Centrifugation Decoded: The Math Behind Separation

In a previous post, you have seen the basic instrumentation and principle of centrifugation, it’s types and application. Now let us look at how it works- the mathematics and theory behind centrifugation.

Centrifugal Force (CF)

It is an outward force felt by an object moving in a circular path.

F=m ω ² r

ω  is the angular velocity= [2π × rpm]/60

r is the radius

However, in order to account for the rotor speed and radius, we measure centrifugal force as Relative Centrifugal Force (RCF)

Relative Centrifugal Force (RCF)

Also known as g force, it refers to the acceleration applied to the sample in a centrifuge. It is measured in multiples of the earth’s gravitation force (for eg: 10,000 g) This force helps separate the components based on size, density, and mass.

Another related term is Revolutions Per Minute (RPM). It measures the rotational speed of the rotor. Typical ranges include low speed (< 10000 ) to high speed (>10000 ). it basically measures how fast it spins but tells us nothing about the force applied.

RCF is better than measuring revolutions per minute (RPM) as it accounts for the radius of the rotor. It depends on the speed and distance from the centre. This allows for consistent results across different centrifuges.

Relationship between RCF and CF

RCF= [rω ²]/ g

Relationship between RCF and RPM

RCF= 1.118 × 10^-5 × r ×(RPM)²

R in both cases is in centimeter.

So, RCF is the actual force applied and RPM tells us how fast the rotor spins.

Same RPM ≠ Same force—- radius changes everything.

Now that we’ve understood how the centrifuge works, let’s dive deeper into what happens at the cellular level- what the particles experience and how they actually separate.

Rate of separation of particles depends on density and particle size. Particle sedimentation can be explained by stoke’s law. It calculates the velocity of sedimentation using 5 parameters

V= [d² (ρ_p– ρ_L) × g]/ 18n

V= sedimentation rate/ velocity

d= diameter of the sphere

ρ_p= particle density

ρ_L= medium density

N= viscosity of the medium

G= gravitational force

This equation can teach us 5 things-

1. Rate of particle sedimentation is proportional to particle size
2. Sedimentation rate is proportional to difference in density between particle and medium
3. Sedimentation rate is zero when particle density is same as medium density
4. Sedimentation rate decreases as the medium viscosity increases
5. Sedimentation rate increases as the gravitational force increases

Big, dense particles in a low-viscosity medium settle the fastest.