What is the difference between a plate settler and a tube settler?

Process by which particulates move towards the bottom of a liquid and form a sediment

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For the human activity, see settler . For the audio drama, see The Settling

Settling pond for iron particles at water works

Settling is the process by which particulates move towards 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 sludge or slurry at the vessel base. Settling is an important operation in many applications, such as mining, wastewater and drinking water treatment, biological science, space propellant reignition,[1] and scooping.

Physics

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Creeping flow past a sphere: streamlines, drag force Fd and force by gravity Fg.

For settling particles that are considered individually, i.e. dilute particle solutions, 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 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 force will be exhibited, which causes the particle to accelerate due to the applied force. When the particle accelerates, the drag force acts in the direction opposite to the particle's motion, retarding further acceleration, in the absence of other forces drag directly opposes the applied force. As the particle increases in velocity eventually the drag force and the applied force will approximately equate, causing no further change in the particle's velocity. This velocity is known as the terminal velocity, settling velocity or fall velocity of the particle. This is readily measurable by examining the rate of fall of individual particles.

The terminal velocity of the particle is affected by many parameters, i.e. anything that will alter the particle's drag. Hence the terminal velocity is most notably dependent upon grain size, the shape (roundness and sphericity) and density of the grains, as well as to the viscosity and density of the fluid.

Single particle drag

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Stokes' drag

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Dimensionless force versus Reynolds number for spherical particles

For dilute suspensions, Stokes' law predicts the settling velocity of small spheres in fluid, either air or water. This originates due to the strength of viscous forces at the surface of the particle providing the majority of the retarding force. Stokes' law finds many applications in the natural sciences, and is given by:

w = 2 ( ρ p &#; ρ f ) g r 2 9 μ {\displaystyle w={\frac {2(\rho _{p}-\rho _{f})gr^{2}}{9\mu }}}

Deviation from the Stokes' Model from increased fluid drag as a particle increases in size.

where w is the settling velocity, ρ is density (the subscripts p and f indicate particle and fluid respectively), g is the acceleration due to gravity, r is the radius of the particle and μ is the dynamic viscosity of the fluid.

Stokes' law applies when the Reynolds number, Re, of the particle is less than 0.1. Experimentally Stokes' law is found to hold within 1% for R e &#; 0.1 {\displaystyle Re\leq 0.1} , within 3% for R e &#; 0.5 {\displaystyle Re\leq 0.5} and within 9% R e &#; 1.0 {\displaystyle Re\leq 1.0} .[2] With increasing Reynolds numbers, Stokes law begins to break down due to the increasing importance of fluid inertia, requiring the use of empirical solutions to calculate drag forces.

Newtonian drag

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Defining a drag coefficient, C d {\displaystyle C_{d}} , as the ratio of the force experienced by the particle divided by the impact pressure of the fluid, a coefficient that can be considered as the transfer of available fluid force into drag is established. In this region the inertia of the impacting fluid is responsible for the majority of force transfer to the particle.

C d = F d 1 2 ρ f U 2 A {\displaystyle C_{d}={\frac {F_{d}}{{\frac {1}{2}}\rho _{f}U^{2}A}}}

For a spherical particle in the Stokes regime this value is not constant, however in the Newtonian drag regime the drag on a sphere can be approximated by a constant, 0.44. This constant value implies that the efficiency of transfer of energy from the fluid to the particle is not a function of fluid velocity.

As such the terminal velocity of a particle in a Newtonian regime can again be obtained by equating the drag force to the applied force, resulting in the following expression

w = 2.46 ( ( ρ p &#; ρ f ) g r ρ f ) 1 2 . {\displaystyle w=2.46\left({\frac {(\rho _{p}-\rho _{f})gr}{\rho _{f}}}\right)^{\frac {1}{2}}.}

Transitional drag

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In the intermediate region between Stokes drag and Newtonian drag, there exists a transitional regime, where the analytical solution to the problem of a falling sphere becomes problematic. To solve this, empirical expressions are used to calculate drag in this region. One such empirical equation is that of Schiller and Naumann, and may be valid for 0.2 &#; R e &#; {\displaystyle 0.2\leq Re\leq } :[3]

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F ρ f U 2 A = 12 R e ( 1 + 0.15 R e 0.687 ) . {\displaystyle {\frac {F}{\rho _{f}U^{2}A}}={\frac {12}{\mathrm {Re} }}\left(1+0.15\mathrm {Re} ^{0.687}\right).}

Hindered settling

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Stokes, transitional and Newtonian settling describe the behaviour of a single spherical particle in an infinite fluid, known as free settling. However this model has limitations in practical application. Alternate considerations, such as the interaction of particles in the fluid, or the interaction of the particles with the container walls can modify the settling behaviour. Settling that has these forces in appreciable magnitude is known as hindered settling. Subsequently, semi-analytic or empirical solutions may be used to perform meaningful hindered settling calculations.

Applications

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The solid-gas flow systems are present in many industrial applications, as dry, catalytic reactors, settling tanks, pneumatic conveying of solids, among others. Obviously, in industrial operations the drag rule is not simple as a single sphere settling in a stationary fluid. However, this knowledge indicates how drag behaves in more complex systems, which are designed and studied by engineers applying empirical and more sophisticated tools.

