Centrifugation

Learning Outcomes

General Idea

Feed added to spinning bowl

Sedimentation of particles occurs in centrifugal field

Flow is upwards at a particular rate which determines residence time in device

Separation happens if sedimentation velocity is high enough for particle to reach side of bowl within residence time

Large particles have higher settling velocities than small particles

Both large and small are still particles, have small Reynolds no.s (<1) and obey Stokes’ Law

The Centrifuge

Separation of milk into skimmed milk and cream is done with a centrifuge

Centrifugal Motion

Compared to gravity

mg

Acceleration constant

In direction of earth

Equilibrium velocity reached

Terminal velocity given by:

mrω2

Acceleration increases with r

Acceleration increases with ω

Away from axis of rotation

Equilibrium velocity never reached

Instantaneous velocity:

Sigma Factor

The capacity of a centrifuge is defined by Σ

Q is the throughput (m3/s) at which all particles with a terminal velocity ≥ uT (m/s) are retained

Σ has units of m2 and is equivalent to the cross sectional area of a thickener with the same capacity

Activity – Determine Σ

The contents of a fermenter are discharged to a centrifuge

Volume of material is 100 m3

Centrifugation time is 5 hrs

Particle size is 3 mm – all particles of this size are separated

Density of solid phase 1090 kg/m3

Cell free liquid density 1025 kg/m3

Cell free liquid viscosity 0.005 Pa.s

Calculate the capacity factor, Σ

Bowl Centrifuge

Sigma Factor – Bowl Centrifuge

For the bowl centrifuge:

ω is the angular velocity (rad/s)

R is the outer radius of the bowl (m)

rc is the radius of the clarified discharge weir (m)

H is the height of the bowl (m)

r is the inner radius of the liquid in the bowl (m)

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

A long thin bowl gives good separation

The Disc Stack Centrifuge

Benefit of Discs

Disc Stack Centrifuge Capacity

For the disc stack centrifuge:

ω is the angular velocity (rad/s)

n is the number of discs

R is the outer radius of the discs (m)

r is the inner radius of the discs (m)

θ is the angle between disc and vertical (rad)

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

Activity

What is the capacity of the following disc stack centrifuge?

No. of discs = 400

Space between discs is 0.01 m

Inner radius = 0.05 m

Outer radius = 0.20 m

Half vertical angle = 45°

Rotational speed = 4500 rpm

What effect does an increase in diameter have on the capacity?

What diameter is needed for the previous example?

Decanter Centrifuge

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