This document discusses filtration and cake filtration principles. It begins by defining filtration and the mechanisms involved. It describes cake filters and how a filter cake forms on the filter medium. The key principles of cake filtration are that resistance increases over time as the cake builds up, requiring either decreasing flow rate or increasing pressure drop to maintain flow. The pressure drop comes from both the filter medium and the cake. Parameters like flow rate, pressure drop, and cake thickness are important to cake filtration.

1. Mechanical Unit Operations
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Week 8 : Filtration
L-25 Filtration
L-26 Principles of cake filtration
L-27 Principles of cake filtration 2
L-28 Filtration equipment
Prof. Nanda Kishore
Professor, IIT Guwahati

2.  Filtration
 Filtration mechanism
 Cake filters
 Filter media and filter aid
 Principles of cake filtration
Principles of centrifugal filtration
 Types and selection of equipment
Outline of discussion
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Filtration
 It is separation of solids from a suspension by passing it through a porous filtering
medium or septum on which solids are deposited whereas fluid passes through
 Filtration is the separation process of solid particles from liquids through a solid
support (or) filter medium.
Mechanism of filtration
Slurry: The suspension of solid and liquid to be filtered.
Filter medium: The porous medium used to retain the solids.
Filter cake: The accumulation of solids on the filter medium.
Filtrate: The clear liquid passing through the filter and collected in the receptor.

4.  In order to have efficient filtration process, the feed is generally modified by pre-
treatment such as
 Heating
 Recrystallizing
 Adding a filter aid, etc.
 Many types of filters have been developed because of variety of duties to be
performed by filters
 such as different types of materials to be filtered
 widely differing process conditions, etc.
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5.  Fluid flows through a filter medium because of a pressure differential across the
medium. Thus, filters are classified as
Operating with atmospheric pressure on upstream side of filter medium
Operating with atmospheric pressure on upstream side and a vacuum on
downstream side of medium
 Higher pressures above atmospheric pressure may be developed by the force of
gravity acting on a column of liquid or by a pump or blower or by centrifugal force
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6.  Gravity filters: Filter medium can be no finer than a coarse screen or a bed of
coarse particles like sand
 Thus in industrial applications, they are restricted to
 draining of liquor from very coarse crystals,
 clarification of potable water,
 treatment of wastewater, etc.
 Industrial filters are generally batch or continuous type which, based on applied
force for filtration, can be classified as:
 Pressure filters
 Vacuum filters
 Centrifugal separators
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7.  Discontinuous filter: during operating cycle, flow of fluid through
the device is continuous, however, it is interrupted periodically to
permit discharging of accumulated solids
 Continuous filter: discharge of both solids and fluid is
uninterrupted as long as equipment is in operation
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Filtration Mechanism
 Based on separation mechanism, filters are divided into three
main groups
1. Cake filters
2. Clarifying filters
3. Cross flow filters

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Cake filters
Relatively large amounts of solids as a cake of crystals or sludge are separated by
cake filters
They include provisions for washing cake and removing some of liquid from solids
before discharge

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Clarifying filters
They remove small amounts of solids
to produce a clean gas or sparkling
clear liquids such as beverages
Particles are trapped inside filter
medium or on its external surface
Pores of filter medium are much larger
in diameter than particles to be
removed unlike the screens

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Cross flow filters
Feed suspension flows under pressure at a fairly
high velocity across the filter medium in cross
flow filters
Thin layer of solids may form on the surface of
medium but high liquid velocity do not allow it
to build up
Ceramic, metal or polymer membrane with
pores small enough to exclude most of
suspended particles are used as filter medium
Portion of liquid passes through medium as clear
filtrate, leaving a more concentrated suspension
as retentate

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Filtration Mechanism

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Filter media
 In industrial applications, a common filter medium is canvas cloth
 Wooden cloth, metal cloth, glass cloth or paper cloth are used as filter media for
corrosive liquids
 Synthetic fabrics such as nylon, polypropylene, and various polyesters can also be
used as chemically resistance filters
 Filtrate may first come through as turbid or cloudy, then gradually clear filtrate
obtained Then cloudy filtrate is returned to the slurry tank for refiltration
Categories of material used as filter media
Woven material
Perforated sheet metal
Bed of granular solid built up on supporting medium
Prefabricated porous solid units
Membrane filter media

