1. Filtration

2. Learning objectives
Explain the basic types and mechanisms of filtration
Exploit the Darcy’s Law equation in order to solve problems for conventional and constant pressure cake filtration
Select filtration media and equipment to meet bioproduct processing requirement

3. Introduction
Filtration is a solid-liquid separation where the liquid passes through a porous medium to remove fine suspended solids.
The main objective of filtration is to produce high-quality drinking water (surface water) or high-quality effluent (wastewater) and also for biopharmaceutical products
Figure 1 Schematic diagrams for dead-end or
conventional filtration. For dead-end filtration the
thickness of the solids buildup increases and the
permeate flux decreases with time, ultimately
reaching zero.

4. Filtration
Filters use a filter cloth or some porous material along with
applied pressure to push smaller particles through the filter,
thus separating elements of the solution based on size.
Filtration for biological materials is generally completed using
batch filtration, rotary drum filtration, or ultrafiltration
methods.
Batch Filtration
Usually performed under constant pressure with a pump that moves the broth or liquor through the filter
Filter cake will build-up as filtration proceeds and resistance to broth flow will increase
The filter press is the typical industrial version of a batch vacuum filter, using a plate and frame arrangement
Can be used to remove cells, but does not work particularly well for animal cell debris or plant seed debris

5. Filtration Rotary Drum Filtration
Solution is vacuumed upward where it crosses a filter septum removed by a positive displacement pump
Filter cake is removed after each rotation to give a fresh surface for filtration
Rotary vacuum filters can be used to efficiently remove mycelia, cells, proteins, and enzymes, though a filter aid or precoat of the septum may be necessary
Ultrafiltration
Utilizes a membrane to separate particles that are much larger than the solvent used
Successful removal occurs in the partical size range of 10 solvent molecular diameters to 0.5 μ

6. Filtration Principles
When a slurry containing suspended solids flow against a filter medium by the application of a pressure gradient across the medium, solids begin to build up on the filter medium
The buildup of solids on the filter medium is called a cake
This type of filtration is sometimes referred to as “dead-end” filtration”
Darcy’s law describes the flow of liquid through a porous bed of solids and can be written as follows:
V: volume of filtrate, t: time, A: cross-sectional
area of exposed lilter medium, Δp: the pressure
drop through the bed of solids (medium plus cake),
µ0: the viscosity of the filtrate, R: resistance of
the porous bed.
(1)

7. Filtration Principles
In this case, R is a combination of the resistance Rm of the filter medium and the resistance Rc of the cake solids:
It is convenient to write the cake resistance Rc in terms of specific cake resistance α as follows:
Thus, the resistance increases with the volume filtered
Combining Eq. (1), (2) and (3), we obtain
(2)
ρc: mass of dry cake solids per volume of filtrate.
(3)
(4)

8. Filtration Principles
For the case of zero filtrate at time zero, integration of this equation yields:
The pressure drop is influence by α, the specific cake resistance
α can be increased if the cake is compressed
Cakes are typically compressible when cells and other biological materials are being filtered
The specific resistance of the cake is directly affected by Δpc, the pressure drops across the cake
(5)

9. Filtration Principles
Studies have shown that the relationship between specific resistance and pressure drop commonly takes the form:
where α’ and s are empirical constants.
The power s has been called the “cake compressibility factor” and has been found to range from zero for incompressible cakes such as sand and diatomite to near unity for highly compressible cakes
(6)

10. Filtration Principles
Figure 2 Filtration data for Streptomyces griseus broth with Δp = 2.0 bar. The filter medium was of cotton cloth, and diatomaceous earth filter aid was added
to the broth. (Data from S. Shirato and S. Esumi, “Filtration of a culture broth of Streptomyces griseus” J. Ferment, Technol. (Japan), vol. 41, p. 87, 1963.)
;1]

11. Example 1 Batch Filtration
A Buchner funnel 8 cm in diameter is available for testing the
filtration of a cell culture suspension, which has a viscosity of 3.0
cp. The data in Table E1 were obtained with a vacuum pressure
of 600 mm Hg applied to the Buchner funnel. The cell solids on
the filter at the end of filtration were dried and found to weigh
14.0 g. Determine the specific cake resistance α and the medium
Resistance Rm. Then estimate how long it would take to obtain
10,000 liters of filtrate from this cell broth on a filter with a surface
area of 10 m2 and vacuum pressure of 500 mm Hg.

