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Sedimentation

Sedimentation describes the motion of molecules in solutions or particle (ecology)|particles in suspension (chemistry)|suspensions in response to an external force such as gravitation|gravity, centrifugal force or electromagnetism|electric force. Sedimentation may pertain to objects of various sizes, ranging from suspension (chemistry)|suspensions of dust and pollen particle (ecology)|particles to cell (biology)|cellular suspensions to solutions of single molecules such as proteins and peptides. Even small molecules such as aspirin can be sedimented, although it can be difficult to apply a sufficiently strong force to produce significant sedimentation. In a sedimentation experiment, the applied force accelerates the particles to a terminal velocity

v_{term}

at which the applied force is exactly canceled by an opposing drag force. For small enough particles (low Reynolds number), the drag force varies linearly with the terminal velocity, i.e.,

F_{drag} = f v_{term}

(Stokes flow) where ''f'' depends only on the properties of the particle and the surrounding fluid. Similarly, the applied force generally varies linearly with some coupling constant (denoted here as ''q'') that depends only on the properties of the particle,

F_{app} = q E_{app}

. Hence, it is generally possible to define a sedimentation coefficient

s \ \stackrel{\mathrm{def}}{=}\   q/f

that depends only on the properties of the particle and the surrounding fluid. Thus, measuring ''s'' can reveal underlying properties of the particle. In many cases, the motion of the particles is blocked by a hard boundary; the resulting accumulation of particles at the boundary is called a sediment. The concentration of particles at the boundary is opposed by the diffusion of the particles. The sedimentation of particles under gravity is described by the Mason-Weaver equation, which has a simple exact solution. The sedimentation coefficient ''s'' in this case equals

m_{b}/f

, where

m_{b}

is the buoyant mass. The sedimentation of particles under the centrifugal force is described by the Lamm equation, which likewise has an exact solution. The sedimentation coefficient ''s'' also equals

m_{b}/f

, where

m_{b}

is the buoyant mass. However, the Lamm equation differs from the Mason-Weaver equation because the centrifugal force depends on radius from the origin of rotation, whereas gravity is presumed constant. The Lamm equation also has extra terms, since it pertains to Circular sector|sector-shaped cells, whereas the Mason-Weaver equation pertains to cuboid|box-shaped cells (i.e., cells whose walls are aligned with the three Cartesian coordinate system|Cartesian axes). Particles with a charge or dipole moment can be sedimented by an electric field or electric field gradient, respectively. These processes are called electrophoresis and dielectrophoresis, respectively. For electrophoresis, the sedimentation coefficient corresponds to the particle charge divided by its drag (physics)|drag (the electrophoresis|electrophoretic mobility). Similarly, for dielectrophoresis, the sedimentation coefficient equals the particle's electric dipole moment divided by its drag (physics)|drag.

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