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Sedimentation coefficient
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Sedimentation coefficient
In chemistry, the sedimentation coefficient (s) of a particle characterizes its sedimentation (tendency to settle out of suspension) during centrifugation. It is defined as the ratio of a particle's sedimentation velocity to the applied acceleration causing the sedimentation.
The sedimentation speed vt is also the terminal velocity. It is constant because the force applied to a particle by gravity or by a centrifuge (typically in multiples of tens of thousands of gravities in an ultracentrifuge) is balanced by the viscous resistance (or "drag") of the fluid (normally water) through which the particle is moving. The applied acceleration a can be either the gravitational acceleration g, or more commonly the centrifugal acceleration ω2r. In the latter case, ω is the angular velocity of the rotor and r is the distance of a particle to the rotor axis (radius).
The viscous resistance for a spherical particle is given by Stokes' law: where η is the viscosity of the medium, r0 is the radius of the particle and v is the velocity of the particle. Stokes' law applies to small spheres in an infinite amount of fluid at the small Reynolds Number limit.
The centrifugal force is given by the equation: where m is the excess mass of the particle over and above the mass of an equivalent volume of the fluid in which the particle is situated (see Archimedes' principle) and r is the distance of the particle from the axis of rotation. When the two opposing forces, viscous and centrifugal, balance, the particle moves at constant (terminal) velocity. The terminal velocity for a spherical particle is given by the equation:
Rearranging this equation gives the final formula:
The sedimentation coefficient has units of time, expressed in svedbergs. One svedberg is 10−13 s. The sedimentation coefficient normalizes the sedimentation rate of a particle to its applied acceleration. The result no longer depends on acceleration, but only on the properties of the particle and the fluid in which it is suspended. Sedimentation coefficients quoted in literature usually pertain to sedimentation in water at 20 °C.
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Sedimentation coefficient
In chemistry, the sedimentation coefficient (s) of a particle characterizes its sedimentation (tendency to settle out of suspension) during centrifugation. It is defined as the ratio of a particle's sedimentation velocity to the applied acceleration causing the sedimentation.
The sedimentation speed vt is also the terminal velocity. It is constant because the force applied to a particle by gravity or by a centrifuge (typically in multiples of tens of thousands of gravities in an ultracentrifuge) is balanced by the viscous resistance (or "drag") of the fluid (normally water) through which the particle is moving. The applied acceleration a can be either the gravitational acceleration g, or more commonly the centrifugal acceleration ω2r. In the latter case, ω is the angular velocity of the rotor and r is the distance of a particle to the rotor axis (radius).
The viscous resistance for a spherical particle is given by Stokes' law: where η is the viscosity of the medium, r0 is the radius of the particle and v is the velocity of the particle. Stokes' law applies to small spheres in an infinite amount of fluid at the small Reynolds Number limit.
The centrifugal force is given by the equation: where m is the excess mass of the particle over and above the mass of an equivalent volume of the fluid in which the particle is situated (see Archimedes' principle) and r is the distance of the particle from the axis of rotation. When the two opposing forces, viscous and centrifugal, balance, the particle moves at constant (terminal) velocity. The terminal velocity for a spherical particle is given by the equation:
Rearranging this equation gives the final formula:
The sedimentation coefficient has units of time, expressed in svedbergs. One svedberg is 10−13 s. The sedimentation coefficient normalizes the sedimentation rate of a particle to its applied acceleration. The result no longer depends on acceleration, but only on the properties of the particle and the fluid in which it is suspended. Sedimentation coefficients quoted in literature usually pertain to sedimentation in water at 20 °C.