12. Example 1
TABLE E1

13. Example 1
Solution
According to Equation (5), we can plot t/(V/A) versus V/A and
obtain α from the slope and Rm from the intercept. We see that the
data are reasonably close to a straight line.
Figure E1 Plot of batch filtration data for the determination of α and Rm.

14. Example 1 A linear regression of the data in this plot gives the
following results (Figure E1):

15. Example 1 From these values, we can calculate α and Rm:
This is a typical value of Rm for a large-pore
(micrometer-sized) filter.

16. Example 1
To determine the time required to obtain 10,000 liters of filtrate
using a filter with an area of 10 m2, we must make the assumption
that α does not change at the new pressure drop of 500 mm Hg.
We use Equation (5) and solve for time:
We calculate the two components of this equation as follows:
and finally

17. Example 1 Thus, this filter is probably undersized for the
volume to be filtered. In addition, from this
calculation we see that at the end of the filtration,
Therefore, the filter medium is contributing very
little of the resistance to filtration, a typical
situation in a lengthy dead-end filtration.

18. Filtration Principles
For products that are recovered in the filtrate, it is often necessary to wash the filter cake with water or a salt solution to maximize the removal of dissolved product from the cake.
Frequently, the wash must be done with more than the volume of the liquid in the cake
This is because some of the product is in stagnant zones of the cake, and transfer into the wash liquid from these zones occurs by diffusion, which takes place at a slower rate than the convective flow of wash through the cake
Data for the washing of the filter cakes has been correlated by Choudhary and Dahlstrom using the following equation:
R’: weight fraction of solute remaining in the cake
after washing (on the basis that R’ = 1.0 prior to
washing), E: percentage wash efficiency, and
N: volume of wash liquid per volume of liquid in
the unwashed cake.
(7)

19. Filtration Principles
Assuming that the liquid viscosity and the pressure drop through the bed solids are the same during the filtration of the solids, the washing rate per cross-sectional area can be found from the filtrate flow rate per unit area given in Equation (4) at the end of the filtration
Thus, for negligible filter medium resistance for filtrate volume Vf at the end of time tf to form the cake, this yields
(8)

20. Filtration Principles
If Vw is the volume of wash liquid applied in time tw, then
Using the definition of (dv/dt)V=Vf from Eq. (8), we obtain
At the end of filtration, the integrated form of the filtration equation (Eq. 5), with Rm neglected, can be written
Substituting this expression for Vf/A in Eq. (10) and simplifying gives
(9)
(10)
(11)
(12)

21. Filtration Principles
From Eq. (11) and (12), the ration of tw to tf is
It is helpful to write tw/tf in terms of n, the ration of the volume Vw of wash liquid to the volume Vr of residual liquid in the cake:
where f is the ratio of Vr to the volume Vf of filtrate at the end of filtration.
The ratio f can be determined by a material balance
Thus, for a given cake formation time tf, a plot of wash time tw versus wash ratio n will be a straight line
(13)
(14)

22. Example 2 Rotary Vacuum Filtration
It is desired to filter a cell broth at a rate of 2000 liters/h
on a rotary vacuum filter at a vacuum pressure of 70
kPa. The cycle time for the drum will be 60 s, and the
cake formation time (filtering time) will be 15 s. The broth
to be filtered has a viscosity of 2.0 cp and a cake solids
(dry basis) per volume of filtrate of 10 g/liter. From
laboratory tests,the specific cake resistance has been
determined to be 9 x 10 cm/g. Determine the area
of the filter that is required. The resistance of the filter
medium can be neglected.

23. Example 2
Solution
We can use the integrated form of the filtration equation, Equation
(5), with Rm = 0:
We solve for A2 to obtain
In applying this equation, it is helpful to focus on the area of the
drum that is submerged, which is where the cake is being formed
and where filtrate is being obtained. Thus, A is the area of that
part of the drum that is submerged. We can calculate the volume
of filtrate that needs to be collected during the cake formation time
of 15 s:

24. Example 2
We use this volume of filtrate with t = 15 s in the equation for A2 to
obtain
The area A’ of the entire rotary vacuum filter can be calculated
from the cake formation time and the total cycle time as
This is a medium-sized rotary vacuum filter, with possible
dimensions of 1.0 m diameter by 1.0 m long.

