Name: Steve L.
Date: July 2003
If centrifugal forces are "Imaginary" or "virtual", then how does a centrifuge manage
to separate particles in immersion according to their mass?
I hope I am understanding your question correctly. I do not know what you mean by "virtual" or
"imaginary". The force is a REAL one. As you spin a tennis ball attached by a string above your
head, you will FEEL the force of that ball trying to escape (centrifugal force). This is a real
force that is generated by the law that objects in motion (on a straight vector or course) tend to
stay in motion (on that straight vector or course). Just like if you were in your car and tried
to turn RIGHT at a corner at a speed
of 50 MPH versus 10 MPH. You would find your body plastered up against the drivers side door.
This is exactly how CENTRIFUGATION works. In a way this force can be considered to be a sort of
ARTIFICIAL GRAVITY, right? If you have seen the movie 2001: A Space Odyssey, you'd know that the
orbiting space station used a rotation hub. In my opinion, that was supposed to be where they got
their artificial gravity.
Now that that is cleared up, lets talk about MASS versus DENSITY. A centrifuge separates by
DENSITY differences just like gravity on the Earth does the same thing to ""AIR"" (note the
double quotes). If you have two, perhaps, orange with pulp, it is conceivable that the pulp
has the higher density (by a very small amount) If you were to centrifugally separate them in
a test tube or what not, you shall surely find a nice thick blob of pulp in the test tube and
pure OJ on top. Of course, it should be noted that if you do have access to a centrifuge always
use a counter weight (with similar liquid media) on the opposite "site" of your test tube (if you
are only separating one tube). Otherwise, you may get the "WALKING WASHING MACHINE" phenomenon.
Centrifugal forces (centripetal for purists) are neither "imaginary" or "virtual". They are very
real, just ask anyone who has been on any rotating amusement park rides. High speed centrifuges
have been "standard" lab equipment dating back to the 1930's when they were used to separate U(235)
from U(238) in the form of UF6. The quantitative details can become algebraically messy, but for an
ideal solution of component "i" having a molecular weight "Mi", molar volume "Vi", in a solvent
having density "d", spinning with an angular velocity "w" radians/sec, at an absolute temperature
"T" kelvins, at two radii "r``" and "r`" from the axis of rotation, the mole fraction of "i" at
radii "r``" and "r`", the mole fraction of "i", at the two radii, Xi`` and Xi`,
is : ln(Xi``/Xi`) = (Mi - d*Vi)*w^2/ 2RT * [r``^2 - r`^2]
where R is the universal gas constant in proper mechanical units, and "ln" is the "natural log".
(Mi - d*Vi) is the balance between the buoyancy and the centripetal force. Should that term be
"adjusted' so that it is zero no separation will occur.
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Update: June 2012