The Dominance role of physics in Pharmaceutical formulation .pdf

THE DOMINANCE ROLE OF PHYSICS IN PHARMACEUTICAL DOSAGE FORM
FORMULATIONS: A ROBUST PRODUCT DEVELOPMENT
Rahul Pal1
, Prachi Pandey2
, Kavya3
, Neelu4
, Priyanka Pal5
, Sudhanshu Singh6
, Ravi Pal7
*1,2,3,4
Department of Pharmaceutics, NIMS Institute of Pharmacy, NIMS University Jaipur, Rajasthan,
303121, India.
5
Research Scholar, GRS College of Pharmacy Kalan Shahjahanpur, India.
6
Research Scholar, Department of Pharmacy, Invertis Institute of Pharmacy, Invertis University,
Bareilly, India.
7
Assistant Professor, JMB Institute of Life Science and Higher Education, Madhotanda Road Pilibhit,
UP, India.
Abstract:
Pharmacy's physical branch delves into the use of physics and chemistry in the field of pharmaceuticals.
In essence, this involves the examination of the influence of dosage forms on their respective
environments at a molecular scale. Physics have the dominance in the formulation for the
pharmaceutical dosage that are either in solid, gas and liquid form. Physics of pharmacy is known as
rheology science that concerns with the deformation of the solids and flow of the liquids. Physics
involves pressure, motion, fluid flows, and energy losses in formulating solid, gas, and liquid dosages.
Physics is involved in various pharmaceutical technological analysis including such as study utilized a
combination of analytical techniques, including differential scanning calorimetry (DSC), X-ray powder
diffraction, solid-state spectroscopy, UV-Visible absorption spectroscopy, and FT-IR spectroscopy,
involving key role for the formulation with their uses perfectly. In this review article main highlights
points considering initially means of fluid dynamics with the fluid flow which are such as laminar,
turbulent and transition flow which are determined by the using Reynold’s Number via Reynold’s
apparatus. Difference between newtonian flow and non-newtonian flow which are time dependent or
time independent, flow is measured by the orfice meter, pilot tube and rotameter and many more. Lastly
the physics of compression of tablet formulation which are explained with removal of gaseous phase
(air) and further proceed for the tablet manufacturing including parameters followed during compression
of individual tablet and some of the pre-formulation of character of given powder or tablet.
Keyword: Physics, Flowability, Newtonian, Non-Newtonian Flow, Tablet Compression and
Compaction.
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Volume 16, Issue 5 2023

1. INTRODUCTION
In physics, engineering (Pharmacy) and physical chemistry, fluid dynamics is a sub-discipline of fluid
mechanics that describes the flow of fluids: liquids and gases. It has several sub-disciplines, including
aerodynamics and hydrodynamics [1]. Throughout pharmacy's history, the oral route has been the most
popular method of drug delivery, with oral solid dosage forms being widely utilized due to their
convenient administration, ease of manufacturing, accurate dosing, and patient adherence. Out of
powders, granules, tablets, pellets, and capsules. Tablets has been the dosage form of primary choice in
the manufacturing or production of a new drug entities and account for some 70–80% of all
pharmaceutical development [2]. A flow-chart of the relationship between solid pharmaceutical dosage
forms is shown in (Fig. 1) for the formulations.
Figure 1: Relationship between different dosage form
There are various methods for producing tablets, including utilizing powders, pellets, granules, and
multi-unit film coatings. To produce a tablet, it is essential for the substance to possess excellent
compressibility. In general, the tableting process involves, applying pressure to a powder bed, thereby
compressing it into a coherent compact. The most straightforward way of creating tablets is by utilizing
the direct compression method, which entails blending the drugs and excipients prior to compaction [2-
3]. In the pharmaceutical industry, compaction stands out as a crucial unit process that determines the
density and strength (hardness/friability) of tablets. It plays a critical part in surveying the mechanical
and physical properties of the tablets amid definition. Dose frame astuteness and bioavailability is
related to the tablet compression handle.