25. Washing of a Rotary Vacuum Filter Cake
Example 3
Washing of a Rotary Vacuum
Filter Cake
For the filtration in Example 2, it is
desired to wash a product antibiotic out
of the cake so that only 5% of the
antibiotic in the cake is left after
washing. We expect the washing
efficiency to be 50%. Estimate the
washing time per cycle that would be
required.

26. Example 3
Solution
From Equation (7) for the washing efficiency of a filter cake
where R’ is the weight fraction of solute remaining in the cake
after washing (on the basis of R’ = 1.0 before washing), E is the
percentage wash efficiency, and n is the volume of wash liquid
per volume of liquid in the unwashed cake. Substituting R’ =
0.05 and E = 50% into this equation gives
From Equation (14), the relationship between the washing time
tw, and the cake formation time tf is given by
where f is the ratio of volume Vr of residual liquid in the cake to
the volume of filtrate Vf after time tf.

27. Example 3
Thus, we need to estimate the volume of residual liquid in the filter
cake to determine tw. At the end of the 15 s cake formation time,
Assuming the cake is 70 wt% water, which is typical for filter
cakes, we find
Thus,
From this result, the estimated washing time is 20% of the cake
formation time.

28. Filter Media and Filter Aids
The filter media must remove the solids to be filtered from the slurry and give a clear filtrate
The pores should not become plugged so that the rate of filtration becomes too slow
The filter medium must allow the filter cake to be removed easily and cleanly
Some widely used filter media are woven fabrics (e.g. woven heavy cloth, glass cloth, etc, no leaching of components are allowed, size of particle trapped: 10 μm), metal fabrics or screens (e.g. nickel,copper, etc, good resistance to leachingand corrosion required, size of particle trapped: 5 μm), and rigid porous media (e.g. sintered stainless steel, silica, pocelain, etc)
For sterile filtration, commonly used are asymmetric membrane filter (cellulose esters or other polymers, pore size: μm)

29. Filter Media and Filter Aids
Certain filters aids may be used to aid filtration
Can be either added directly to the feed or applied to the filtration equipment
These are often diatomaceous earth or kieselguhr and perlite which is composed primarily of silica.
Also used are wood cellulose and other inert porous solids
Can be use as a precoat before the slurry is filtered to prevent gelatinous-type solids from plugging the filter medium and also give clearer filtration
Can also be added to the cake during filtration to increases the porosity of the cake and reduces resistance of the cake during filtration

30. Types of Filtration Equipment
Plate-and-frame filter presses
Consist of plates and frames assembled alternately with a filter cloth over each side of the plates
The plates have channels cut in them so that clear filtrate liquid can drain down along each plate
The feed slurry is pumped into the press and flows through the duct into each of the open frames so that slurry fills the frames
The filtrate flows through the filter cloth and the solids build up as a cake on the frame side of the cloth

31. Types of Filtration Equipment
2. Leaf filters
Developed for larger volumes of slurry and more efficient washing
Each leaf is a hollow wire framework covered by a sack of filter cloth
The slurry enters the tank and is forced under pressure through the filter cloth, where the cake deposits on the outside of the leaf
The wash liquid follows the same path as the slurry. Hence, the washing is more efficient than the through wishing in plate-and-frame filter presses

32. Types of Filtration Equipment
3. Continuous rotary filters
(a) continuous rotary vacuum-dryer filter
Filters, washes and discharges the cake in continuous, repeating sequence
covered with a suitable filtering medium
rotates and an automatic valve in the center serves to activate the filtering, drying, washing, and cake-discharge functions in the cycle
The filtrate leaves through the axle of the filter
(b) continuous rotary disk filter
consist of concentric vertical disks mounted on a horizontal rotating shaft
operates on the same principle as the vacuum rotary-drum filter
Each disk is hollow and covered with a filter cloth and is partly submerged in the slurry
The cake is washed, dried and scraped off when the disk is in the upper half of its rotation

33. Types of Filtration Equipment
(c) continuous rotary horizontal filter
This type is a vacuum filter with the rotating annular filtering surface divided into sectors
As the horizontal filter rotates, it successively receives slurry, is washed, is dried and the cake is scraped off