Settling
Encyclopedia
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.
Settling is an important operation in many applications, such as mining
, wastewater treatment
, biological science, space
propellant
reignition,
and particle mechanics.
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 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.
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:
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
, within 3% for 
and within 9% 
. With increasing Reynolds numbers, Stokes law begins to break down due to fluid inertia, requiring the use of empirical solutions to calculate drag forces.
,
, 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.
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
:
using an Imhoff tank
or cone.
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 isn’t 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 the top of the water then is collected. In water and waste water treatment a flocculant is often added prior to settling to form larger particles that settle out quickly in a settling tank 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
.
Sediment
Sediment is naturally occurring material that is broken down by processes of weathering and erosion, and is subsequently transported by the action of fluids such as wind, water, or ice, and/or by the force of gravity acting on the particle itself....
. Particles that experience a force, either due to gravity or due to centrifugal motion
Centrifuge
A centrifuge is a piece of equipment, generally driven by an electric motor , that puts an object in rotation around a fixed axis, applying a force perpendicular to the axis...
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
Slurry
A slurry is, in general, a thick suspension of solids in a liquid.-Examples of slurries:Examples of slurries include:* Lahars* A mixture of water and cement to form concrete* A mixture of water, gelling agent, and oxidizers used as an explosive...
at the vessel base.
Settling is an important operation in many applications, such as mining
Mining
Mining is the extraction of valuable minerals or other geological materials from the earth, from an ore body, vein or seam. The term also includes the removal of soil. Materials recovered by mining include base metals, precious metals, iron, uranium, coal, diamonds, limestone, oil shale, rock...
, wastewater treatment
Wastewater Treatment
Wastewater treatment may refer to:* Sewage treatment* Industrial wastewater treatment...
, biological science, space
Outer space
Outer space is the void that exists between celestial bodies, including the Earth. It is not completely empty, but consists of a hard vacuum containing a low density of particles: predominantly a plasma of hydrogen and helium, as well as electromagnetic radiation, magnetic fields, and neutrinos....
propellant
Rocket propellant
Rocket propellant is mass that is stored in some form of propellant tank, prior to being used as the propulsive mass that is ejected from a rocket engine in the form of a fluid jet to produce thrust. A fuel propellant is often burned with an oxidizer propellant to produce large volumes of very hot...
reignition,
and particle mechanics.
Physics
Drag (physics)
In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...
force that is due to the motion of the particle through the fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....
. 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 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
Limit (mathematics)
In mathematics, the concept of a "limit" is used to describe the value that a function or sequence "approaches" as the input or index approaches some value. The concept of limit allows mathematicians to define a new point from a Cauchy sequence of previously defined points within a complete metric...
, causing no further change in the particle's velocity. This velocity is known as the terminal velocity
Terminal velocity
In fluid dynamics an object is moving at its terminal velocity if its speed is constant due to the restraining force exerted by the fluid through which it is moving....
, 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
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...
and density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
of the fluid.
Stokes' drag
Stokes law
Stokes' law can refer to:*Stokes' law for friction force*Stokes' law law describing attenuation of sound in Newtonian liquidsFor integration, see Stokes' theorem....
predicts the settling velocity of small spheres in fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....
, 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:
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
, within 3% for and within 9% . With increasing Reynolds numbers, Stokes law begins to break down due to fluid inertia, requiring the use of empirical solutions to calculate drag forces.Newtonian drag
Defining a drag coefficientDrag coefficient
In fluid dynamics, the drag coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment such as air or water. It is used in the drag equation, where a lower drag coefficient indicates the object will have less aerodynamic or...
,
, as the ratio of the force experienced by the particle divided by the impact pressureImpact pressure
In compressible fluid dynamics, impact pressure is the difference between total pressure and static pressure. In aerodynamics notation, this quantity is denoted as q_c or Q_c....
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.
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
Terminal velocity
In fluid dynamics an object is moving at its terminal velocity if its speed is constant due to the restraining force exerted by the fluid through which it is moving....
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
Transitional drag
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:Hindered settling
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
Settleable solids are the particulates that settle out of a still fluid. Settleable solids can be quantified for a suspensionSuspension (chemistry)
In chemistry, a suspension is a heterogeneous fluid containing solid particles that are sufficiently large for sedimentation. Usually they must be larger than 1 micrometer. The internal phase is dispersed throughout the external phase through mechanical agitation, with the use of certain...
using an Imhoff tank
Imhoff tank
The Imhoff tank, named for German engineer Karl Imhoff , is a chamber suitable for the reception and processing of sewage. It may be used for the clarification of sewage by simple settling and sedimentation, along with anaerobic digestion of the extracted sludge...
or cone.
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 isn’t 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
Storage tank
A storage tank is a container, usually for holding liquids, sometimes for compressed gases . The term can be used for reservoirs , and for manufactured containers. The usage of the word tank for reservoirs is common or universal in Indian English, American English and moderately common in British...
are used for separating solids and/or oil from another liquid. In food processing
Food processing
Food processing is the set of methods and techniques used to transform raw ingredients into food or to transform food into other forms for consumption by humans or animals either in the home or by the food processing industry...
, the vegetable is crushed and placed inside of a settling tank with water. The oil floats the top of the water then is collected. In water and waste water treatment a flocculant is often added prior to settling to form larger particles that settle out quickly in a settling tank leaving the water with a lower turbidity
Turbidity
Turbidity is the cloudiness or haziness of a fluid caused by individual particles that are generally invisible to the naked eye, similar to smoke in air. The measurement of turbidity is a key test of water quality....
.
In winemaking
Winemaking
Winemaking, or vinification, is the production of wine, starting with selection of the grapes or other produce and ending with bottling the finished wine. Although most wine is made from grapes, it may also be made from other fruit or non-toxic plant material...
, the French term for this process is débourbage. This step usually occurs in white wine production before the start of fermentation
Fermentation (wine)
The process of fermentation in wine turns grape juice into an alcoholic beverage. During fermentation, yeast interact with sugars in the juice to create ethanol, commonly known as ethyl alcohol, and carbon dioxide...
.
See also
- Drag equationDrag equationIn fluid dynamics, the drag equation is a practical formula used to calculate the force of drag experienced by an object due to movement through a fully enclosing fluid....
- SedimentationSedimentationSedimentation is the tendency for particles in suspension to settle out of the fluid in which they are entrained, and come to rest against a barrier. This is due to their motion through the fluid in response to the forces acting on them: these forces can be due to gravity, centrifugal acceleration...
- Settling basinSettling basinA settling basin, settling pond or decant pond are devices used to treat turbidity in industrial wastewater. The basins are used to control water pollution in diverse industries such as agriculture, aquaculture, and mining....
- Suspension (chemistry)Suspension (chemistry)In chemistry, a suspension is a heterogeneous fluid containing solid particles that are sufficiently large for sedimentation. Usually they must be larger than 1 micrometer. The internal phase is dispersed throughout the external phase through mechanical agitation, with the use of certain...
- Total suspended solidsTotal suspended solidsTotal suspended solids is a water quality measurement usually abbreviated TSS. It is listed as a conventional pollutant in the U.S. Clean Water Act. This parameter was at one time called non-filterable residue , a term that refers to the identical measurement: the dry-weight of particles trapped...