The tablet which are prepared with the following steps involving and compression used in the
manufacturing. The validation of term comes as dissolution test for their validation process [4].
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The formulation of compressed tablets is a concern process involving many variables, number of
engineering principles and complete understanding of the physics of compression has been an ongoing
process. the most High-dose low compressible medications that display a non-linear relationship in
tablet tensile strength and compression force are of particular interest to the study of compression
physics. When a dosage form is prepared then lots of steps involving during the manufacturing or
formulation which are generally, known as the flows of fluids and liquid. Rheology is the main branch
which known as the flow of formulation.
Rheology is the science that deals with study of how matter flows, initially as a fluid but also as "soft
solids" or solids that flow plastically in response to an applied force rather than deforming elastically.
Rheology is the science that relates between deformation (strain) and force (stress) of engineering
materials under a set of loading and environmental conditions. Added term Rheology is a branch of
science that deals with how the matter (solids, liquids, and gases) flows. It is particularly interested in
how time-dependent behaviour changes in response to stresses [5].
The realm of rheology pertains to the study of the behaviors and characteristics of fluid motion and solid
distortion. It is of great significance for pharmacists involved in the production of various dosage forms,
including but not limited to gels, ointments, creams, simple liquids, and pastes, to have a thorough
understanding of the fluid dynamics of liquids. These systems change their flow, behaviour when
exposed to different stress conditions. Various techniques such as mixing, pipeline flow, and container
filling are employed in the processing of materials when creating dosage forms. Variations in flow rate
affect the choices made for selecting the appropriate mixing equipment. The way drugs are administered
and the ability to use syringes or pour medication from containers or squeeze ointment from tubes is
determined by the changes in the flow properties of the dosage form [4-5].
The major importance of rheology in the pharmacy as:
a) Pharmaceutical product formulations, such as emulsions, suppositories, cosmetic creams, lotions,
and tablet coatings, require careful consideration of rheology during formulation and analysis.
b) Materials are mixed and flowed, packaged into containers, and removed before to use using any
method, such as pouring from a bottle, extruding from a tube, or passing through a syringe
needle [5-6].
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2. FLOW OF FLUID IN PHARMACEUTICALS FORMULATIONS: The principles of fluid
dynamics fall under the branch of fluid mechanics known as fluid flow. This refers to the movement of a
liquid that has been acted upon by imbalanced forces. This motion remains as long as unbalanced forces
are applied. In the pharmaceutical formulations majorly lots of flows are working to each other for their
flowability.
The choice depends on whether or not their flow properties are in accordance to Newton’s law of low.
The major of the streams depicted within the given specified information for the superior clarification [6].
The stream isolated in two majorly portrays within the given (Fig. 1):
Figure 2: Type of Flows in Pharmaceuticals
2.1 TYPES OF FLUID FLOW: Fluid flow has different kinds of parts such as; steady or unsteady,
viscous or non-viscous, compressible or incompressible, and rotational or irrotational. Some of these
characteristics shows the properties of the liquid itself, and others focus on how the fluid is moving.
01. Unsteady or Steady Flow: Depending on the fluid's velocity, fluid flow can be categorized into
two broad categories, which are described below:
• Steady: In the steady fluid flow, majorly the velocity of the fluid is constant at every point.
• Unsteady: The velocity of the fluid may vary between any two points when the flow is
unsteady.
02. Non-viscous or Viscous Flow: Flow of liquid can be viscous or non-viscous. Viscosity can be
measured as thickness of a fluid, and more viscous fluids such as motor oil or shampoo are
called viscous fluids.
Laminar flow, also known as streamline flow, is characterized by the movement of fluids in contiguous
layers that run parallel to each other, with no mixing or disturbance between them. The turbulent flow
scenario involves the presence of disorderly characteristics, such as a swift alteration of both pressure and
flow rate [5-7].
