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The sedimentation coefficient 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.
The sedimentation speed v t {\displaystyle v_{t}} is also the terminal velocity. It is constant because the force applied to a particle by gravity or by a centrifuge is balanced by the viscous resistance of the fluid through which the particle is moving. The applied acceleration a can be either the gravitational acceleration g, or more commonly the centrifugal acceleration ω 2 r {\displaystyle \omega ^{2}r}. In the latter case, ω {\displaystyle \omega } is the angular velocity of the rotor and r is the distance of a particle to the rotor axis.
The viscous resistance for a spherical particle is given by Stokes' law: 6πηr0v, 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: mrω, 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 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 velocity. The terminal velocity for a spherical particle is given by the equation: