Multi-technique separation Nature of Bioseparation

ERT 313 :
BIOSEPARATION ENGINEERING
Introduction to BioSeparation Process
& Some Mechanical-Physical Separation
Process
By; Mrs Hafiza Binti Shukor
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
Students should be able to;
DEFINE and EXPLAIN the meaning, nature and
application of Bioproducts and Bioseparation
Engineering.
DESCRIBE and REPEAT the Bioseparation
techniques/processes and RIPP (Recovery, Isolation,
Purification and Polishing) scheme.
DEVELOP techniques/processes and RIPP (Recovery,
Isolation, Purification and Polishing) scheme for
downstream processes.
DESCRIBE and DISC USS about some mechanicalphysical separation technique like cell disruption,
centrifugation and electrophoresis
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
BIOPROD UCT?
Chemical substances / combination of
chemical substances that are made by
LIVING THING range from methanol
to whole cells.
Derived by EXTRACTION from whole
plants and animals
By synthesis in bioreactors containing
cells / enzymes
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
BIOLOGICAL PROD UCTS (with
different classification)
Biological products - chemical classification
Solvents, e.g. ethanol, acetone, butanol
Cells, e.g. bakers yeast, brewers yeast, freeze dried lactobacillus
Crude cellular extracts, e.g. yeast extract, soy extracts
Organics acids, e.g. citric acid, lactic acid, butyric acid
Vitamins, e.g. ascorbic acid, vitamin B12
Amino acids e.g. lysine, phenylalanine, glycine
Gums and polymers, e.g. xanthan, gellan, dextran
Antibiotics, e.g. penicillins, rifanpicin, streptomycin
Proteins, e.g. industrial enzymes, egg proteins, milk proteins, whey protein
therapeutic enzymes, monoclonal antibodies, plasma proteins
Sugars and carbohydrates, e.g. glucose, fructose, starch, dextran
Lipids, e.g. glycerol, fatty acids, steroids
Nucleic acids, e.g. plasmids, therapeutic DNA
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
Biological products - applications
Industrial chemicals, e.g. solvents, organic acids, industrial enzymes
Agrochemicals, e.g. biofertilizers, biopesticides
Pharmaceuticals, e.g. antibiotics, hormones, monoclonal antibodies,
plasma proteins, vaccines
Food and food additives, e.g. whey proteins, milk proteins, egg proteins,
soy proteins
Nutraceuticals, e.g. vitamins, amino acids, purified whey proteins
Diagnostic products, e.g. glucose oxidase, peroxidase
Commodity chemicals, e.g. detergent enzymes, insecticides
Laboratory reagents, e.g. bovine serum albumin, ovalbumin, lysozyme
Cosmetic products, e.g. plant extracts, animal tissue extracts
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
BIOLOGICAL PROD UCTS (with
different bioseparation process)
Product
Nature of bioseparation required
Alcoholic beverages:
Clarification, distillation
Beer, wine, spirits
Organic acids:
Acetic acid, citric acid
Vitamins:
Vitamin C, vitamin B12, riboflavin
Amino acids:
Lysine, glycine, phenylalanine
Antibiotics:
Precipitation, filtration, adsorption,
solvent extraction
Precipitation, filtration, adsorption,
solvent extraction
Precipitation, filtration, adsorption,
solvent extraction
Penicillins, neomycin, bacitracin
Precipitation, filtration, adsorption,
solvent extraction
Carbohydrates:
Precipitation, filtration, adsorption
Starch, sugars, dextrans
Lipids:
Glycerol, fats, fatty acids
Precipitation, filtration, adsorption,
solvent extraction
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
Proteins:
Food and food additives
Nutraceuticals
Industrial enzymes
Hormones
Pharmaceutical enzymes
Plasma derived products
Monoclonal antibodies
Growth factors
Clotting factors
Thrombolytics
r-DNA derived proteins
Diagnostic proteins
Vaccines
Filtration, precipitation, centrifugation,
adsorption, chromatography, membrane
based separations
DNA based products:
Filtration, precipitation, centrifugation,
DNA probes, plasmids, nucleotides, adsorption, chromatography, membrane
oligonucleotides
based separations
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
OVERVIEW OF BIOPROCESSING OF
BIOCHEMICAL & PHARMACE UTICAL
PRODUCTS
 One of the major segments within
biotechnology where R&D is bioprocessing
which deals with the manufacture of
biochemicals, food, neutraceuticals and
agrochemicals.
 New biologically derived product have
been developed, approved and licensed.
 Eg: Monoclonal antibodies (used for
treatment of canser)
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
OVERVIEW OF BIOPROCESSING OF
BIOCHEMICAL & PHARMACE UTICAL
PROD UCTS
 all biochemicals & pharmaceutical
product MUST be extensively P U RIFIED
before used in respective application.
Bioprocessing / downstream processing of
biochemical & pharmaceuticals products refer
to the SYSTEMATIC study of the scientific
and engineering principle utilized for the large
scale purification of biological products.
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
OVERVIEW OF BIOPROCESSING OF
BIOCHEMICAL & PHARMACE UTICAL
PROD UCTS
2 categories of bioprocessing :
i) reactive bioprocessing
-bio-separation process
follows some form of
biological reactions
ii)extractive bioprocessing
-almost entirely involves
bioseparation
ERT 313/4 BIOSEPARATION ENGINEERING
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REACTIVE BIOPROCESSING
 Bioseparation follow some form of
BIOLOGICAL REACTION
Eg: Antibiotic production (separation &
purification following microbial fermentation)
Upstream
processing
Biocatalyst
Screening
Formulation
Media
optimization
Biological
Reaction
Bioseparation
Biological
products
Fermentation
Cell culture
Enzymatic reaction
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
EXTRACTIVE BIOPROCESSING
 Almost entirely involved bioseparation
(With extractive bioseparation, upstream
processing involves raw material acquisition &
pre-treatment)
Eg: Manufacture of plasma proteins from
blood
Upstream
processing
Bioseparation
Biological
products
Synthesis in
VIVO in their
respective
natural source
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
Bioseparations engineering
• Definition: Recovery, isolation, purification
and polishing of products synthesized by
biotechnological processes
• Extended definition: Final polishing steps of
processes such as biotechnology based effluent
treatment and water purification
Bioproduct/s
Upstream
processing
Bioreaction
Downstream
processing
Impurities
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
Why do we need bioseparation?
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Enrichment of target product
Reduction in bulk
Removal of specific impurities
Enhancement of product stability
Achievement of product specifications
Prevention of product degradation
Prevention of catalysis other than the type desired
Prevention of catalyst poisoning
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
Challenges in Bioseparations
Engineering
•Low product concentration
•Large number of impurities,
•Thermolabile bioproducts.
•Narrow operating pH and ionic strength window
•Shear sensitivity of bioproducts
•Low solubility of bioproducts in organic solvents
•Instability of bioproducts in organic solvents
•Stringent quality requirements
•Percentage purity
•Absence of specific impurities
An ideal bioseparation process should combine high throughput
with high selectivity, and should ensure stability of product.
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
A Good Bioseparation Process:
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Ensures desired purity of product
Ensures stability of product
Keeps cost low
Is reproducible
Is scalable
Meets regulatory guidelines
ERT 313/4 BIOSEPARATION ENGINEERING
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Economic Importance of Bioseparation
Engineering
The purification of biological product from their
respective starting material. Eg: cell culture media
: technically difficult and expensive
The critical limiting factor in the
commercialization of biological product
Many cases, bioseparation cost can be a
substantial component of the total cost of
bioprocessing
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
Economic importance of bioseparation
engineering (cost of bioseparation)
Product
Bioseparation
cost (%)
Solvents e.g. ethanol, acetone
15-20
Cells, e.g. bakers yeast, brewers yeast
20-25
Crude cellular extracts, e.g. yeast extract
20-25
Organics acids, e.g. citric acid, lactic acid
30-40
Vitamins and amino acids e.g. lysine, ascorbic acid
30-40
Gums and polymers, e.g. xanthan, gellan
40-50
Antibiotics, e.g. penicillins, rifanpicin
20-60
Industrial enzymes, e.g. Amyloglucosidase, glucose isomerase
40-65
Non-recombinant therapeutic proteins, e.g. pancreatin, papain
50-70
r-DNA products, e.g. recombinant insulin, recombinant streptokinase
60-80
Monoclonal antibodies
50-70
Nucleic acid based products
60-80
Plasma proteins, human albumin, human immunoglobulins
70-80
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
Strategies for Bioseparation
A large number of bioseparation methods are available
The strategy is based on how best these can be utilized
for a given separation
The following need to be taken into account:
•
The volume of process stream
•
The relative abundance of the product in this
process stream
•
The intended use of the product, i.e. purity
requirements
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The cost of the product
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Stability requirements
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
Conventional strategy:
The RIPP scheme
• Recovery, isolation, purification and polishing
• Based on a logical arrangement of bioseparation
methods
• Low-resolution (less selectivity), high-throughput
(product) techniques (e.g. precipitation, filtration,
centrifugation, crystallization) are first used for recovery
and isolation
• High-resolution techniques (e.g. adsorption,
chromatography, electrophoresis) are then used for
purification and polishing
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
Conventional strategy:
The
RIPP
scheme
Biotechnological processes usually yield products at
very low concentrations in the product stream.
The product of interest also needs to be separated from
a large number of impurities, some of which have
physical and chemical properties not too different from
the product.
If such a product stream is sent directly to a highresolution separation device, it will soon be
overwhelmed and fail to function properly.
Therefore it makes sense to use high throughput-low
resolution techniques first to significantly reduce the
ENGINEERING
volume/concentration of process stream. ERT 313/4 BIOSEPARATIONSEM
2 (2010/2011)
Conventional strategy:
The RIPP scheme
These high throughput-low resolution steps are
referred to as recovery and isolation steps.
The processed product stream is then further
processed by high resolution-low throughput steps to
get pure finished products.
With the advent of membrane separation processes it
is now possible to replace the conventional RIPP
scheme. Membrane processes give high throughput
and can be fine-tuned/optimized to give very high
resolution. The use of membrane technology reduces
the number of bioseparation steps and hence
contributes towards high product recovery.
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
The RIPP Scheme
• Multi-technique separation
• Process design should take into consideration the
following:
• The nature of starting material
• The initial location of the target product
• The volume of process stream
• The relative abundance of the product in the starting
material
• The susceptibility to degradation of the product
• The desired physical form of the final product
• The quality requirements
• Costing
ERT 313/4 BIOSEPARATION ENGINEERING
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Commonly Used Bioseparation
Processes
Low resolution-high throughput
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Cell disruption
Precipitation
Centrifugation
Liquid-liquid extraction
Leaching
Filtration
Supercritical fluid extraction
Microfiltration
Dialysis
High resolution-low throughput
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Ultracentrifugation
Adsorption
Packed bed chromatography
Affinity separation
Electrophoresis
High resolution-high throughput
•Ultrafiltration
•Fluidized bed chromatography
•Membrane chromatography
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
Objective & Typical Unit Operations of
The 4 Stages in Bioseparation
Stage
Objectives
Typical unit
operation
Recovery
(separation of
insoluble)
Remove/ collect cells, cells debris /other
particulate.
Reduce volume
Filtration,
sedimentation,
extraction,
adsorption
Isolation of
product
Remove material have properties widely
different from those desired in product.
Reduce volume
Extraction,
adsorption,
ultrafiltration,
precipitation
Purification
Remove remaining impurities which
typically similar to desired product in
chemical functionality & physical
properties.
Chromatography,
affinity method,
functional
precipitation
Polishing
Remove liquid.
Convert product to crystallized form
Drying,
crystallization
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
Nature of Bioseparation
• Largely based on chemical separation
techniques
• Chemical separation techniques are modified
based on specific requirements
• Novel separations may be necessary in some
cases
• High throughput/productivity
• High selectivity
• Need to satisfy stringent quality requirements
• Need to take into account degradable material
• Low temperature operations
• Multi-technique separation
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
Different Attributes of Bioseparation
• Dilute biological products
• Impurities & by-product also present
• Stringent require for product (quality
requirement)
• Susceptible to denaturation &
degradation
• Thermo bile
• Multi technique separation
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
Basis of Separation
Biological products are separated based on one or several of
the following in combination:
• Size, e.g. filtration, membrane separation, gelfiltration, centrifugation
• Density, e.g. centrifugation, sedimentation, flotation
• Diffusivity, e.g. membrane separation, supercritical
fluid extraction
• Shape, e.g. centrifugation, filtration, sedimentation
• Polarity, e.g. extraction, chromatography, adsorption
• Solubility, e.g. extraction, membrane separation,
precipitation, crystallization
• Electrostatic charge, e.g. adsorption, membrane
separation
• Mobility, e.g. electrophoresis, membrane separation
• Volatility e.g. distillation, membrane distillation,
pervaporation
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
Cell culture
supernatant
Microfiltration
Filtrate
Precipitation
Ammonium
sulfate
Precipitate
Buffer
Solution
Monoclonal antibody
purification
Ultrafiltration
Ion-exchange
chromatography
Monoclonal
antibody
Gel
filtration
Buffer
Buffer
Ultrafiltration
ERT 313/4 BIOSEPARATION ENGINEERING
SEM 2 (2010/2011)
HOW TO CHOOSE
SEPARATION METHOD
1. What is the product?
2. What is the value of product?
3. What is the acceptable product quality for the
proposed end use?
4. Where is the product in the complex mixture?
5. What are the physical and chemical properties
of the product and the impurities?
6. Is the product stable?
7. What are the economic of the various isolation
procedure?
8. Are they any contamination / health risk?
9. Can the isolation procedure be scaled up?
ERT 313/4 BIOSEPARATION ENGINEERING
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RULES OF THUMB FOR
BIOSEPARATIONS
1. Keep the number of step to a
minimum.
2. Select the component that is easiest
to remove first
3. Leave the most difficulty isolation
step for last
ERT 313/4 BIOSEPARATION ENGINEERING
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Current Paradigm in The Bioseparation
Replacement of the conventional RIPP scheme
by using new techniques which can
significantly cut down the number of steps
needed to bioseparation
Some of these new and emerging techniques
are:
• Membrane chromatography
• Expanded-bed chromatography
• High-resolution ultrafiltration
ERT 313/4 BIOSEPARATION ENGINEERING
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CELL DISR UPTION
ERT 313/4 BIOSEPARATION ENGINEERING
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Cell disruption / lysis is a method or process for
releasing biological molecules from inside a cell
(breaking / lysing cells and tissues)
Biotechnological products produced by different
types of cells can be intracellular or extracellular.
If these are intracellular (inside the cell), the cells
have to be disrupted to release these products
before further separation can take place.
ERT 313/4 BIOSEPARATION ENGINEERING
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Types of Cell Need to Disruption
Ease
of cell
breaks
 Bacteria ( gram +ve @ gram –ve)
 Yeast
 Culture (plant culture @ animal culture)
Gram-positive
Gram-negative
Thick wall
No wall (got multilayer
enveloped)
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Some Elements of Cell Structure
Prokaryotic Cells
• Cells that do not contain a membrane-enclosed
nucleus.
• The bacteria cell envelope consists of an inner plasma
membrane that separates all contents of the cell from
the outside world, a peptidoglycan cell wall, and outer
membrane
• Bacteria cells with a very thick cell wall stain with
crystal violet (Gram stain) and are called “Gram
positive”, while those with thin cell wall stain very
weakly – “Gram negative”
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Some Elements of Cell Structure
Eukaryotic cells
• Eukaryotic cells (cells with nuclei and internal
organelles) are considerably more complicated than
prokaryotic cells, and bioproducts may have to
released from intracellular particles that are
themselves coated with membranes and/or consist
of large macromolecular aggregates
• The eukraryotes includes fungi, and, of course, the
higher plants and animals
• The cell membrane of animal cells is easily broken,
whereas the cell wall of plants is strong and
relatively difficult to break
ERT 313/4 BIOSEPARATION ENGINEERING
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Figure : Eukaryotic cells. Simplified diagrammatic representation of
an animal cell and a plant cell.
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Different cell disruption techniques are used. These
include:
Physical methods
•Disruption in ball mill or pebble mill
•Disruption using a colloid mill
•Disruption using French press
•Disruption using ultrasonic vibrations
Chemical methods
•Disruption using detergents
•Disruption using enzymes e.g. lysozyme
•Combination of detergent and enzyme
•Disruption using solvents
ERT 313/4 BIOSEPARATION ENGINEERING
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Mechanical Methods for Cell Lysis
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Sonication
Ball milling
Pestle homogenization
Shearing devices
(blender)
• High pressure
homogenizers
• Bead mills
ERT 313/4 BIOSEPARATION ENGINEERING
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Bead mill
Cascading
beads
Rolling
beads
Cells being
disrupted
• Disruption takes place due to the grinding action of the
rolling beads and the impact resulting from the cascading ones
• Bead milling can generate substantial heat
• Application: Yeast, animal and plant tissue
• Small scale: Few kilograms of yeast cells per hour
• Large scale: Hundreds of kilograms per hour.
ERT 313/4 BIOSEPARATION ENGINEERING
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Colloid mill
Rotor
Disrupted
cells
Cell
suspension
Stator
• Typical rotation speeds: 10,000 to 50,000 rpm
• Mechanism of cell disruption: High shear and turbulence
• Application: Tissue based material
• Single or multi-pass operation
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Separation of cells and medium
• Recovery of cells and/or medium
(clarification)
– For intracellular enzyme, the cell
fraction is required
– For extracellular enzymes, the culture
medium is required
• On an industrial scale, cell/medium
separation is almost always
performed by centrifugation
– Industrial scale centrifuges may be
batch, continuous, or continuous with
ERT 313/4 BIOSEPARATION ENGINEERING
desludging
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CENTRIF UGATION
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A centrifuge is used for separating particles from a
solution according to their size, shape, density and
viscosity of the medium by the application of an
artificially induced gravitational field.
In bioprocesses, these particles could be cells, sub
cellular components, viruses and precipitated forms
of proteins and nucleic acids.
Centrifugation can be used to separate cells
from a culture liquid, cell debris from a broth, and a
group of precipitates.
Centrifugation may be classified into two types:
•Analytical centrifugation
•Preparative Centrifugation
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Analytical centrifuges are used in laboratories for smallscale separation and sample preparations.
Typical liquid volumes handled is about 1 – 1000 ml.
Fig. below shows a simplified diagram of an analytical
centrifuge.
Tubes containing the samples are attached to a rotating
device and the centrifugal action drives the motion of
particles/precipitated large molecules towards the bottom
of the tube (sedimentation). Typical rotating speed is
<10000 rpm.
Supernata
Centrifuge
tube
nt
Precipitate
Rotor
ERT 313/4 BIOSEPARATION ENGINEERING
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Industrial centrifuges
Tubular Bowl Centrifuge
• Most useful for solid-liquid separation with
enzymatic isolation
• Can achieve excellent separation of
microbial cells and animal, plant, and most
microbial cell debris in solution
Disc Bowl Centrifuge
• Widely used for removing cells and animal
debris
• Can partially recover microbial cell debris
and protein precipitates
ERT 313/4 BIOSEPARATION ENGINEERING
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Perforate Bowl Basket Centrifuge
• Exception at separation of adsorbents,
such as cellulose and agarose
Zonal Ultracentrifuge
• Applied in the vaccine industry
because it can easily remove cell debris
from viruses
• Can collect fine protein precipitates
• Has been used experimentally to purify
RNA polymerase and very fine debris
in enzymes
ERT 313/4 BIOSEPARATION ENGINEERING
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Properties of industrial centrifuges
• Tube
– High centrifugal force – Limited solids capacity
– Good dewatering
– Difficult to recover protein
– Easy to clean
• Chamber
– Large solids capacity – No solids discharge
– Cleaning difficult
– Good dewatering
– Bowl cooling possible – Solids recovery difficult
• Disc type
– Poor dewatering
– Solids discharge
– Difficult to clean
– No foaming
– Bowl cooling possible
ERT 313/4 BIOSEPARATION ENGINEERING
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Centrifugation properties of different cell types
• Bacteria
– Small cell size
– Resilient
– High speed required
– Low cell damage
• Yeast cells
– Large cells
– Resilient
– Lower speed required
– Low cell damage
• Filamentous fungi
– Mycelial
– Resilient
– Lower speed required
– High water retention in pellet
• Cultured animal cells
– Large cells
– Very fragile
– Very susceptible to damage
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Forced Developed in Centrifugal Separation
1. Introductions
• Centrifugal separators use the common principal
that an object whirled about an axis or center
point a constant radial distance from the point is
acted on by a force
• The object is constantly changing direction and is
thus accelerating, even though the rotational
speed is constant
• This centripetal force acts in a direction toward
the center of rotation
ERT 313/4 BIOSEPARATION ENGINEERING
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Forced Developed in Centrifugal Separation
• In cylindrical container, the contents of fluid and
solids exert an equal and opposite force, called
centrifugal force, outward to the walls of the
container
• This cause the settling or sedimentation of
particles through a layer of liquid or filtration of a
liquid through a bed of filter cake held inside a
perforated rotating chamber
ERT 313/4 BIOSEPARATION ENGINEERING
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Forced Developed in Centrifugal Separation
FIGURE 1. Sketch of centrifugal separation:
(a) initial slurry feed entering,
(b)settling of solids from a liquid,
(c) separation of two liquid fractions.
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• In Fig. 1a a cylindrical bowl is shown rotating,
with a slurry feed of solid particles and liquid
being admitted at the center.
• The feed enters and is immediately thrown
outward to the walls of the container as in Fig.
1b
• The liquid and solids are now acted upon by
the vertical and the horizontal centrifugal forces
• The liquid layer then assumes the equilibrium
position, with the surface almost vertical
• The particles settle horizontally outward and
press against the vertical bowl wall
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• In Fig. 1c two liquids having
different densities are being
separated by the centrifuge
• The denser fluid will occupy the
outer periphery, since the
centrifugal force on it is greater
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Equations for centrifugal force
• In circular motion the acceleration due to the centrifugal force is
(1)
• The centrifugal force Fc in N (lbf) acting on the particle is given by
(2)
where gc = 32.174 lbm·ft /lbf•s2
• Since ω= v/r, where v is the tangential velocity of the particle in m/s
(ft/s)
(3)
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• Often rotational speeds are given as N (rev/min)
(4)
(5)
• Substituting Eq. (4) into Eq. (2),
(6)
• The gravitational force on a particle is
(a)
• In terms of gravitational force, the centrifugal force is:
(7)
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Example 1
A centrifuge having a radius of the bowl
of 0.1016 m (0.333 ft) is rotating at
N = 1000 rev/min.
a) Calculate the centrifugal force
developed in terms of gravity forces.
(b) Compare this force to that for a bowl
with a radius of 0.2032 m rotating at
the same rev/mm.
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Solution:
For part (a), r = 0.1016 m and N = 1000. Substituting into Eq. (7),
For part (b), r = 0.2032 m. Substituting into Eq. (7),
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