Clearing factor

Last updated November 11, 2019

In centrifugation the clearing factor or k factor represents the relative pelleting efficiency of a given centrifuge rotor at maximum rotation speed. It can be used to estimate the time $t$ (in hours) required for sedimentation of a fraction with a known sedimentation coefficient $s$ (in svedbergs):

Centrifugation is a technique which involves the application of centrifugal force to separate particles from a solution according to their size, shape, density, viscosity of the medium and rotor speed. Not only is this process used to separate two miscible substances, but also to analyze the hydrodynamic properties of macromolecules. More-dense components of the mixture migrate away from the axis of the centrifuge, while less-dense components of the mixture migrate towards the axis, i. e., move to the center. Chemists and biologists may increase the effective gravitational force on a test tube so as to more rapidly and completely cause the precipitate (pellet) to gather on the bottom of the tube. The remaining solution (supernatant) may be discarded with a pipette.. Centrifugation of protein solution, for example, allows elimination of impurities into the supernatant.

Sedimentation 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, or electromagnetism. In geology, sedimentation is often used as the opposite of erosion, i.e., the terminal end of sediment transport. In that sense, it includes the termination of transport by saltation or true bedload transport. Settling is the falling of suspended particles through the liquid, whereas sedimentation is the termination of the settling process. In estuarine environments, settling can be influenced by the presence or absence of vegetation. Trees such as mangroves are crucial to the attenuation of waves or currents, promoting the settlement of suspended particles.

The sedimentation coefficient(s) of a particle characterizes its sedimentation during centrifugation. It is defined as the ratio of a particle's sedimentation velocity to the applied acceleration causing the sedimentation.

t={\frac {k}{s}}

The value of the clearing factor depends on the maximum angular velocity $\omega$ of a centrifuge (in rad/s) and the minimum and maximum radius $r$ of the rotor:

In physics, angular velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time. There are two types of angular velocity: orbital angular velocity and spin angular velocity. Spin angular velocity refers to how fast a rigid body rotates with respect to its centre of rotation. Orbital angular velocity refers to how fast a point object revolves about a fixed origin, i.e. the time rate of change of its angular position relative to the origin. In general, angular velocity is measured in angle per unit time, e.g. radians per second. The SI unit of angular velocity is expressed as radians/sec with the radian having a dimensionless value of unity, thus the SI units of angular velocity are listed as 1/sec. Angular velocity is usually represented by the symbol omega. By convention, positive angular velocity indicates counter-clockwise rotation, while negative is clockwise.

Radius segment in a circle or sphere (from its center to its perimeter or surface) and its length

In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the Latin radius, meaning ray but also the spoke of a chariot wheel. The plural of radius can be either radii or the conventional English plural radiuses. The typical abbreviation and mathematical variable name for radius is r. By extension, the diameter d is defined as twice the radius:

A turbine is a rotary mechanical device that extracts energy from a fluid flow and converts it into useful work. The work produced by a turbine can be used for generating electrical power when combined with a generator. A turbine is a turbomachine with at least one moving part called a rotor assembly, which is a shaft or drum with blades attached. Moving fluid acts on the blades so that they move and impart rotational energy to the rotor. Early turbine examples are windmills and waterwheels.

k={\frac {\ln(r_{\rm {max}}/r_{\rm {min}})}{\omega ^{2}}}\times {\frac {10^{13}}{3600}}

As the rotational speed of a centrifuge is usually specified in RPM, the following formula is often used for convenience:^[1]

Revolutions per minute is the number of turns in one minute. It is a unit of rotational speed or the frequency of rotation around a fixed axis.

k={\frac {2.53\cdot 10^{5}\times \ln(r_{\rm {max}}/r_{\rm {min}})}{({\rm {{RPM}/1000)^{2}}}}}

Centrifuge manufacturers usually specify the minimum, maximum and average radius of a rotor, as well as the $k$ factor of a centrifuge-rotor combination.

