Centrifugal Separation

Bhanu Pratap Singh ChoudharyM. Tech (FPEM)

Contents• Principle• Solid – liq. Separation

– Settling rates– Residence time– Terminal velocity– Critical diameter– Critical flow rate

• Sigma values and scale up issues • Liq - liq. Separation• Selection of Separation Technique (Liquid–Solid): General Selection• Classification of Sedimentation Equipment• Tubular Centrifuge • Cream Separator• Examples of sedimentation centrifuge• Numerical Problems

Principle: • Centrifugal force acting on particle of mass m at a

radial location r is

• The angular velocity is related to the linear velocity as,

• If rotating speed is N rev/min, then

• and the centrifugal force in Newton is calculated as

• gravitational force on a particle of mass m,

• The ratio of centrifugal to gravitational force can be computed as

Numerical

• If N=1000 rev/min if radius of a centrifuge bowl is 1. R = 0.1016 m2. R = 0.2032 m

• Use formula :

• What do you observe ?

Answers :

1. 113.6g2. 227.2g

• This is representing that force is 113.6 & 227.2 times the gravitational force in both the cases

Settling rates in Centrifuge: • If a centrifuge is used for

sedimentation

• a particle of a given size can be removed from the liquid in the bowl if sufficient residence time of particle in the bowl is available for the particle to reach the wall.

• For a particle moving radially at its terminal velocity, the diameter of smallest particle removed can be calculated.

• b = length of bowl

• A particle is removed if it has sufficient residence time to reach the wall.

• rB = distance of particle from the axis of rotation at the end of residence time

q = volumetric flow rate at the steady state of the liquid (m^3 /s)V = volume of the liquid column in the centrifuge (in m^3)

Terminal Velocity

• In Stokes law regime (Re < 0.1), terminal velocity is expressed in gravitational field as :

• The terminal velocity in the centrifugal force field becomes

• As we know

• So Integrating

• q = volumetric flow rate at the steady state of the liquid

• V = volume of the liquid column in the centrifuge

• Combining Eq. (7.9) and (7.10),

• Dp ( calculated from the above equation)

– Particles with diameter < Dp

• will not reach the wall of the bowl• will go out with the exit liquid.

– Larger particles reach the wall and are removed from the liquid.

• A cut point/ critical diameter Dpc is defined as the diameter of the particle that reaches half the distance between r1 and r2 within residence time, tT.

Critical flow rate

At this qc, particles with diameter greater than Dpc will settle to the wall and most of the smaller particles (D<Dpc) will remain in the liquid.

Sigma values and scale up issues

• the volumetric flow rate is expressed in terms of terminal velocity under gravity and geometric factor

• vt ug is the terminal velocity under gravity

• Σ is a physical characteristic of centrifuge, not the fluid-particle system

Physical interpretation of Σ • Σ has the unit of area.

• It is area in m2 of a gravitational settler that will leave same sedimentation characteristics as the centrifuge at the same feed rate.

• If different centrifuges are used efficiency factors have to be used as

Separation of liquids • the neutral zone is

important in equipment

• design to determine the position of feed and discharge pipes

Note : For Derivation, please refer - C. J. Geankoplis, Transport Processes and Unit Operations, Prentice Hall of India, New Delhi, 1997.

Numerical

Solution :

Numerical

Formula :

212

22

1222ln18

rrb

rrrqD

ppc

Particle diameter

Solid feed concentration

Suggested Use

> 1000 mm > 3% Screens

5 mm – 20 mm 1 to 50 % Settlers, filters or Centrifuges

< 300 mm 0.01 to 20 % Thickeners

> 20 mm greater than 50 % Dryers

0.01 - 150 mm - consider deep bed filter, or dissolved air flotation

0.6 - 40 mm < 0.1 %, Ultrafiltration

Selection of Separation TechniqueLiquid–Solid: General Selection

Classification :

Tubular Centrifuge (liq-liq)

Cream Separator

Examples of Sedimentation Centrifuge

• Disc type: (Westfalia, Alfa-Laval, Robatel) – continuous: Centrifugal field about 104 g– and 100 rps with residence times of 1 to 10 s.

Power 3 to 10 kW s/L of feed.

• Differential type: (Podbielniak; Quadronic) – continuous: Centrifugal field about 500 g – 25 rps with about 10 to 75 s residence time.

Power 1 kW s/L.

Numerical :A dilute slurry contains small solid food particles having a diameter of 0.05 mm which are to be removed by centrifugation. The particle density is 1050 kg/m3 and the solution density is 1000 kg/m3. The viscosity of the liquid is 0.0012 Pa-s. A centrifuge at 3000 RPM is to be used. The bowl dimensions are b = 100.1 cm, r1 = 5 cm and r2 = 30 cm.

Calculate ?1- Angular velocity2- Volume 3- Volumetric flow rate

Hint :

Answers

s

radiansrev

radian

min

rev

2.314

min

60

123000

s

mq

3

29.0

32750.0 mV

Problem for Practice

Thanks