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A SEMINAR ON COMPACTION
AND COMPRESSION
Presented by
Dharmendra chaudhary
M.Pharm-1st Year
Dept. of Pharmaceutics
N.E.T college of pharmacy

COMPACTION AND COMPRESSION
 Compaction of powder is the term used to describe a
situation in which these material are subjected to some
level of applied mechanical force over the powdered
solids.
 Hence compaction can be defined as “the compression
and consolidation of a two phases (particulate solid –gas)
system due to an applied force “.
 Compression is a reduction in bulk volume of the material
as a result of displacement of gaseous phase .
 Consolidation is an increase in the mechanical strength
of the material resulting from particle-particle interaction.

Derived Properties of Powders or Granules: Some derived
properties which help in quantification of imp. variables are
 Volume
 Density
 Porosity
 Flow properties.
Volume:
 Measurement of volume of powder is not easy as the
measurement of mass of powders ,because in powders there will
be inter and intra- particular voids . Hence three types of volume
can be considered for a powdered mass, they are,
 True volume
 Granular volume
 Bulk volume

 True Volume of the powder (vp): It is a volume of the particles
excluding the inter and intra particulate spaces in a powder or it is
volume of powder itself
 Granular Volume of the powder(Vg): It is a volume of the particles
including intra particulate voids or it is the volume of powder itself
and volume of intra particulate spaces.
 Bulk Volume of the powder(Vb): comprises the true Volume and inter
and intra particulate voids or it is volume of powder itself and volume
of intra and inter particle spaces.

DENSITY
 Density (q); it is the ratio of weight to volume of substance. By
considering the three types of volume of powders, we can define the
respective densities as,
 True density: Mass of the powder/ True volume of the powder.
 Granular density: Mass of the powder/ granule volume of the powder.
 Bulk density: It is the ratio of total mass of the powder to the bulk
Volume of the powder. It is measured by pouring the weighed powder
into a measuring cylinder and the volume is noted.
 It is expressed in gm/ml and is given by
Db = M/Vo.
 Where , M is the total mass of the powder
Vo is the Bulk Volume of the powder

POROSITY
 Porosity: The space b/w the particles in a powder are known to be
voids. The volume occupied by such voids is known to be void
volume.
Void volume (v) = bulk volume –True volume
 The porosity of the powders is defined as ratio of the void volume to
the bulk volume of the of the packing.
Porosity = void volume /bulk volume.
=V/Vb
=[vb-vp/vb]
 Porosity is frequently expressed in percent
=[1-vp/vb] x 100
The relation b/w porosity and compression is important
because porosity determines the rate of disintegration, dissolution
and drug absorption.

FLOW PROPERTIES
 To get uniformity of the weight of the tablet, the powder should
possess a good flow property. Flow properties of the powders
depend on the-
 Particle size,
 Shape,
 Porosity and density,
 Moisture of the powder.
Particle size:The rate of flow of powder is directly proportional to the
diameter to the particles.
 Beyond particular point, flow properties decreases as the particle
size in increases. Because in small particle (10µ) the vanderwaal’s ,
electrostatic and surface tension forces causes cohesion of the
particles resulting poor flow .

 As the particle increases, influence of gravitational force on the
diameter increases the flow property. But appropriate blends of fines
& coarses improves flow characteristic, as the fines get absorbed
and coarse particle reduce friction.
Particle shape:
Spherical, smooth particles improves flow properties, surface
roughness leads to poor flow due to friction and cohesiveness , flat
and elongated particles tend to pack loosely, obstructing the flow
Density & porosity:
Particles having high density and low internal porosity tend to posses
good flow properties.
Moisture:
The higher moisture content, the flow property will be poor owing to
cohesion and adhesion.

ANGLE OF REPOSE
The flow characteristic are measured by angle of repose . Angle of
repose is defined as the maximum angle possible b/w the surface of
a pile of powder and the horizontal plane.
tanØ= h/r
Ø = tan-1(h/r)
Where, h = height of pile
r =Radius of the base of pile.
Ø = Angle of repose .
 The angle of repose is calculated by measuring the height and radius
of heap of powder formed.
 The frictional forces in a loose powder can be measured by Angleof
repose.
 The lower the angle of repose, better will be flow property.
 The values of angle of repose are given below:

ANGLE OF REPOSE
Angle of repose (in
degrees)
Type of Flow
<25
25-30
30-40
>40
Excellent
Good
Passable
Very poor

CARR’S CONSOLIDATION INDEX
 It indicates powder flow properties. It is expressed in percentage.
 It is defined as:
Consolidation Index = I = Tapped density-Poured density /
Tapped density
Therefore = Dt- Db/Dt x 100
 Where, Dt is the tapped density of the powder
Db is the Poured density of the powder
Determination of Tapped density & Poured density.
 It is determined by passing a fixed quantity of powder into a
measuring cylinder and the volume is noted .
 CI can be calculated by founding out by tapped density and Poured
density of powder.