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Requirements of septum
 Retain solids to be filtered and provide acceptable clean filtrate
 Should not plug or blind
 Should be chemically resistant and strong enough physically to withstand the process conditions
 Should permit cake formed to discharge cleanly and completely
 Should not be prohibitively expensive
It should-
1) be capable of delivering a clear filtrate at a suitable production
rate.
2) have sufficient mechanical strength.
3) be inert.
4) retain the solids without plugging at the start of filtration.
5) Not absorb dissolve material.
6) Sterile filtration imposes a special requirement since the pore size must not exceed the
dimension of bacteria or spores.

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Filter aids
 Very fine or slimy solids often form a dense impermeable cake that can quickly plug
any filter medium that is fine enough to retain such fines
 Feasible filtration of such solids require that porosity of cake be increased to
permit passage of liquor at a reasonable rate
 It can be accomplished by adding a filter aid (which is inert) to slurry before start of
filtration
Ex. Diatomaceous silica, perlite, purified wood cellulose, or any other inert porous
solid which can enhance filtration rate
 Subsequently filter aid may be separated from the filter cake by dissolving the
solids or by burning out the filter aid
 If the solids have no value, then both solids and filter aid can be discarded

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Handling of filter aids
Filter aids may be used in either or both two ways:
1) Pre- coating technique: by forming a pre-coat over the filter medium by filtering a
suspension of the filter aid.
2) Body- mix technique: A small proportion of the filter aid (0.1- 0.5 %) is added to the
slurry to be filtered. This slurry is recirculated through the filter until a clear filtrate is
obtained, filtration then proceeds to completion.
Different flow rates can be achieved depending on grade of
aid-
1. Low flow rate: fine grade filter aids- mainly used for clarity
2. Fast flow rate: coarse grade filter aids- acceptable filtrate.
Examples of filter aids
Diatomite (Keiselgur) , obtained from natural siliceous deposits.
Perlite , it is an aluminium silicate. Cellulose, Asbestos, charcoal, talc, bentonite, fullers
earth etc.

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Principles of cake filtration
 Principles are analogous to the case of flow through porous media or packed or fixed
beds (where resistance to flow is independent of time)
 In cake filtration, resistance to flow increases with time as filter medium becomes
clogged or filter cake builds up
Thus, Ergun’s equation should be modified accordingly
 Important parameters of interest are
flow rate through the filter and
pressure drop across the unit
 As the time of filtration increases, gradually either
flow rate decreases or
pressure drop increases

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 In constant pressure filtration, the pressure drop is held constant and the flow rate
allowed to fall with time
 In constant rate filtration, pressure drop is progressively increases to give constant
filtration rate (this is very rare)
 In cake filtration, the liquid passes through two resistance in series
•Resistances because of formation of cake
•Resistance of filter medium
 Filter medium resistance is normally important only during the early stages of cake
filtration
 Cake resistance is zero at the start of the filtration and increases with time as
filtration proceeds
 If cake is washed after it is filtered, both resistances are constant during the
washing period; and that of the filter medium is usually negligible

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Pressure drop in Cake filtration
Overall pressure drop at any time is sum of pressure drops over
medium and cake
Let pa is inlet pressure, pb is outlet pressure and P’ is pressure at
boundary between cake and medium, then
overall pressure drop (∆p) = pa– pb
= (pa – p’) + (p’ – pb)
= ∆pc+ ∆pm
Where ∆pc and ∆pm are pressure drop over the cake and medium
Consider a thin layer of cake of thickness dL lying in the cake at a
distance L from filter medium and corresponding pressure at this layer
is p
This layer consists of thin bed of solid particles through which filtrate
is flowing
In this filter bed, the velocity is sufficiently low to ensure laminar flow

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 In constant pressure filtration, the pressure drop is held constant and the flow rate
allowed to fall with time
 In constant rate filtration, pressure drop is progressively increases to give constant
filtration rate (this is very rare)
 In cake filtration, the liquid passes through two resistance in series
•Resistances because of formation of cake
•Resistance of filter medium
 Filter medium resistance is normally important only during the early stages of cake
filtration
 Cake resistance is zero at the start of the filtration and increases with time as
filtration proceeds
 If cake is washed after it is filtered, both resistances are constant during the
washing period; and that of the filter medium is usually negligible

