Introduction
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.

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

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

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:
(1)
• where V is the volume of filtrate, t is time, A is the cross-sectional area of exposed lilter medium,
Δ p is the pressure drop through the bed of solids (medium plus cake),
µ
0 is the viscosity of the filtrate, and R is the resistance of the porous bed. In this case, R is a combination of the resistance R m of the filter medium and the resistance R c of the cake solids:
(2)
• It is convenient to write the cake resistance R c in terms of specific cake resistance α as follows:
(3)
• where
ρ c is the mass of dry cake solids per volume of filtrate.
• Thus, the resistance increases with the volume filtered
• Combining Eq. (1), (2) and (3), we obtain
(4)

Filtration Principles
•
For the case of zero filtrate at time zero, integration of this equation yields
(5)
• This is a convenient form of the integrated equation
•
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
Δ p c
, the pressure drops across the cake
• Studies have shown that the relationship between specific resistance and pressure drop commonly takes the form:
(6)
• 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

Filtration Principles
Figure 2 Filtration data for Streptomyces griseus broth with Δ p = 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]

Example 1
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
R m
. 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 m 2 and vacuum pressure of
500 mm Hg.
TABLE E1

Example 1
According to Equation (5), we can plot t /( V / A ) versus V / A and obtain α from the slope and R m 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 R m
.
A linear regression of the data in this plot gives the following results (Figure E1):

Example 1
From these values, we can calculate α and R m
:
This is a typical value of R m for a large-pore (micrometer-sized) filter
.
To determine the time required to obtain 10,000 liters of filtrate using a filter with an area of 10 m 2 , 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:

Example 1
We calculate the two components of this equation as follows: and finally
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.

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 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:
(7)
• where R ’ is the weight fraction of solute remaining in the cake after washing (on the basis that R ’ = 1.0 prior to washing), E is the percentage wash efficiency, and n is the volume of wash liquid per volume of liquid in the unwashed cake.
• 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 V f to form the cake, this yields at the end of time t f
(8)

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

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

Example 2
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.
We can use the integrated form of the filtration equation, Equation (5), with R m
= 0:
We solve for A 2 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:

Example 2
We use this volume of filtrate with t = 15 s in the equation for A 2 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.

Example 3
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.
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 t w
, and the cake formation time t f is given by

Example 3 where f is the ratio of volume V r of residual liquid in the cake to the volume of filtrate V f after time t f
. Thus, we need to estimate the volume of residual liquid in the filter cake to determine t w
. 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.

Filter Media and Filter Aids
• The filter media must fulfill a number of requirements
• First and foremost, it must remove the solids to be filtered from the slurry and give a clear filtrate
• Also, 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 twill or duckweave heavy cloth, other types ot woven heavy cloth, wooded cloth, paper, felted pads of cellulose, metal cloth, nylon cloth, dacron cloth, and other synthetic cloths
• Certain filters aids may be used to aid filtration
• These are often diatomaceous earth or kieselguhr 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

Types of Filtration Equipment
•
•
•
•
•
•
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
The filtrate flows between the filter cloth and the face of the plate though the channels of the outlet
The filtration proceeds until the frames are completely filled with solids

Types of Filtration Equipment
• The leaf filter was developed for larger volumes of slurry and more efficient washing
• Each leaf is a hollow wire framework covered by a sack of filter cloth
• A number of these leaves are hung in parallel in a closed tank
• 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 filtrate flows inside the hollow framework and out a header
• 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

Types of Filtration Equipment
(a) continuous rotary vacuum-dryer filter
• This filter, filters, washes and discharges the cake in continuous, repeating sequence
• The drum is covered with a suitable filtering medium
• The drum 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
• This filter consist of concentric vertical disks mounted on a horizontal rotating shaft
• The filter 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
(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

Types of Filtration Equipment