 Grading of the powder for their flow properties according toCarr’s
index:
 Carr’s index(%)
5-15
Type of flow
Excellent
12-18 Good
18-21 Fair to passable
23-35 Poor
33-38 Very poor
>40 Very very poor

COMPRESSION PROPERTIES
This involves compressibility and compactability .
 Compressibility can be defined as the ability of a powder to
decease in volume under pressure.
 Powders are normally compressed into tablets using a pressure of
about 5.0kg/cm2. The process is called compaction & compression.
 Compactability can be defined as ability of powder to be
compressed in to a tablet of a certain strength or hardness.
 These two relate directly to the tabletting performance.
 For proper compression to occur the tablet should be plastic
i.e., capable of permanent deformation and it should also exhibit
certain degree of brittleness.

 Acc. If the drug is plastic , then the excipients chosen should be
brittle (lactose, calcium phosphate) and if the drug is brittle, then the
excipients should be plastic (Microcrystalline cellulose).
 Plastic material: when materials are ductile they deform by
changing the shape, since no fracture , no new surface are
generated during compression, which leads to poorer bonding.
Increase the dwelling time at compression will increase bonding
strength.
 Elastic material:
Some materials, paracetamol is an example and there is very little
permanent change caused by compression: the material rebounds
when compression load is released.
If the bound is weak, the compact will self-destruct and the top will
detach (capping) or the whole cylinder cracks into horizontal layers
(lamination).

PROCESS OF COMPRESSION
In pharmaceutical tabletting an appropriate volume of granules in a die
cavity is compressed b/w an upper & lower punch to consolidate the
material in to a single solid matrix, which is subsequently ejected from
the die cavity as an intact tablet. The subsequent events that occur in
the process are:
1.Transitional repacking.
2.Deformation at the point of contact.
3.Fragmentation .
4.Bonding.
5.Deformation of the solid body.
6.Decompression.
7.Ejection.

TRANSITIONAL REPACKING OR PARTICLE
REARRANGEMENT
 The particle size distribution and shape of granule determines initial
packing. In the initial stages of compression, the punch and particle
movement occur at low pressure.
 During this particle move with respect to each other & smaller
particles enter the voids b/w the larger particles. As a result the
volume decreases and bulk density of granulation increases.
 Spherical particles undergo less rearrangement than irregular
particles as spherical particle tend to assume a close packing
arrangement initially.
 To achieve a fast flow rate required for high speed presses the
granulation is generally processed to produce spherical or oval
particles; thus, particle rearrangement and energy expended in
rearrangement are minor consideration in the total process of
compression.

DEFORMATION AT THE POINT OF CONTACT
 When a stress is applied to a material, deformation(change of form)
occurs. If the deformation disappears completely (returns to original
state) upon the release of stress, it is an elastic deformation. If the
deformation that does not completely recover after release of stress
is known as plastic deformation.
 The force required to initiate plastic deformation is known as yield
stress. When the particles of the granulation are so closely packed
so that no further filling of the void can occur, a further increase of
compressional force causes deformation at the point of contact.
 Both plastic and elastic deformation may occur although one type
predominates for a given material.
 Deformation increases the area of true contact and formationof
potential bonding areas.

2compactionncompression 140214012446-phpapp01 (1)-converted

FRAGMENTATION
 As the compressional load increases the deformed particle starts
undergoing fragmentation. Because of the high load, the particle
breaks into smaller fragments leading to the formation of new
bonding areas. The fragments undergo densification with infiltration
of small fragments into voids.
 In some materials where the shear stress is greater than thetensile
strength, the particles undergo structural break down. This iscalled
brittle fracture.
Example: sucrose – shear strength is greater than the tensile
strength.
 With some materials fragmentation does not occur because the
stresses are relieved by plastic deformation. Plastic deformation may
be thought of as a change in particle shape and as the sliding group
of particles in an attempt to relieve stress(viscoelastic flow). Such
deformation produces new, clean surface that are potential bonding
areas.
 Irrespective of behavior of large particles, small particles may deform
plastically, a process known as microsquashing, and the proportion
of fine powder in a sample may therefore be significant.