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2.2 NEWTONIAN FLOW: A fluid is said to be Newtonian if it complies with Newton's law of
viscosity. (Liquid) Dilatant flow, simple pseudoplastic flow, and simple plastic flow. Newton was the
first to study the flow properties of liquid in quantitative terms.
Figure 3: Newtonian Fluid graph representation
Newtonian law, “States that the shear stress between adjacent fluid is proportional to the velocity
gradient between two layers or shear rate. Liquid that obeys newton’s law of flow are called as
Newtonian Fluids.”
Higher the velocity of a liquid-greater the force per unit area (shearing stress/F) required to produce a
certain rate of shear (G).
(F ∝ G) or (
∝ G) or (
∝ G) or (
∝ G) or (F = ηG)
Where, η = The coefficients of viscosity or simply or absolute viscosity or dynamic viscosity, F= Force
per unit area, G = Rate of shear.
The newtonian flow is describe with the below section for proper generally newtonian is rate of shear
ratio.
A Newtonian fluid is one in which there is a linear relationship between shear stress and shear rate and
whose viscosity does not change with shear rate according to Newton's Law of Viscosity [7].
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2.3. NON-NEWTONIAN FLOW: When the fluid doesn’t obey Newton’s law of viscosity, it is known
as Non-Newtonian fluid. They don't follow Newton's law of flow, and their viscosity isn't constant.
Blood and honey are examples. Plastic, pseudoplastic, and dilatant flow are the three classes.
heterogeneous dispersion, liquid/solid. ointments, liquid suspensions, emulsions, and colloidal solutions.
It shown on (Fig. 4):
Figure 4: Non-Newtonian Flows Representations
Table 1: List of Flows Behaviours and including Example
Sr. No. Type of Behaviour Description Examples
01. Thixotropic Stress over time leads to decrease
viscosity
solid honey becomes liquid
and Honey- Keep stirring,
02. Rheopectic Stress over time leads to increase
viscosity
Cream- the longer you
whip it the thicker it gets
03. Shear thinning With increase in stress, viscosity
decreases
Tomato sauce
04. Shear Thickening or
Dilatant
With increase in stress, viscosity
increases
Corn-starch
The different type of time dependent and time independent flow has been determined by the different
types of method involving and the example also include in individual, described in the (Table 01).
Non-Newtonian fluids change their viscosity or flow behaviors under stress. These fluids may suddenly
become thicker and behave like solids if a force is applied to them (it will hit, shake, or leap), or they
may exhibit the opposite behaviour and become runnier than they were before. Remove the stress (let
them sit still or only move them slowly) and they will return to their earlier state [8].
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Table 2: List of Methods determined Flow and Examples
Sr.
No.
Type of Flow Method of Viscosity Determination Example Including
01. Newtonian Flow
(5%)
- Capillary Viscometer
(Ostwald Viscometer)
- Falling & Rising Body
(Sphere)
Water, alcohol, air,
glycerol, and thin motor
oil.
02. Non-Newtonian
Flow
- Cup and Bob Viscometer
- Cone & Plate Viscometer
Plastic Flow (74%): Particle
in suspension/emulsion
Pseudoplastic Flow (50%):
Tragacanth, CMC, Sodium-
CMC
Dilatant Flow:
Deflocculated suspension of
Mg. Magma,
Others: Salt solutions,
blood, starch solutions [8].
Time dependent flow- Time-dependent flows include rheopexy and anti-rheopexy, thixotropy, and anti-
thixotropy, among others.
Time Independent flow- Dilatant flow, plastic, and pseudoplastic Typically, the different forms of
time-dependent or time-independent flows are categorized as follows: Which type of dependency, such
as (Table 3).
Table 3: The time dependent and independent flows
Sr. No. Dependent/Independent Flow Flows Types
01. Time Dependent Flow Thixotropy, Anti-Thixotropy, Rheopexy
and Anti-rheopexy.
