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## Centrifugation

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**Centrifugation**Downstream Processing Short Course Kevin Street May 2007 Gavin Duffy**Learning Outcomes**• After this lecture you should be able to… • Explain centrifugation • Compare centrifugal and gravitational forces • Describe different types of centrifuge • Define the sigma factor • Write the sigma factor for a bowl and disc stack centrifuges • Determine the sigma factor for a given specification**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 http://www.nzifst.org.nz/unitoperations/mechseparation4.htm**Centrifugal Motion**• Centrifugal acceleration = rω2 • ω is the angular velocity in rad/s • r is the radius of rotation • Centrifugal force = mrω2 • m is the mass of the particle**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: Compared to gravity d is particle diameter (m) ρp is the particle density (kg/m3) ρf is the fluid density (kg/m3) g is acceleration due to gravity (m/s2) is the fluid viscosity (Pa.s) uT is the terminal velocity of the particle r is the distance from axis of rotation ω is the angular 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 m – 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**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**http://drugtopics.mediwire.com/main/Default.aspx?P=Content&ArticleID=172950 Large particles have higher settling velocities than small particles Cellular debris ends up at the outer edge of the bowl Soluble intracellular material passes through with the clarified liquid Discs give a higher sigma factor**Benefit of Discs**The discs split the stream into a large number of very thin layers thereby improving separation Solids flow downwards on bottom face of disc Liquid flows upwards on top face of disc Sigma factor no. 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**Rotating Bowl Rotating scroll Clarified liquid http://www.sgconsulting.co.za/Products/Decanters/Decanters.htm