BONDING AND CONSOLIDATION
 The hypothesis favoring for the increasing mechanical strength of a
bed of powder when subjected to rising compressive forces can be
explained by the following theory.
I. Mechanical theory
II. Intermolecular theory
III. Liquid-Film surface theory
 Mechanical theory: During compression the particles undergoes
elastic,plastic or brittle deformation and the edges of the particle
intermesh, forming a mechanical bond.
 If only mechanical bond exists, the total energy of compression is
equal to the sum of energy for deformation, heat, and energy
absorbed for each constituent.
 Mechanical interlocking is not a major mechanism.

 Intermolecular theory: The molecules at the surface of a solid have
unsatisfied intermolecular force( surface free energy), which interact
with other particles in true contact.
 Absolutely clean surface will bond with the strength of the crystalline
material, whereas adsorbed materials restrict bondings.
 According to this theory, under pressure the molecules at the point of
contact b/w new, clean surfaces of the granules are close enough to
each other (separation by 50nm) so that the van der Waals force
interact to consolidate the particles.
A MCC tablets are compressed close enough together so that
H-bonding b/w them occurs. It appears that a very little compression
or fusion occurs in compression of MCC. Although aspirin crystal
undergo slight deformation at low pressure, it appears that H-
bonding has strongly bonded the tablets, because the granules
retain their integrity with further increase in pressure.

 Liquid-surface film theory:Thin liquid films form which bond the
particles together at the particle surface. The energy of compression
produces melting or solution at the particle interface followed by
subsequent solidification or crystallization thus resulting in the
formation of bonded surfaces. Due to the applied pressure, the
particles may melt (due to lowering of M.pt.) or dissolve (due to
increased solubility). As the pressure is released, solidification and
crystallization occur.
 The intermolecular forces theory and the liquid-surface film theory
are believed to be the major bonding mechanisms in tablet
compression.
 Many pharmaceutical formulations require a certain level of residual
moisture to produce high quality tablets. The role of moisture in the
tableting process is supported by the liquid-surface film theory.

DEFORMATION OF SOLID BODY
As the applied pressure is further increased, the new bonded
solid is consolidated towards a limited density by plastic &/or
elastic deformation within the die.

DECOMPRESSION
 The success or failure to produce an intact tablet depends on the
stress induced by elastic rebound and the associated deformation
process during compression and ejection.
 As the upper punch is withdrawn from the die, the tablet is confined
in the die by radial pressure. Consequently any dimensional change
during decompression must occur in axial direction.
 As the movement of tablet is restricted by the residual die wall
pressure and the friction within the die wall, the stress from the axial
elastic recovery and the radial contraction causes splitting (capping)
of tablet unless the shear stress is relieved by plastic deformation.
 Thus capping is due to uniaxial relaxation, in the die cavity at the
point where the upper punch pressure is released & some mayalso
occur at ejection. It has been demonstrated that if decompression
occurs simultaneously in all directions, capping is reduced or
eliminated.

 Stress relaxation of plastic deformation is time dependent. Materials
having slow rate of stress relaxation crack in the die upon
decompression. The rate of stress relieve is slow for acetaminophen
so cracking occurs within the die whereas with MCC the rate is rapid
and hence intact tablet result.
 A slower operational speed provides more time for stress relaxation
and hence can prevent cracking.
 A tablet press that provides precompression allows some stress
relaxation before final compression.
 Shape of tablet may be selected to reduce stress gradient within the
tablet. In deep oval punches the material in dome expand radially,
but main body of tablet cannot expand radially instead is constrained
by the die wall, large shear stress develop. Flat faced punches can
be used to reduce stress gradient.

EJECTION
 As the lower punch raises & pushes the tablet upward there is a
continued residual die wall pressure and considerable energy may
be expanded due to die wall friction.
 As the tablet is removed from the die, the lateral pressure is
relived, and the tablet undergoes elastic recovery with an increase
(2-10%) in the volume of that portion of the tablet removed fromthe
die.
 During ejection that portion the tablet with in the die is under
strain, and if exceeds the shear strength of the tablet, the tabletcaps
adjacent to the region in which the strain had just removed.

