Batch Settling
Content
BATCH SETTLING OF SOLID SLURRIES
Objectives:
1. Vertical Cylinders: Obtain the batch settling data for the given calcium carbonate slurry (i.e. the settling rate versus concentration of slurry), and demarcate the different settling regimes. (‘free settling” and ‘hindered settling’) 2. Tilted Cylinders: Obtain the batch settling data in the free settling regime for different angles. Observe the flow patterns during the settling.
Apparatus:
Vertical settling cylinder, inclined settling cylinder, glass rod, stop watch
Reagents:
Water, Calcium Carbonate
Theory:
Introduction: Settling is the process by which particulates settle to the bottom of a liquid and form a sediment. Particles that experience a force, either due to gravity or due to centrifugal motion will tend to move in a uniform manner in the direction exerted by that force. For gravity settling, this means that the particles will tend to fall to the bottom of the vessel, forming a slurry at the vessel base.
Figure.1 Force rces acting on a particle during settling
For settling particles that are co onsidered individually, i.e. dilute particle solution ns, there are two main forces enacting upon any particle. The primary force is an applied force, such as gravity, and a drag force that is due to the motion of the particle through the fluid. The T applied force is usually not affected by the particle's velocity, whereas the drag force is a function of the particle velocity. For a particle at rest no drag for force will exhibited, which causes the particle to t accelerate due to the applied force. When the p particle accelerates, the drag force acts in the di irection opposite to the particle's motion, retard rding further acceleration, in the absence of oth her forces drag directly opposes the applied d force. As the particle increases in velocit ty eventually the drag force and the applied forc ce will approximately equate, causing no furth her change in the particle's velocity. This velocit ity is known as the terminal velocity, settling g velocity or fall velocity of the particle. This is s readily measurable by examining the rate of fall f of individual particles. The terminal velocity of the par rticle is affected by many parameters, i.e. anythin ng that will alter the particle's drag. Hence the te erminal velocity is most notably dependent upon n grain size, the shape (roundness and sphericit ity) and density of the grains, as well as to th he viscosity and density of the fluid.
The behaviour of settling particles in slurry can be conveniently studied in small batch experiments. The data is then useful for designing large scale settling tanks which have a number of applications (e.g. clarification of waste water). The main information required for design is the settling rate of the particles as a function of the system parameters such as particle size and shape, concentration, geometry of the system, etc. The effect of concentration on the settling slurry continuously increases with time. The effect of geometry of the system on the settling rate can be significant. When the cylinder is tilted, Boycott (1920) found that the settling rate increases due to shorter sedimentation path. This phenomenon is known as the Boycott effect, and is used to enhance the rate of settling in some applications.
(i) Vertical Cylinders: Depending on the concentration of the slurry, two regimes of settling are possible, free settling and hindered settling. As the name implies, in free settling, each particle is unaffected by the motion of the neighboring ones and its terminal velocity is given by
ଶ ݃൫ߩ − ߩ൯ܦ ܷ௧ = ( ) 18ߤ
18ߤܷ௧ ଵ/ଶ ܦ = ( ) ݃൫ߩି ߩ൯ ܥ = 24/ܴ ߝ = 1 − ܥ/ߩ
*All above equations are valid only for Reynolds no. Re < 1. Where
ߩ and ߩ are the densities of the particle and the suspending medium respectively,
D p is the diameter of the particle, CD is the drag coefficient And Reynolds no. Re = (ܦ ܷ௧ ߩ /ߤ) The model assumed for describing Free Settling, has some limitations in practical application. Such as the interaction of particles in the fluid, or the interaction of the particles with the container walls can modify the settling behavior. Settling that has these forces in appreciable magnitude is known as hindered settling. In the hindered settling regime due to particle-particle interactions and up draft of liquid, the velocity of individual particles is considerably smaller. The settling velocity ( U s ) may be estimated by an empirical equation of the form. ܷௌ = ܷ௧ ߝ where ߝ is the volume fraction of the fluid and n is a constant.
where ߝ
= 1 − ܥ/ߩ ߩ = ߩ௦ ∗ (1 − ߝ ) + ߩ ∗ ߝ
In this case the following bulk values of density and viscosity are used instead of liquid density and viscosity.
