3.3 Accelerated Motion and Life
43
suspensions and determining particle properties from the viscous drag force while
the particle moves toward greater radii.
The ultracentrifuge that was developed by the Swedish chemist Theodor Svedberg in the early 1920’s, with rotations of thousands per second, was capable of a
million-g. He could separate and weigh large biological molecules. In the 1930’s,
Jesse Beams, using magnetically suspended rotors in a vacuum, made the rotors spin
at more than a million revolutions per second, with rotational accelerations greater
than a billion times the acceleration of gravity. 23
Suspensions in a Centrifuge
Bodies in a liquid suspension undergoing accelerations much larger than free fall
will separate from the liquid much faster than ordinary gravity causes. The rate of
sedimentation depends on the fluid viscosity, the relative density of the particles,
their size, and their shape.
Because fluids are necessarily compressible, 24 there will be a gradient of fluid
density in a centrifuge. 25 Suspended particles of different densities can be made to
accumulate at the location where the fluid density matches that of the suspended
particle, called the ‘isopycnic’ point.
Centrifuges for biological and medical labs typically have a rotor with a seven
centimeter diameter and rotate at up to sixty thousand revolutions per minute
(making about 300,000 g’s). These can be used to separate mixtures of proteins;
different kinds of RNA; etc. At 10,000 g’s, blood plasma, which normally makes up
about (55 ± 5)% by volume of blood, can be separated from blood cells in about
30 min.
Sedimentation Speed
Consider the forces on a body, such as a red-blood-cell, suspended in a liquid, such
as blood plasma. In a centrifuge, several forces will act on the cell: Gravity (a body
force), pressure forces (from the adjoining liquid, acting on the cell surface), and
viscous forces if the cell moves through the liquid. To simplify this discussion,
take the centrifuge axis vertical and the motion of its rotor and liquid containers
horizontal. Suppose the rotor spins with angular speed ω. The net result of pressure
23 Walter Gordy, Jesse Wakefield Beams, Biographical Memoirs 54, [Nat Acad of Sci, Eng, Med]
(1983).
24 Special Relativity Theory forbids perfectly rigid bodies: Suppose such a body existed. Knock
one side of the body. Then the other side must move instantaneously with the first side. One has
made a signal from one end to the other move at an infinite speed. But Relativity limits signals to
speeds no greater than c, which is found to be the speed of light.
25 The average solution density itself can be adjusted by dissolving material which disperses at a
molecular level, such as sugar or CsCl in water.
43
suspensions and determining particle properties from the viscous drag force while
the particle moves toward greater radii.
The ultracentrifuge that was developed by the Swedish chemist Theodor Svedberg in the early 1920’s, with rotations of thousands per second, was capable of a
million-g. He could separate and weigh large biological molecules. In the 1930’s,
Jesse Beams, using magnetically suspended rotors in a vacuum, made the rotors spin
at more than a million revolutions per second, with rotational accelerations greater
than a billion times the acceleration of gravity. 23
Suspensions in a Centrifuge
Bodies in a liquid suspension undergoing accelerations much larger than free fall
will separate from the liquid much faster than ordinary gravity causes. The rate of
sedimentation depends on the fluid viscosity, the relative density of the particles,
their size, and their shape.
Because fluids are necessarily compressible, 24 there will be a gradient of fluid
density in a centrifuge. 25 Suspended particles of different densities can be made to
accumulate at the location where the fluid density matches that of the suspended
particle, called the ‘isopycnic’ point.
Centrifuges for biological and medical labs typically have a rotor with a seven
centimeter diameter and rotate at up to sixty thousand revolutions per minute
(making about 300,000 g’s). These can be used to separate mixtures of proteins;
different kinds of RNA; etc. At 10,000 g’s, blood plasma, which normally makes up
about (55 ± 5)% by volume of blood, can be separated from blood cells in about
30 min.
Sedimentation Speed
Consider the forces on a body, such as a red-blood-cell, suspended in a liquid, such
as blood plasma. In a centrifuge, several forces will act on the cell: Gravity (a body
force), pressure forces (from the adjoining liquid, acting on the cell surface), and
viscous forces if the cell moves through the liquid. To simplify this discussion,
take the centrifuge axis vertical and the motion of its rotor and liquid containers
horizontal. Suppose the rotor spins with angular speed ω. The net result of pressure
23 Walter Gordy, Jesse Wakefield Beams, Biographical Memoirs 54, [Nat Acad of Sci, Eng, Med]
(1983).
24 Special Relativity Theory forbids perfectly rigid bodies: Suppose such a body existed. Knock
one side of the body. Then the other side must move instantaneously with the first side. One has
made a signal from one end to the other move at an infinite speed. But Relativity limits signals to
speeds no greater than c, which is found to be the speed of light.
25 The average solution density itself can be adjusted by dissolving material which disperses at a
molecular level, such as sugar or CsCl in water.