FORCE INVOLVED IN COMPRESSION AND
FACTORS AFFECTING HARDNESS OF TABLET
Presented by
Dharmendra chaudhary
M.Pharm-1st Year
Dept. of Pharmaceutics
N.E.T college of pharmacy

FORCES INVOLVED IN COMPRESSION
Forces, which influence the compaction of granules.
Force distribution:
 The fundamentals of tabletting have been carried out on single-station
press or even on isolated punch & punches with hydraulic press.
 When force is being applied to top of a cylindric powder mass, the
following basic relationship applies, since there must be an axial
(vertical) balance of forces.
 the system is represented diagrammatically .
FA= FL + FD
Where,
FA = force applied to upper punch
FL = proportion of FA force transmitted to lower punch,
FD =reaction at the die wall due to friction at the surface

 Because of this inherent difference b/w the force applied at the upper
punch & that affecting material close to the lower punch, a mean
compression force applied is given by :
FM= FA + FL
2
 Fm gives practically friction independent measure of compaction load
which is more relevant than FA.
(i.e. FL= FA.e –
 In single statiokh
n/d
press applied force transmission decays exponentially
)to over come this, appropriate geometric force FG
might be used,
FG= FAx FL
Use of these parameters are more appropriate than FA when determining
relationship b/w compression force and tablet properties like tablet
strength.

DEVELOPMENT OF RADIAL FORCE ( FR)
 As the compression force is increased and any repacking of the
tabletting mass is completed, the material may be regarded to some
extent as a single solid body.
 When compressive force is applied in one direction (vertical) results
in the decrease in height (ΔH) but in case of unconfined solid
body, this would be accompanied by an expansion in the horizontal
direction of ΔD. The ratio of these two dimensional changes isknown
as poission ratio(λ) of the material, defined as:
λ = ΔD/ΔH
 The Poisson ratio is characteristic constant for each tablet.
 Under the condition like compression the material is not free to
expand in horizontal plane bcoz its confined to die. Consequently, a
radial die-wall force FR develops perpendicular to die wallsurface.
 Material with high Poisson ratio give higher FR value.

 Classical friction theory can be applied to obtain a relationship
b/w axial frictional force FD and radial force FR as;
FD =µw.FR
where, µw is coeff. of die wall friction.
 Frictional effect represented by, µw arises from shearing of
adhesions that occurs as the particles slide along the die wall. Its
magnitude is related to shear strength S and effective area of
cntct Ae b/w twosurfaces.
 Force transmission is maxm when FD is minimum which is
achieved by adequate lubrication of die wall(lower S) and
maintaining minm tablet ht.(reducing Ae ).
 Degree of lubrication is compared to measure FA &FD and
determine ratio of FL/FA. This is called the coeff. of lubrication
efficeincy or R value.
 It approaches1 for perfect lubrication, and in practice as high as
0.98 may be achieved.Values below0.8 indicate poor lubrication.

EJECTION FORCES
 Radial die forces & die wall friction also affect the ease with which
the compressed tablet can be removed from the die. Theforce
necessary to eject a finished tablet follows a distintictive pattern of
three stages.
 The first stage involves distinctive peak force required to initiate
ejection, by breaking of tablet/die wall adhesions.
 A smaller force usually follows, that is required push the tablet up
the die wall.
 The final stage is marked by a decline in force of ejection as the
tablet emerges from the die.
 Variation on this pattern are sometimes found when lubrication is
inadequate and/or “slip-stick” conditions occur b/w tablet and die
wall.
 Worn dies, which cause the bore to become barrel shaped gives rise
abnormal ejection force and may lead to failure of tablet structure.
 A direct connection exists b/w FD and force required to eject tablet
from die, FE. For eg.well lubricated system(large R value) have been
shown to have smaller FE values.

COMPACTION PROFILES
Many attempts have been made to minimize the amount of
applied force transmitted radially to the die walls. All such
investigations lead to characteristic hysteresis curves called as
compaction profiles. Radial pressure is developed due to the attempt
of material to expand horizontally. The plot of radial pressure against
axial pressure leads to hysteresis curve called as compaction profile.
When the elastic limit of the material is high, elastic
deformation may make the major contribution, and on removal of the
applied load, the extent of the elastic relaxation depends on the
value of the material’s modules of elasticity (young’s modulus).
Lower the modulus higher will be the elastic relaxation. Then there
will be the danger of structural failure. Higher the modulus value
results in low decompression hence lesser risk of structural failure.