For example, 'settling tanks' are used for separating solids and/or oil from another liquid. In food processing, the vegetable is crushed and placed inside of a settling tank with water. The oil floats to the top of the water then is collected. In drinking water and waste water treatment a flocculant or coagulant is often added prior to settling to form larger particles that settle out quickly in a settling tank or (lamella) clarifier, leaving the water with a lower turbidity.

In winemaking, the French term for this process is débourbage. This step usually occurs in white wine production before the start of fermentation.[4]

Settleable solids analysis

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Settleable solids are the particulates that settle out of a still fluid. Settleable solids can be quantified for a suspension using an Imhoff cone. The standard Imhoff cone of transparent glass or plastic holds one liter of liquid and has calibrated markings to measure the volume of solids accumulated in the bottom of the conical container after settling for one hour. A standardized Imhoff cone procedure is commonly used to measure suspended solids in wastewater or stormwater runoff. The simplicity of the method makes it popular for estimating water quality. To numerically gauge the stability of suspended solids and predict agglomeration and sedimentation events, zeta potential is commonly analyzed. This parameter indicates the electrostatic repulsion between solid particles and can be used to predict whether aggregation and settling will occur over time.

The water sample to be measured should be representative of the total stream. Samples are best collected from the discharge falling from a pipe or over a weir, because samples skimmed from the top of a flowing channel may fail to capture larger, high-density solids moving along the bottom of the channel. The sampling bucket is vigorously stirred to uniformly re-suspend all collected solids immediately before pouring the volume required to fill the cone. The filled cone is immediately placed in a stationary holding rack to allow quiescent settling. The rack should be located away from heating sources, including direct sunlight, which might cause currents within the cone from thermal density changes of the liquid contents. After 45 minutes of settling, the cone is partially rotated about its axis of symmetry just enough to dislodge any settled material adhering to the side of the cone. Accumulated sediment is observed and measured fifteen minutes later, after one hour of total settling time.[5]

See also

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• Drag equation &#; Equation for the force of drag
• Zeta potential &#; Electrokinetic potential in colloidal dispersions
• Sedimentation &#; Tendency for particles in suspension to settle down
• Settling basin &#; structure using sedimentation to remove matter from wastewater

  Pages displaying wikidata descriptions as a fallback

• Suspension (chemistry) &#; Heterogeneous mixture of solid particles dispersed in a medium
• Total suspended solids &#; Water quality parameter

References

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Tube settlers which are also known as plate settlers or lamella clarifiers are used to increase settling performance within a sedimentation basin. Tube settlers consist of inclined plates or channels that provide a settling surface area for particles in wastewater and drinking water. The total settling area is the sum of the projected area in horizontal direction multiplied with the total amount of plates or channels.

To explain how tube settlers are designed lets take a look at the following example: A drinking water plant has a monthly maximum flow of 1MGD or 3,785m3/day. The amount of total suspended solids entering the plant is 200mg/l and the effluent permit requires 30mg/l. At first, we have to determine the settling velocity of the particles. The settling velocity of the particles very much depends on their size and shape. In general, smaller particles settle slower, hence they have a lower settling velocity. Particles which are smaller than 25 Micrometer can usually not be settled down at all because drag forces (turbulences, rising particles and others) within the sedimentation basin are bigger than the particle settling force. Also, spherical shaped particles settle better than flat shaped particles as their form offers less contact area for drag forces.

Stokes law is a good basis to calculate the settling velocity of particles. The formula: vs settling velocity of the particle has to be bigger as all drag forces  ) calculates the drag force depending on the density delta of the fluid and the particle, the size and form of the particle as well as the laminar flow in the tank.

In our example we have mostly sand and gravel that needs to be removed. The minimum particle size is 50 Micrometer and the density delta between the water and the particles shall be 12.5lbs/ft3 or 200kg/m3. Sand and gravel have a rounded shape therefore we will use a form factor of 0.8. The resulting settling velocity has to be bigger as 1.67m/h or 5.49ft/h.

As stokes law assumes laminar flow, no other colliding particles and other factors but we want to design a sedimentation tank we have to consider an additional safety factor. Depending on the retention time and water turbidity different safety factors can be applied but we will just use a safety factor of 2. Therefore, the resulting settling velocity of the particles is 1.67m/h divided by 2 equals 0.835m/h or 2.75ft/h.

Knowing the settling velocity, we can now determine the total required amount of tube settlers. AET LLC offers different types of tube settlers but for drinking water applications the LS50 design is usually used. This tube settler type has a channel distance of about 1.75in or 45mm and a projected surface area of 3.3 to 3,5ft2/ft3 (11 to 11.5m2/m3). Now to determine the total required amount of tube settlers the settling velocity of the particles has to be bigger as the total projected surface area of the tube settlers divided by the water flow. Solving the equation to x results in a total required projected surface area of 2,046ft2 or 189m2. Dividing this result by 3.3ft2/ft3 equals the total required amount of 623ft3 or 17.2m3 of tube settlers for this application.

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