Conversion of centrifuge speed and centrifugal force: (calculation formula of centrifuge separation factor)
1. The meaning of separation factors:
The ratio of the partition coefficients of the two solutes under the same conditions in the same extraction system. The larger (or smaller) the separation factor, the better the separation effect of the two solutes. If the separation factor is equal to 1, the two solutes cannot be separated. The separation factor on the centrifuge refers to the relative centrifugal force.
2. The main factors affecting the separation factors:
Centrifugal force Centrifugal force (F) Centrifugal force does not exist as a real force. It is an imaginary force in the non-inertial system for calculation convenience. Please see the following explanation: Centripetal force makes the object attracted to a central point, or repulsive or any effect that tends to the point. Descartes interpreted centrifugal force as a tendency for objects to maintain their "limited amount". The difference between them is that the centripetal force is in the inertial reference system, and the centrifugal force is the force in the non-inertial system. When we deal with physics problems, we are all in the inertial system (Newton's law is established at this time), so the concept of centrifugal force is generally not used. Since it is not a concept at all, we cannot compare their direction and size.
F = mω2r
ω: rotation angular velocity (radian / second) r: distance of the rotating body from the rotation axis (cm) m: particle mass Relative centrifugal force (RCF)
RCF is the multiple of the actual centrifugal force converted into gravity acceleration. G is the acceleration of gravity (9.80665m / s2)
The same rotation as one revolution is equal to 2Ï€ radians, so the angular speed of the rotor is expressed in the number of revolutions per minute (revolutions per minute n or r / min): In general, low speed centrifugation is often expressed in r / min.
3. Calculation formula of separation factor:
RCF = F centrifugal force / F gravity = mωˆ2r / mg = ωˆ2r / g = (2 * π * r / r * rpm) ˆ2 * r / g Note: rpm should be converted to revolutions / second For example: diameter 1000mm, speed 1000 / Min centrifuge, the separation factors are:
RCF (1000) = (2 * 3.1415 * 16.667) ^ 2 * 0.5 / 9.8
= 104.72 ^ 2 * 0.5 / 9.8
= 560
Settlement coefficient of settling centrifuge:
1. Sedimentation coefficient (sedimentation coefficient, s) According to the definition of sedimentation coefficient by Svedberg (founder of centrifugation method-Swedish protein chemist) in 1924: the speed of particles moving in the unit centrifugal force field. The settlement coefficient is expressed in time. When centrifugation is used, the measure of the settling velocity of macromolecules is equal to the speed per unit centrifugal field. Or s = v / ω2r. s is the sedimentation coefficient, ω is the angular velocity (radians / second) of the centrifugal rotor, r is the distance from the center of rotation, and v is the sedimentation velocity. The settling coefficient is expressed in terms of settling time per unit of gravity, and is usually in the range of 1 to 200 × 10 ^ -13 seconds. The factor of 10 ^ -13 is called the settling unit S, which is 1S = 10 ^ -13 seconds.
2. Basic principle When an object rotates around the central axis, it will be subjected to centrifugal force F. When the mass of an object is M, the volume is V, the density is D, the radius of rotation is r, and the angular velocity is ω (radians / second), we have:
F = Mω2r or F = VDω2r (1)
The above shows that the centrifugal force received by the centrifuged substance is directly proportional to the mass, volume, density, centrifugal angular velocity and radius of rotation of the substance. The greater the centrifugal force, the faster the centrifuged material settles.
In the centrifugation process, the centrifuged material must also overcome the obstacles of buoyancy and friction. The buoyancy F} and the friction F} are expressed by the following formulas:
F '= V.D'.ω2r (2)
F '' = f dr / dt (3)
Where D} is the density of the solution, f is the coefficient of friction, and dr / dt is the settling velocity (change in the radius of rotation per unit time).
Under certain conditions, the basic principles can be:
F = F '+ F' '
VD ω2r = V.D'ω2r + f. Dr / dt
dr / dt = Vω2r (D-D ') / f (4)
Equation (4) shows that the settling velocity is directly proportional to the volume and density difference of the centrifuged material and inversely proportional to f. If S is the settling velocity under the unit force field (ω2r = 1), then
S = V (D-D ') / f. S is the settlement coefficient.
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