A centrifuge is a piece of equipment that puts an object in rotation around a fixed axis, applying a force perpendicular to the axis of spin (outward) that can be very strong. The centrifuge works using the sedimentation principle, where the centrifugal acceleration causes denser substances and particles to move outward in the radial direction. At the same time, objects that are less dense are displaced and move to the center. In a laboratory centrifuge that uses sample tubes, the radial acceleration causes denser particles to settle to the bottom of the tube, while low-density substances rise to the top.

For runs with a rotational speed lower than the maximum rotor-speed, the $k$ factor has to be adjusted:

k_{\rm {adj}}=k\left({\frac {\mbox{maximum rotor-speed}}{\mbox{actual rotor-speed}}}\right)

²

The K-factor is related to the sedimentation coefficient $S$ by the formula:

$T={\frac {K}{S}}$

Where $T$ is the time to pellet a certain particle in hours. Since $S$ is a constant for a certain particle, this relationship can be used to interconvert between different rotors.

${\frac {T_{1}}{K_{1}}}={\frac {T_{2}}{K_{2}}}$

Where $T_{1}$ is the time to pellet in one rotor, and $K_{1}$ is the K-factor of that rotor. $K_{2}$ is the K-factor of the other rotor, and $T_{2}$ , the time to pellet in the other rotor, can be calculated. In this manner, one does not need access to the exact rotor cited in a protocol, as long as the K-factor can be calculated. Many online calculators are available to perform the calculations for common rotors.

Related Research Articles

In mechanics and physics, simple harmonic motion is a special type of periodic motion or oscillation where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement.

Torque tendency of a force to rotate an object

Torque, moment, moment of force or "turning effect" is the rotational equivalent of linear force. The concept originated with the studies by Archimedes of the usage of levers. Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object. Another definition of torque is the product of the magnitude of the force and the perpendicular distance of the line of action of force from the axis of rotation. The symbol for torque is typically $, the lowercase Greek letter tau . When being referred to as moment of force, it is commonly denoted by M .$

A flywheel is a mechanical device specifically designed to efficiently store rotational energy. Flywheels resist changes in rotational speed by their moment of inertia. The amount of energy stored in a flywheel is proportional to the square of its rotational speed and its mass. The way to change a flywheel's stored energy without changing its mass is by increasing or decreasing its rotational speed. Since flywheels act as mechanical energy storage devices, they are the kinetic-energy-storage analogue to electrical capacitors, for example, which are a type of accumulator. Like other types of accumulators, flywheels smooth the ripple in power output, providing surges of high power output as required, absorbing surges of high power input as required, and in this way act as low-pass filters on the mechanical velocity of the system.

Differential centrifugation is a common procedure in biochemistry and cell biology used to separate organelles and other sub-cellular particles on the basis of sedimentation rate. Although often applied in biological analysis, differential centrifugation is a general technique also suitable for crude purification of non-living suspended particles. In a typical case where differential centrifugation is used to analyze cell-biological phenomena, a tissue sample is first lysed to break the cell membranes and release the organelles and cytosol. The lysate is then subjected to repeated centrifugations, where particles that sediment sufficiently quickly at a given centrifugation force for a given time form a compact "pellet" at the bottom of the centrifugation tube. After each centrifugation, the supernatant is removed from the tube and re-centrifuged at an increased centrifugal force and/or time. Differential centrifugation is suitable for crude separations on the basis of sedimintation rate, but more fine grained purifications may be done on the basis of density through equilibrium density-gradient centrifugation.

Fictitious force A force on objects moving within a reference frame that rotates with respect to an inertial frame.

A fictitious force is a force that appears to act on a mass whose motion is described using a non-inertial frame of reference, such as an accelerating or rotating reference frame. An example is seen in a passenger vehicle that is accelerating in the forward direction - passengers perceive that they are acted upon by a force in the rearward direction pushing them back into their seats. An example in a rotating reference frame is the force that appears to push objects outwards towards the rim of a centrifuge. These apparent forces are examples of fictitious forces.