02. Time Independent Flow Plastic, Pseudoplastic and Dilatant Flow.
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3. TIME INDEPENDENT FLOWS: Time independent flows are important as non-Newtonian fluid
flow in formulation manufacturing. It includes dilatant flow, plastic flows, and pseudo-plastic flows,
which are all considered non-Newtonian fluid flows.
01. DILATANT FLOW: The viscosity of these fluids increases as shear rate increases. When the stress
get removed, the dilatant system move back to its original/normal state. As stress is more particle will
move fast and these takes an open form of packing. The basic example of dilatant flows is corn starch in
water, and there are numerous other examples that are explained in the following sections (Table.02).
02. PLASTIC FLOW (FLOWABILITY): Plastic flow curves cross the shearing stress axis at a
specific location known as the yield value rather than going through the origin (assuming the straight
portion of the curve is projected to the axis). The material that exhibits plastic flow, such material is
known as Bingham Bodies.
A Bingham Body do not flow until the yield value's shearing stress is increased. The substance acts as
an elastic material when stresses below the yield value. The rheogram's graphical depiction is known as
mobility, which is akin to newtonian systems' fluidity. The plastic viscosity is its opposite reciprocal:
Where, f is the intercept on the shear stress axis and yield value (dynes/cm2
), plastic flow is determined
with the presence of flocculated particle in concentrated suspension. The above describes all newtonian
and non-newtonian fluids (Fig. 5).
Figure 5: Shown the different types of flows as graphical representation
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03. PSEUDOPLASTIC FLOW: A characteristic of different polymers in solution in contrast to plastic
systems composed of flocculated particles as in suspension. The origin marks the start of the consistency
curve of a pseudo-plastic substance, indicating the absence of any yielding point. The viscosity of a
pseudo-plastic substance will decrease with increasing the shear rate, and the system is known as shear-
thinning system [6-7].
4. TIME DEPENDENT FLOW
THIXOTROPY: The Phenomenon where fluids take a while to return to their natural state after being
freed from shear stress. Thixotropy is used to thin fluids under shear.
Example: Pectin gels and Xantham gum solution.
THIXOTROPY IN FORMULATION: Pharmaceutical systems like suspensions and creams should
have a high consistency inside the container while yet being easy to pour and spread. Greater the
thixotropy then the lowering the rate of settling of solid particles in the formulations. Thixotropy
commonly enhancing the retention time and thereby increased bioavailability (BA) of the products.
Thixotropy is useful in the development of pharmaceutical suspensions and emulsions and their stability.
They must be poured easily from container (low viscosity). Thixotropy and anti-thixotropy well
explained with the given (Fig. 6).
Figure 6: Thixotropy and Anti-Thixotropy fluid flow
ANTI-THIXOTROPY: Negative thixotropy, or anti-thixotropy, refers to the phenomenon wherein the
viscosity of polymer solutions increases under the influence of flow. This effect has been widely
observed. Here, a simple quantitative model describing the time dependence of the shear stress or
viscosity is presented. If viscosity increases with time it is known as anti-thixotropy flow [8].
The majorly fluid flow is 3 which are shown as additional flows in the given below (Fig. 7) for the
completion of review data.
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Figure 7: Type Flows of fluids
The time dependent viscosity is mainly of the 3 types which are defined as the following and the basic
examples included in the given (Table 4) such as:
Table 4: List of viscosity parameter and other related information
Sr. No. Name of Viscosity Information Examples
01. Thixotropy Gel-Sol transformation Petrolatum, bentonite gel
(Magma) and suspending agent
dispersion.
02. Anti-Thixotropy
or Negative Thixotropy
Sol-Gel-Sol
transformation
Magnesia magma.
03. Rheopexy Sol-Gel transformation Flocculated suspension
(1-10% solid content)
All the information about the viscosity with their suitable example is explained in the above table.
