In chemistry, the sedimentation coefficient (s) of a particle characterizes its sedimentation (tendency to settle out of suspension) during centrifugation.
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.
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:
Stokes' law applies to small spheres in an infinite amount of fluid at the small Reynolds Number limit.
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:
The sedimentation coefficient has units of time, expressed in svedbergs.
The result no longer depends on acceleration, but only on the properties of the particle and the fluid in which it is suspended.
The sedimentation coefficient is in fact the amount of time it would take the particle to reach its terminal velocity under the given acceleration if there were no drag.
Also for non-spherical particles of a given shape, s is proportional to m and inversely proportional to some characteristic dimension with units of length.
For a given shape, m is proportional to the size to the third power, so larger, heavier particles sediment faster and have higher svedberg, or s, values.
Thus, when measured separately they have svedberg values that do not add up to that of the bound particle.
For example ribosomes are typically identified by their sedimentation coefficient.
Despite 80+ years of study, there is not yet a consensus on the way to perfectly model this relationship while also taking into account all possible non-ideal terms to account for the diverse possible sizes, shapes, and densities of molecular solutes.
[2] But in most simple cases, one of two equations can be used to describe the relationship between the sedimentation coefficient and the solute concentration:
For compact and symmetrical macromolecular solutes (i.e. globular proteins), a weaker dependence of the sedimentation coefficient vs concentration allows adequate accuracy through an approximated form of the previous equation:[2][3]
During a single ultracentrifuge experiment, the sedimentation coefficient of compounds with a significant concentration dependence changes over time.
Using the differential equation for the ultracentrifuge, s may be expressed as following power series in time for any particular relation between s and c.