Centrifugation: It's Principal

CENTRIFUGATION:

Centrifugation is a process that involves the use of centrifugal force for the sedimentation of heterogeneous mixtures with a centrifuge used in industry and in laboratory settings. The word “Centrifugal” came from two Latin words ‘Centrum’ which means ‘Center’ and ‘Fugere’ which means ‘To Flee’. Centrifugal force is the apparent force that draws a rotating body away from the center of rotation. It is caused by the inertia of the body.

Centrifugal Force is used to provide the driving force for two operations-

1.             To create a pressure difference in the filtration process.
2.             To reduce gravitational force in the sedimentation process.

PRINCIPLES FOR CENTRIFUGATION:

Centrifugation is based on the well-known principle that an object that is rotated about the center point at a constant radial distance from the point is acted upon by a force.

The operations using centrifugal force are described by equations including the gravitational constant. It is convenient, therefore, to measure the centrifugal force in terms of a ratio to the gravitational force and this is known as the centrifugal effect, which is the number of times the centrifugal force is greater than the gravitational force. The centrifugal effect is then inserted in the appropriate equation with the gravitational force.

The centrifugal effect is obtained as follows-

Consider a body of mass ‘m’ rotating in a circular path of radius ‘r’ at a velocity ‘v’. The force acting on the body in a radial direction is given below-

F=mv²/r  …………….. (1)

Here,

F=Centrifugal force

M= Mass of body                                                                  

v= Velocity of body

r = Radius of the circle of rotation.

The same body will be acted upon by a gravitational force

G=mg……………… (2)

Where,

G= Gravitational force

g= Gravitational constant

The centrifugal effect is the ratio of the two forces, so that

C=F/G

=(mv²)/mgr

=v²/gr

=((2πnr)²)/gr

[v=2πnr, where n=speed of rotation]

=4π²r²n²/gr

=4π²rn²/g

=(4π²n² d/2)/g

   

 [r=d/2  ,where,d=diameter of rotation    ]

=2π²n²d/g

So, the Centrifugal effect,

     C=2π²n²d/g 

The gravitational constant has a value of 9.807 ms¯² so that the equation maybe simplified to-

Centrifugal effect, C=2.013n²d……….. (3)

‘n’ is expressed as s¯¹ and  ‘d’ is in m.

From equation (3), It is shown that c∝n²d    

So, The centrifugal effect is directly proportional to the diameter and the square of the speed of rotation.

We can conclude by the equation that we can modify a centrifugal machine as well as a centrifugal effect by modifying the speed of rotation or the diameter of the apparatus. But it is wise to modify the speed of rotation other than the diameter. Increasing the diameter is not so effective, because after a certain point it can produce tremendous pressure difference and it can break down the apparatus. Besides, it is a very hazardous task. So, when the diameter is increased then the rotating speed must be matched by calculation.

 But it is easy to modify the speed of rotation. By increasing the speed of rotation, we can increase the centrifugal effect. Thus, tiny particles can be separated by centrifugation.