ߤ 10ଵ.଼ଶ∗(ଵିఌ) = ߤ ߝ
Assuming that the concentration is nearly uniform over the cylinder, the concentration at any time is given by
C
C0 H 0 H
where C0 is the initial concentration, H0 is the initial height of the suspension-clear liquid interface (constant height before stirring), H is the height at time t. ii) Tilted Cylinders:
The theory for an increased rate of the settling for inclined cylinders was proposed by Ponder-Nakamura and Kuroda (PNK) based on the increased projected area available for settling. The Volumetric rate of increase if the clear fluid (S) according to the PNK theory is given by
S= W Ut (b secθ + H tanθ)
where : S is Volumetric rate of settling W is width of the cylinder. b is the breadth of the cylinder (b=W for square column) H is the height of the liquid column. θ is the inclination of cylinder with the surface.
Procedure:
Vertical Cylinder: 1. Make slurry with 50g CaCO3 in 2 liters of water. 2. Record the initial height of the slurry bed. 3. Mix the system thoroughly with the help of a glass rod. 4. Wait for a minute and then observe the height below the clear liquid. 5. Record height of the interface after every one minute till a constant height is reached. 6. Similarly carry out a similar run with slurry of 75g CaCO3 in 2 liters water.
Tilted Cylinder: 1 . Fix the angle of the cylinder to 15° value. 2 . Make slurry with 50g CaCO3 in 2 liters of water. 3 . Record the initial height of the slurry bed below the clear liquid before mixing. 4 . The system is then thoroughly mixed with the help of glass rod.
5. After mixing wait for a minute and then observe the height below the clear liquid.. 6. Record height of the interface after every one minute till a constant height is reached. 7. Repeat for 250 inclination.
Analysis:
1) Plot height of interface vs. time data and instantaneous velocity of interface vs. concentration of slurry. 2) Figure out the no. of points that could be used for smoothing (using moving average) the velocity vs. concentration curve and use it to smoothen the curve. 3) Identify the regimes using the graph you think captures them better and clearly. 4) Calculate Ut using the appropriate regime in the above mentioned graph and the hence the diameter of the particle. Confirm that the assumption on Reynold’s no. holds. 5) For the hindered settling regime plot a graph from which value of ‘n’ can be found out. The relation from which ‘n’ will be found out has Ut in it, and hence use the graph plotted to find out the value of Ut and compare this value from Ut obtained from free settling regime. 6) Find particle diameter and volumetric rate of settling using parameters from hindered settling regime. 7) Compare the results and try to explain the discrepancies (deviations from theoretical values/ deviations from expected results), if any. 8) Do error analysis taking +10% error in physical properties’ values used in calculations.
Objectives:
1. Vertical Cylinders: Obtain the batch settling data for the given calcium carbonate slurry (i.e. the settling rate versus concentration of slurry), and demarcate the different settling regimes. (‘free settling” and ‘hindered settling’) 2. Tilted Cylinders: Obtain the batch settling data in the free settling regime for different angles. Observe the flow patterns during the settling.
Apparatus:
Vertical settling cylinder, inclined settling cylinder, glass rod, stop watch
Reagents:
Water, Calcium Carbonate
Theory:
Introduction: Settling is the process by which particulates settle to the bottom of a liquid and form a sediment. Particles that experience a force, either due to gravity or due to centrifugal motion will tend to move in a uniform manner in the direction exerted by that force. For gravity settling, this means that the particles will tend to fall to the bottom of the vessel, forming a slurry at the vessel base.
Figure.1 Force rces acting on a particle during settling
For settling particles that are co onsidered individually, i.e. dilute particle solution ns, there are two main forces enacting upon any particle. The primary force is an applied force, such as gravity, and a drag force that is due to the motion of the particle through the fluid. The T applied force is usually not affected by the particle's velocity, whereas the drag force is a function of the particle velocity. For a particle at rest no drag for force will exhibited, which causes the particle to t accelerate due to the applied force. When the p particle accelerates, the drag force acts in the di irection opposite to the particle's motion, retard rding further acceleration, in the absence of oth her forces drag directly opposes the applied d force. As the particle increases in velocit ty eventually the drag force and the applied forc ce will approximately equate, causing no furth her change in the particle's velocity. This velocit ity is known as the terminal velocity, settling g velocity or fall velocity of the particle. This is s readily measurable by examining the rate of fall f of individual particles. The terminal velocity of the par rticle is affected by many parameters, i.e. anythin ng that will alter the particle's drag. Hence the te erminal velocity is most notably dependent upon n grain size, the shape (roundness and sphericit ity) and density of the grains, as well as to th he viscosity and density of the fluid.