A
B
C
D
E
C’
O
Axial pressure →
Radialpressure→
<
Dotted line O to A represents a
highly variable response due to
repacking, while at A, elastic
deformation becomes dominant and
continues until elastic limit B is
reached.
From B to point of maxm
compression C, deformation is
predominantly plastic, or brittle
fracture is taking place.
The decompression process C to
D is accompanied by elastic
recovery, and if a second yield point
(D) is reached, by plastic
deformation or brittle fracture D to
E.
The decompression line B to C’
represents the behavior of largely
elastic material.

 The area of hysteresis loop (OABC’) indicates the extent of
departure from ideal elastic behavior, since for a perfectly
elastic body, line BC’ would coincide with AB.

PROPERTIES OF TABLET INFLUENCED BY
COMPRESSION
1.Density and porosity:
 The apparent density of a tablet is exponentially related to applied
pressure (or compressional force) until the limiting density of the
material is achieved.
 As compressional force increases the density of tablet also
increases as a result of decrease in bulk volume.
 As the porosity and apparent density are inversely proportional, the
plot of porosity against log of compression force gives linear plot
with a negative slope.
2. Hardness and tensile strength

Specific surface area:
 Specific surface area initially increases to a maximal value as
the force increases, indicating the formation of new surface
due to fragmentation of granules.
 Further increase in force produce a progressive decrease in
surface area due to bonding of particles.
Disintegration:
 Usually as the applied pressure used to prepare a tablet is
increased, the disintegration time increases (lactose/aspirin
alone).
 Frequently, there is exponential relationship b/w disintegration
time and pressure (aspirin-lactose).
 In some formulation there is minimum value when
app.pressure is plotted against log of disintegration time (with
10% and 15% starch in sulfadiazine tablets)

 For tablets compressed at low pressure, there is a large void,
and the contact of starch grains in the interparticular space is
discontinuous. Thus there is a lag time before the starch
grains, which are swelling due to imbibitions of water, contact
and exert a force on surrounding tablet structure.
 For tablets compressed at certain applied pressure, the
contact of starch grains is continuous with the tablet
exertsstructure, and the swelling of starch immediately
pressure, causing the most rapid disintegration.
 For tablets compressed at pressures greater than that
producing minm disintegrtaion time, the porosity is such that
more time is required for the penetration of water into the
tablet, hence increase in disintegration time.

 Dissolution: The effect of applied pressure on dissolution rate
may be considered from viewpoint of disintegrating and non-
disintegrating tablets.
 Shah & Parrot showed that, the dissolution rate is independent
of applied pressure from 53 to 2170 kg/cm2 for non-
disintegrating spheres of aspirin, benzoic acid, salicycic acid,
an equimolar mix.of aspirin & salicylic acid, aspirin & caffeine.
 Mitchell and Savill found dissolution rate of aspirin disk to be
independent of pressure over 2000 -13000 kg/cm2 and
independent of particle size of granules used to prepare disks.
Similar observation was found for benzoic acid disks.

 The effect of applied pressure on dissolutionof disintegrating tablet
is difficult to predict.
 If fragmentation of granules occur during compression, the
dissolution is faster as the applied pressure is ↑ed , bcoz of ↑se in
specific surface area.
 If bonding of particle is predominate phenomena in compression, ↑se
in applied pressure, ↓se dissolution.
The four most common dissolution-pressure relations are:
1. The dissolution is more rapid as pressure is increased.
2. The dissolution is slowed as pressure is increased.
3. The dissolution is faster, to a maxm, as force is increased, and
further increase in force slows dissolution.
4. The dissolution is slowed to a minm as pressure is ↑ed, and then
further an increase in pressure speeds dissolution.