LAMINAR FLOW: It is also termed as "Streamline flow," and it occurs when fluid flows in parallel
layers with no interruptions between them. The inverse of turbulent flow (Rough).
In fluids dynamics (scientific study of the properties of moving fluids), laminar flow is- “A flow regime
characterised by high momentum diffusion, low momentum conversion, and time-independent pressure
and velocity.” *Momentum diffusion refer to the spread of momentum (diffusion) between particle of
substance usually liquids.
Laminar flow is generated when the body moves low velocity to the fluid’s medium. Fluids slide
parallel, smoothly, or in predictable routes in laminar flows. Laminar flow is characterised by thin,
parallel layers that occurs over a flat, horizontal surface.
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The term "streamline" or "smooth" is attributed to the way in which layers glide seamlessly over each
other. The routes are consistent and devoid of any variations. Laminar flow is typically characterized by
three circumstances: slow fluid movement, relatively high viscosity, and a relatively small flow channel.
Example: Blood flow though the capillaries is laminar flow, as it satisfies the 3 conditions, most type of
fluid is turbulent and there is no poor transfer of heat energy.
TURBULENT FLOW (TURBULENCE):
Typically happened when the liquid was moving quickly. There are erratic variations and the flow is
"chaotic." Low momentum diffusion, high momentum convection, fast changes in fluid pressure and
velocity, and efficient thermal energy transfer are all included.
The speed of the fluids at a point is continuously undergoing changes in both magnitude and direction.
In turbulent flow is generated when the body moves with high velocity relative to the fluid does not flow
in parallel layers but undergoes irregular fluctuations and mixing, there is a disruption between the
layers. The both laminar and turbulent flow is explained or show in the above (Fig. 8) for the proper
explanation following:
Figure 8: The Laminar and Turbulent Flow
Examples including in turbulent flow:
- The external flow of water/air over vehicles such as cars/ships/submarines.
- Flow of most liquids though pipes.
For the determination of the types of fluids during the formulations, lots of flows are considered which
mainly of determined with the help of Reynold’s number are necessary, described below section [7-9].
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5. REYNOLD’S NUMBER: Reynolds number is a dimensionless quantity that is used to determine the
type of flow pattern as laminar or turbulent while flowing through a pipe. Reynolds number is defined
by the ratio of inertial forces to that of viscous forces. Reynold The majority of numbers are
dimensionless. It is crucial for regulating the fluid's flow pattern and velocity.
The Reynolds number calculated high (greater than 2000), then the flow through the pipe is said to be
turbulent. If Reynolds number is low (less than 2000), the flow is said to be laminar. These values are
acceptable in terms of mathematics, despite the fact that laminar and turbulent flows are typically
categorised based on a range. Laminar flow falls below Reynolds number of 1100 and turbulent falls in
a range greater than 2200 proper explained in the given (Table 5). Laminar flow refers to the smooth
movement of fluid through regular channels.
Reynold Number is the ratio of inertial forces to the viscous forces and denoted with Re.
Where, Re is the Reynolds number, V is the velocity of flow, ρ is the density of the fluid, D is the pipe
diameter and μ/η is the viscosity of the fluid, The proper flows with type of flow explained in the given
(Table 5), with their Re value for the different types of flows.
Table 5: List of Reynold’s number range and types of flows
Sr.
No.
Reynold’s Number
(Re) Range
Type of Flow Suitable Example
01. Re < 2000 or less than
1000 (or 2000)
Laminar Flow or Streamline
Flow or Viscous Flow
Viscous liquid through a tube or
pipe.
02. Re > 4000 Turbulent Flow Blood flow in arteries.
03. Re < 2000-4000 Laminar to Turbulent Flow Smoke rising in a straight path.
05. 0.1 to 200 Unsteady Flow Valve is closed at the discharge
end of the pipeline [10].
The major application in Reynold number is predict the nature of low and rate of sedimentation in
suspension.