The behaviour of settling particles in slurry can be conveniently studied in small batch experiments. The data is then useful for designing large scale settling tanks which have a number of applications (e.g. clarification of waste water). The main information required for design is the settling rate of the particles as a function of the system parameters such as particle size and shape, concentration, geometry of the system, etc. The effect of concentration on the settling slurry continuously increases with time. The effect of geometry of the system on the settling rate can be significant. When the cylinder is tilted, Boycott (1920) found that the settling rate increases due to shorter sedimentation path. This phenomenon is known as the Boycott effect, and is used to enhance the rate of settling in some applications.
(i) Vertical Cylinders: Depending on the concentration of the slurry, two regimes of settling are possible, free settling and hindered settling. As the name implies, in free settling, each particle is unaffected by the motion of the neighboring ones and its terminal velocity is given by
ଶ ݃൫ߩ − ߩ൯ܦ ܷ௧ = ( ) 18ߤ
18ߤܷ௧ ଵ/ଶ ܦ = ( ) ݃൫ߩି ߩ൯ ܥ = 24/ܴ ߝ = 1 − ܥ/ߩ
*All above equations are valid only for Reynolds no. Re < 1. Where
ߩ and ߩ are the densities of the particle and the suspending medium respectively,
D p is the diameter of the particle, CD is the drag coefficient And Reynolds no. Re = (ܦ ܷ௧ ߩ /ߤ) The model assumed for describing Free Settling, has some limitations in practical application. Such as the interaction of particles in the fluid, or the interaction of the particles with the container walls can modify the settling behavior. Settling that has these forces in appreciable magnitude is known as hindered settling. In the hindered settling regime due to particle-particle interactions and up draft of liquid, the velocity of individual particles is considerably smaller. The settling velocity ( U s ) may be estimated by an empirical equation of the form. ܷௌ = ܷ௧ ߝ where ߝ is the volume fraction of the fluid and n is a constant.
where ߝ
= 1 − ܥ/ߩ ߩ = ߩ௦ ∗ (1 − ߝ ) + ߩ ∗ ߝ
In this case the following bulk values of density and viscosity are used instead of liquid density and viscosity.
ߤ 10ଵ.଼ଶ∗(ଵିఌ) = ߤ ߝ
Assuming that the concentration is nearly uniform over the cylinder, the concentration at any time is given by
C
C0 H 0 H
where C0 is the initial concentration, H0 is the initial height of the suspension-clear liquid interface (constant height before stirring), H is the height at time t. ii) Tilted Cylinders:
The theory for an increased rate of the settling for inclined cylinders was proposed by Ponder-Nakamura and Kuroda (PNK) based on the increased projected area available for settling. The Volumetric rate of increase if the clear fluid (S) according to the PNK theory is given by
S= W Ut (b secθ + H tanθ)
where : S is Volumetric rate of settling W is width of the cylinder. b is the breadth of the cylinder (b=W for square column) H is the height of the liquid column. θ is the inclination of cylinder with the surface.
Procedure:
Vertical Cylinder: 1. Make slurry with 50g CaCO3 in 2 liters of water. 2. Record the initial height of the slurry bed. 3. Mix the system thoroughly with the help of a glass rod. 4. Wait for a minute and then observe the height below the clear liquid. 5. Record height of the interface after every one minute till a constant height is reached. 6. Similarly carry out a similar run with slurry of 75g CaCO3 in 2 liters water.
Tilted Cylinder: 1 . Fix the angle of the cylinder to 15° value. 2 . Make slurry with 50g CaCO3 in 2 liters of water. 3 . Record the initial height of the slurry bed below the clear liquid before mixing. 4 . The system is then thoroughly mixed with the help of glass rod.
5. After mixing wait for a minute and then observe the height below the clear liquid.. 6. Record height of the interface after every one minute till a constant height is reached. 7. Repeat for 250 inclination.
Analysis:
1) Plot height of interface vs. time data and instantaneous velocity of interface vs. concentration of slurry. 2) Figure out the no. of points that could be used for smoothing (using moving average) the velocity vs. concentration curve and use it to smoothen the curve. 3) Identify the regimes using the graph you think captures them better and clearly. 4) Calculate Ut using the appropriate regime in the above mentioned graph and the hence the diameter of the particle. Confirm that the assumption on Reynold’s no. holds. 5) For the hindered settling regime plot a graph from which value of ‘n’ can be found out. The relation from which ‘n’ will be found out has Ut in it, and hence use the graph plotted to find out the value of Ut and compare this value from Ut obtained from free settling regime. 6) Find particle diameter and volumetric rate of settling using parameters from hindered settling regime. 7) Compare the results and try to explain the discrepancies (deviations from theoretical values/ deviations from expected results), if any. 8) Do error analysis taking +10% error in physical properties’ values used in calculations.
