Practical Technology Section: Analysis of Centrifugal Force in Centrifuges

　　 Centrifuge The sedimentation is directly related to centrifugal force, which in turn is linked to the centrifugation method and the rotational speed!

　　The sequential application of centrifugal sedimentation field-flow fractionation can significantly extend the molecular-weight separation range in a single experiment. There are two main approaches to achieving this sequential operation: gradually varying the centrifuge’s rotational speed or altering the density of the carrier medium. Often, the concentration of sucrose is increased in the aqueous phase. Initially, a strong field is applied to separate the smallest-molecular-weight samples; then, the rotational speed is gradually reduced or rotation is completely halted to allow the larger-molecular-weight samples to elute from the column channel. Using this sequential approach, polystyrene particle latexes of different sizes were successfully separated—a separation equivalent to a difference of 1,000-fold in molecular weight.

　　Rate-zonal centrifugation involves first filling a centrifuge tube with a density gradient medium (such as sucrose, glycerol, KBr, CsCl, etc.) before centrifugation. The sample to be separated is then layered either on top of the gradient liquid, at the bottom of the centrifuge tube, or midway through the gradient layers, and the entire mixture is subjected to centrifugation together with the gradient medium. After centrifugation, the medium exhibits its lowest density near the axis of rotation (X1) and its highest density at the point farthest from the axis of rotation (X2). However, the maximum density of the medium must be lower than the minimum density of the particles in the sample—that is, ρP > ρm. This method relies on the differing sedimentation rates of the particles being separated; particles with different sedimentation rates will settle into distinct density gradient layers, forming a series of zones that enable their separation. During centrifugation and after it is completed, the gradient medium serves as both a supporting medium and a stabilizer when sampling, preventing mechanically induced vibrations from causing the already-separated particles to mix again.

　　Since ρP > ρm, it follows that S > 0. Therefore, the centrifugation time in this centrifugal method must be strictly controlled—ensuring both sufficient time for various particles to form distinct bands within the medium gradient and preventing any single particle from reaching the bottom before the separation is complete. If the centrifugation time is too long, the entire sample may settle completely at the bottom of the centrifuge tube; if the centrifugation time is insufficient, the sample will not yet have been adequately separated. As this method involves incomplete sedimentation, the sedimentation process is significantly influenced by the size of the substances involved. It is typically applied when the substances differ in size but have identical densities. Commonly used density gradients include Ficoll, Percoll, and sucrose.

　　Conversion between centrifuge speed and centrifugal force: (Centrifuge separation factor calculation formula)

　　1. The meaning of the separation factor:

　　The ratio of the distribution coefficients of two solutes under the same conditions within the same extraction system. The larger (or smaller) the separation factor, the better the separation effect between the two solutes; when the separation factor equals 1, the two solutes become indistinguishable. On a centrifuge, the separation factor refers to the relative centrifugal force.

　　2. Main factors affecting separation:

　　Centrifugal force, as a genuine force, simply does not exist—it is merely a fictitious force introduced for convenience in non-inertial reference frames. Consider the following explanation: The centripetal force causes an object to experience an attraction, repulsion, or any other tendency toward a central point. Descartes interpreted centrifugal force as an inherent tendency of objects to maintain their “quantities” unchanged. The key distinction between the two is that centripetal force operates within an inertial reference frame, whereas centrifugal force arises in a non-inertial reference frame. When we solve physics problems, we typically work within inertial reference frames (where Newton’s laws hold true), so we generally do not need to invoke the concept of centrifugal force. Since these are fundamentally different concepts, we cannot compare their directions or magnitudes.

　　F = mω²r

　　ω: Angular velocity of rotation (radians/second)

　　r: Distance of the rotating body from the axis of rotation (cm)

　　m: Particle mass

　　Relative centrifugal force (RCF)

　　RCF is the factor by which the actual centrifugal force is converted into gravitational acceleration.

　　g is the acceleration due to gravity (9.80665 m/s²).

　　Since one full rotation corresponds to 2π radians, the angular velocity of the rotor is expressed in terms of the number of rotations per minute (rotations per minute, or r/min): In general, low-speed centrifugation is typically reported in units of r/min.

　　3. Separation factor calculation formula:

　　RCF = Centrifugal force / Gravitational force = mω²r / mg = ω²r / g = (2πr / r × rpm)² × r / g Note: rpm should be converted to revolutions per second.

　　For example: A centrifuge with a diameter of 1000 mm and a rotational speed of 1000 rpm has a separation factor of:

　　RCF(1000) = (2 × 3.1415 × 16.667)^2 × 0.5 / 9.8

　　=104.72² × 0.5 / 9.8

　　=560

　　Due to space limitations, that’s all for today’s information on centrifugal force in centrifuges—stay tuned for the next installment!