brownian motion, particle concentration, sedimentation interface, causes of error, and points for improvement.
Particle sedimentation experiments are important experiments for understanding the relationship between the stability of dispersed systems and the physical properties of particles.