21. For the derivation of equation of pressure drop, Kozeny-Carmann equation for low
Reynolds numbers:
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22. Incompressible cake
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Filter cake of this type are called incompressible
i.e., resistance is independent of pressure drop, ∆p and of position, L
where 𝛂 is specific cake resistance

23. Compressible cake
 Industrial slurries are mixture of agglomerates or flocsconsisting of loose assemblies of very small
particles
Resistance of such cakes depends on properties of flocs rather than on geometry of individual
particles (experimental observation)
Resistance of such a cake is sensitive to method used in preparing slurry and to age and
temperature of material. And such filtration cake is called as compressible filter cake
 In such a compressible cake, specific cake resistance varies with distance from septum
 Because cake nearest to the septum is subject to the greatest compressive force and has the
lowest void fraction. This makes the pressure gradient non-linear
 Local value of αmay also very with time
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Empirical equation for cake resistance
 By conducting constant pressure experiments at various ∆p, the variation of α with
∆p can be found
 If αis independent of ∆p, the cake is called to be incompressible
 In general, α increases with ∆pas most cakes are compressible at least to some
extent
 For highly compressible cakes α increases rapidly with ∆p
α= αo(∆p)S
where αo and S are empirical constants
 Here S is the compressibility coefficient of the cake
If S = 0, it is incompressible cake
S > 0, it is compressible cake (usually varies between 0.2 and 0.8)

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Principles of centrifugal filtration
 Basic constant pressure filtration theory can be modified to apply to centrifugal
filtration
 This theory applies after the cake has been deposited and during flow of clean
filtrate or fresh liquid through the cake
 Assumption
 Effects of gravity and of changes in kinetic energy of liquid are neglected
 Pressure drop from centrifugal action equals the drag of the liquid flowing through
the cake
 Cake is completely filled with liquid
 Flow of liquid is laminar
 Resistance of the filter medium is constant
 Cake is nearly incompressible, i.e., average specific cake resistance can be used as
constant

26.  Nomenclature
• r1 = radius of inner surface of liquid
• ri = radius of inner face of cake
• r2 = inside radius of basket
• b = height of the basket
• ω = angular velocity, rad/s
• q = volumetric flow rate of liquid
• ρ = density of liquid
 Pressure drop from centrifugal action is
given by:
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Types of filtration equipment
 Plate and Frame filters
 Leaf filters
 Rotary vacuum filters
 Cross flow filtration
Rotary vacuum filters and cross flow filtration are continuous filtration
equipment.

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Selection of equipment
 Properties of filtrate, particularly viscosity and density.
 Nature of the solid particles, particularly their size, shape and size distribution and
packing characteristics.
 Solid to liquid ratio
 Need for recovery of solid or liquid.
 Need for batch or continuous operation.

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Plate and frame filter press

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Centrifugal filter

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Rotary vacuum drum filter

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[1] D.W. Green, R.H. Perry, Perry’s Chemical Engineers’ Handbook, 8th Ed., McGraw Hill, 2007.
[2] W.L. McCabe, J. Smith and P. Harriot, Unit Operations of Chemical Engineering, 7th Ed., McGraw
-Hill, International Edition, 2005.
[3] E. Ortega-Rivas, Unit Operations of Particulate Solids: Theory and Practice, CRC Press, FL, 2012.
[4] J.F. Richardson, J.H. Harker, Coulson and Richardson’s Chemical Engineering, 2nd Volume, 5th
Ed., Butterworth-Heinemann, 2003.
[5] C.J. Geankoplis, Transport Processes and Unit Operations, 4th Ed., Prentice Hall, India, 1993.
[6] G.G. Brown et al., Unit Operations, 1st Ed., CBS Publishers & Distributors, 2005.
[7] W. L. Badger and J. T. Banchero, Introduction to Chemical Engineering, Tata McGraw-Hill,
International Edition, 1997.
Books and references

33. Thank You
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Bhavikkumar Mahant: ch19d752@smail.iitm.ac.in