Thermodynamic beta Reciprocal product of temperature with the Boltzmann constant, frequently used in exponentials in physics and chemistry and relating statistical mechanics to information theory

In statistical thermodynamics, thermodynamic beta, also known as coldness, is the reciprocal of the thermodynamic temperature of a system:

$.$

An electromagnetic reverberation chamber is an environment for electromagnetic compatibility (EMC) testing and other electromagnetic investigations. Electromagnetic reverberation chambers have been introduced first by H.A. Mendes in 1968. A reverberation chamber is screened room with a minimum of absorption of electromagnetic energy. Due to the low absorption very high field strength can be achieved with moderate input power. A reverberation chamber is a cavity resonator with a high Q factor. Thus, the spatial distribution of the electrical and magnetic field strengths is strongly inhomogeneous. To reduce this inhomogeneity, one or more tuners (stirrers) are used. A tuner is a construction with large metallic reflectors that can be moved to different orientations in order to achieve different boundary conditions. The Lowest Usable Frequency (LUF) of a reverberation chamber depends on the size of the chamber and the design of the tuner. Small chambers have a higher LUF than large chambers.

Plasma parameters define various characteristics of a plasma, an electrically conductive collection of charged particles that responds collectively to electromagnetic forces. Plasma typically takes the form of neutral gas-like clouds or charged ion beams, but may also include dust and grains. The behaviour of such particle systems can be studied statistically.

The Lamm equation describes the sedimentation and diffusion of a solute under ultracentrifugation in traditional sector-shaped cells. It was named after Ole Lamm, later professor of physical chemistry at the Royal Institute of Technology, who derived it during his Ph.D. studies under Svedberg at Uppsala University.

The tip-speed ratio, λ, or TSR for wind turbines is the ratio between the tangential speed of the tip of a blade and the actual speed of the wind, $. The tip-speed ratio is related to efficiency, with the optimum varying with blade design. Higher tip speeds result in higher noise levels and require stronger blades due to larger centrifugal forces.$

In laser physics, gain or amplification is a process where the medium transfers part of its energy to the emitted electromagnetic radiation, resulting in an increase in optical power. This is the basic principle of all lasers. Quantitatively, gain is a measure of the ability of a laser medium to increase optical power.

Rotational diffusion is a process by which the equilibrium statistical distribution of the overall orientation of particles or molecules is maintained or restored. Rotational diffusion is the counterpart of translational diffusion, which maintains or restores the equilibrium statistical distribution of particles' position in space.

The primary application of wind turbines is to generate energy using the wind. Hence, the aerodynamics is a very important aspect of wind turbines. Like most machines, there are many different types of wind turbines, all of them based on different energy extraction concepts.

A yaw rotation is a movement around the yaw axis of a rigid body that changes the direction it is pointing, to the left or right of its direction of motion. The yaw rate or yaw velocity of a car, aircraft, projectile or other rigid body is the angular velocity of this rotation, or rate of change of the heading angle when the aircraft is horizontal. It is commonly measured in degrees per second or radians per second.

In astrophysics, the virial mass is the mass of a gravitationally bound astrophysical system, assuming the virial theorem applies. In the context of galaxy formation and dark matter halos, the virial mass is defined as the mass enclosed within the virial radius $of a gravitationally bound system, a radius within which the system obeys the virial theorem. The virial radius is determined using a "top-hat" model. A spherical "top hat" density perturbation destined to become a galaxy begins to expand, but the expansion is halted and reversed due to the mass collapsing under gravity until the sphere reaches virial equilibrium-it is said to be virialized . Within this radius, the sphere obeys the virial theorem which says that the average kinetic energy is equal to minus one half times the average potential energy,, and this radius defines the virial radius.$

The motor size constant and motor velocity constant are values used to describe characteristics of electrical motors.

In statistical mechanics, the Darwin–Fowler method is used for deriving the distribution functions with mean probability. It was developed by Charles Galton Darwin and Ralph H. Fowler in 1922-1923.

References

↑ "Basics of Centrifugation"

External links

Beckman Coulter lab resources and manuals
Appendix F of the Cell Biology Laboratory Manual

This fluid dynamics–related article is a stub. You can help Wikipedia by expanding it.

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[1] "Basics of Centrifugation"