Pressure
(MN/cm2)
t50% (min)
Starch paste Methylcellulose
solution
Gelatin solution
200 54.0 0.5 10.0
400 42.0 0.8 4.5
600 35.0 1.1 3.0
800 10.0 1.2 4.6
1000 7.0 1.4 4.9
2000 3.3 1.8 6.5
Table: Effect of compressional force on dissolution of
Sulfadimide tablets prepared with various garnulating agents

FACTORS AFFECTING STRENGTH OF TABLETS
 The ability of a tablet to withstand mechanical handling and transport
has been evaluated by various types of tests (abrasion, bending,
idention, hardness, diametral crushing).
 The strength of a tablet may be expressed as a tensile strength
(breaking stress of a solid unit in kg/cm2).
 Factors affecting tablet strength are
I. Particle size
II. Moisture content
III. Lubricants
IV. Applied pressure

1.PARTICLE SIZE:-
 A decrease in particle size resulted in the increase in thetablet
strength.
 Very large particle often exists as agglomerates of small crystal on
compression such agglomerates , being more friable than the
crystal, breakdown in smaller units. The strength of the tablets
prepared from such aggregates is higher.
 With very fine particle , such as those produced by a fluid energymill
, the powder are very cohesive even in the uncompressed state. On
compaction strong compact of tablet can be formed.
 At a given pressure the use of a very small particle increases the
chances of grapping & the volume of air entrapped also increases.
 General equation formed for the effect of particle sizeis
Fc = Ka/√d
 Where, K= constant
a= material constant lies between (0.2 to 0.47)
Fc= hardness of the impact
d= diameter of the granule

2. MOISTURE CONTENT:-
 In the preparation of the pharmaceutical tablet , it is generally
accept that a small proportion of the moisture is present and
in some cases this is required to form a coherent tablets.
 Wet granulation of the powder material with hydrophilic
additive was shown to yield tablet whose mechanical strength
is dependant on the optimum content above or below with
the tablets strength was reduced
 With the optimum moisture content there is :
Die wall lubrication
Inter-particulate lubrication
Hydro-dynamic resistance to consolidation
Expression of intestinal liquid to the die wall

 At low moisture content: ↑ed die wall friction due to ↑ed
stress ratio, poor tablet hardness.
 At high moisture content: moisture acts as lubricant , hence
↓ed die wall friction
 At further content: Further
moisture,
↑se in moisture
↓se in compact strength due to
↑se in
↓se in
interparticulate bond.
 Hence a granulation should contain an optimum moisture
content.
 It has been reported that the optimum moisture content for
starch granulation of lactose is approximately 12% and that
of phenacetin is 3%.

3. LUBRICANTS
 The chief purpose of a lubricant is to minimize friction at die
wall, although they often enhances flow of granules by
decreasing inter-particular friction.
 Lubrication mechanism: The polar portion of lubricant adhere
to oxide-metal surface and interpose a film of low shear
strength at interface b/w die wall and tablet.
 A lubricant reduces ejection force.
 Although a lubricant is added to facilitate its process of
tableting, its presence affects several properties of tablet.
 The effect of lubricant on mechanical strength of tablet
depends on mechanism of bonding.
 The strongest bonds are formed b/w clean, new surface; and
for material that undergo plastic and/or elastic deformation. In
such cases lubricants acts as a physical barrier b/w new
surface. Hence strength decreases.

 Eg. A tablet of MCC, whose bonding occurs primarily through
plastic deformation and flow, is mechanically weakened by
lubricant. The addition of Mag.stearate markedly decrease
axial and tensile strength in MCC as well as Lactose tablet.
 For materials that are brittle and fragment, new, clean
surfaces are formed and readily bond during compression,
and the lubricant has little detrimental effect on strength of
tablets.
 Dibasic calcium phosphate dihydrate is consolidated by brittle
fraction, and its axial and radial tensile strength are not
significantly changed by addition of as much as 3% of
mag.stearate.
 Stearic acid, hydrogenated veg.oil, talc and PEG 4000 may be
used in concn as great as 8% for brittle material with only a
slight to moderate change in tensile strength.

4. EFFECT OF APPLIED PRESSURE
 At higher forces due to fragmentation new surfaces are
formed causing an increase in surface area, hence more area
is available for bond formation, hence more will be the
hardness of the compact.
 There is a linear relationship b/w tablet hardness and the
logarthim of applied pressure except at high pressures.
 According to Balshin eqn.
rFc = Fc0 V-m
Where,
Fc0 = strength of the tablet when Vr =1 (i.e. completely
consolidated)
m = is a constant for particular system

Vr is the relative volume defined as Vr = 1/1-ε
Where ε is the porosity of the compact
 And, shotton and Ganderton gave a general equation for
the effect of applied pressure on the strength of the
compact.
Log P = nFc + C
Where, P= applied pressure
Fc= strength of the compact
C= constant
When we extraplot the plot of logP vs Fc ,the intercept
gives the value of C, which probably represents the
minimum pressure required for the formation of tablet.

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