# Sedimentation

Sedimentation

Downstream Processing

Short Course

May 2007

Kevin Street

Gavin Duffy

Bioprocess Overview

Solid
-
liquid

Separation

Concentration

Purification

Formulation

Intra
-
Cellular

Product

Final Product

Extra
-
Cellular

Product

Cell Disruption

Upstream Processing

Centrifugation/Sedimentation,

Extraction, Filtration

Evaporation, Ultrafiltration,

Chromatography

Crystallisation, freeze drying,

Spray drying, sterile filtration

Chemical/Enzymatic/

Mechanical/Physical

Basic Biotechnology, 2
nd

Ed, Ch 9

Learning Outcomes

After this lecture you should be able to…

Describe the sedimentation process and equipment

Describe the motion of particles in free fall

Calculate the terminal velocity of a particle

Sedimentation

This is the separation of a liquid from particles
suspended in the liquid

A particle, falling from rest, accelerates under the force
of gravity

The drag force increases so the acceleration decreases

(liquid viscosity is important here)

Acceleration eventually becomes zero

the terminal
velocity is reached

Terminal velocity is reached quickly, e.g. a 100

m
particle in water reaches 2 mm/s in 1.5 ms

Upward velocity of liquid must be less than terminal
velocity for sedimentation to work

We must know the terminal velocity!

Sedimentation Tank

Single Particle Terminal velocity

For low Particle Reynolds number:

Creeping flow

Drag coefficient increases with velocity

Stokes law region

For high Particle Reynolds number:

Inertial flow (fluid must accelerate out of path)

Drag coefficient constant

18
2
g
d
u
f
p
T

2
1
74
.
1

f
f
p
T
g
d
u

Drag coefficient

The drag coefficient is defined as:

R’ is the drag force per unit projected area (N)

u is the velocity (m/s)

ρ
f

is the fluid density (kg/m
3
)

(What are the units of C
D
?)

Stokes’ law region:

Intermediate region:

Newton’s law region:

2
2
u
R
C
f
D

p
D
C
Re
24

44
.
0
Re
24

p
D
C
44
.
0

D
C
Drag curve for motion of a particle in fluid

Introduction to Particle Technology, Martin Rhodes, Ch 1

Stokes’

Newton’s

BL separation

Sphericity

Sphericity = surface area of equivalent sphere

surface area of particle

Equivalent sphere = sphere of same volume as particle

Deviation from sphere does not matter in Stokes’ law
region as much as in Newton’s law region

Particles fall with their small surface pointed
downwards in Stokes’ law region

The largest surface is pointed downwards in
Newton’s law region

Activity

Calculate Terminal Velocity

What are the particle Reynolds number and terminal
velocity for the following system?

Diameter 3

m

Density of solid phase 1090 kg/m
3

Cell free liquid density 1025 kg/m
3

Cell free liquid viscosity 0.005 Pa.s

Data taken from a case study of r
-
HSA production with recombinant
Pichia Pastoris

prepared by L Van der Wielen, European Federation on
Biotechnology

If you don’t know which region…

Calculate C
D
Re
2

from the following eqn:

Use result to draw a line on the drag curve

For example, suppose C
D
Re
2

= 8

Then,

for Re = 10

Re
2

= 100

C
D

= 0.08

for Re = 1

Re
2

= 1

C
D

= 8

for Re = 0.1

Re
2

= 0.01

C
D

= 800

Use these points to draw the line and read the Particle
Reynolds number. The velocity is then obtained

2
3
2
3
4
Re

g
d
C
f
p
f
p
D

…..use the Re v Drag coefficient chart

x

x

x

The Thickener

Feed added gently just below surface

Upward velocity of liquid must be less than u
T

Capacity depends on area: big area = low velocity (Q = va)

Degree of thickening depends on residence time which depends
on height

Can heat tank to reduce viscosity and increase u
T

Limit to solids flux

http://www.filtration
-
and
-
separation.com/thickener/sld004.htm

20/4/07

Batch Settling Test

Thickener Area Calculation

where

A = area (m
2
)

Q
0

= feed rate of suspension (m
3
/s)

Y = mass ratio liquid to solid in feed

U = mass ratio liquid to solid in underflow

C = particle volume fraction (1
-
ε
)

ρ
s

= density of solid (kg/m
3
)

u
T

= terminal velocity at conc. C (m/s)

ρ
f

= density of liquid (kg/m
3
)

f
T
s
u
C
U
Y
Q
A

0
Activity

Calculate Terminal Velocity

based on worked example 2.1 from Rhodes.