# 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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