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6. THE DOMINANCY OF PHYSICS IN DOSAGE FORM FORMULATION WITH
COMPRESSION
The intricacies of the functioning of tablets are quite challenging, and significant scientific involvement
is indispensable for the study of the compression of individual component tablets. Hence, it is
unsurprising that most blend investigations predominantly concentrate on uncomplicated dual systems in
lieu of elaborate multi-component mixtures. The employment of instrumentation in the investigation of
tablet formulation facilitates a comprehensive comprehension of the physicochemical intricacies
inherent to the tableting process. Force-time and force-displacement estimations can be gotten from
instruments punches and passes on. Afterward, this information can be fitted to numerical conditions to
explain the compaction behavior. The parameters gotten from the logical treatment of compaction data
can be utilized to predominant get it the extreme quality characteristics of a given blend. They may
differ in size, shape, hardness, thickness, dissolution characteristics and disintegration; and in other
aspects. They are classified, as per the method of manufacture, as compressed tablets or molded tablet
[11]. Tablets are compressed solid dosage forms consisting of active ingredients and suitable
pharmaceutical excipients for oral administration. The tablets are classified according to their methods
of manufactures such as compressed tablet & molded tablet.
The act of consolidating granules within a die cavity in pharmaceutical tablet formulation involves
compressing them between an upper and lower punch to create a cohesive, solid matrix. This matrix is
then removed from the die cavity and shaped into a tablet [12].
6.1. COMPRESSION OF TABLET: The term is also known as the ‘Physics of Compression’, it
generally, consists as compression-consolidation of two phases which are (solid-gas). The reduction in
the bulk volume of materials is due to the removal or displacement of gaseous phase (air) with the
applied pressure, known as Compression and another term is defined as the increasement in mechanical
strength of material due to particle-particle interaction. Generally, relating to the compression new term
will arise, compressibility “The ability of a material to undergo a reduction in volume as a result of an
applied pressure and is represented by a plot of tablet porosity against compaction pressure.” In
simple term, consolidation, is described as increase in mechanical strength of material resulting from
particle-particle interactions [13].
Compression known as the first process which are plays an important role in the tablet or other solid
dosage form formulation on the pharmaceutical industry level.
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COMPACTION: The compaction is described as “The compression and consolidation of a particulate
solid-gas system as a result of an applied force, forming a compact but porous mass of a definite
geometry”. With relating this here, compatibility, “The ability of material to produce the tablet with
sufficient strength under the effect of densification and is represented by a plot of tablet tensile
strength against tablet strength”. Transformation of powder into coherent specimen caused by applied
pressure is compaction [14].
Compaction = Compression + Consolidation
EQUIPMENTS ESSENTIAL FOR THE TABLET COMPRESSION:
The tablet pressing contraption is an electromechanical apparatus that employs compressive force to
shape powder into tablets that are all equal in size and thickness. The numbers of equipment’s utilized
within the tablet detailing for the strong dose shape as well as routine.
Principle: The basic principle of behind the tablet compression machine is hydraulic pressure. This
pressure is transmitted under reduced through the static fluid. Static fluid transmits any applied external
pressure to all directions in the same ratio [16].
Types of machines for tablet compression:
• Single station tablet press.
• Multi-station tablet press.
Basic components of tablet compression machine: The lots of steps or parts as well as the components
which are role in formulations, some of the steps discussed as following:
- Hopper: Holds the feeding material that are to be compressed
- Die: The cavity that defines the size and shape of the powder.
- Dosing Plow: Pushes a small, precise amount of product into the die cavity.
- Punches: Compress the granulating material within the die.
- Turrets: Holds the upper and lower punches (Heart of the tablet compression machine).
- Cam Track: Guides the movements of the punches,
- Ejection Cam: Pushes the bottom upward, ejecting the finished tablet from the die cavity [17].
There are mainly of two types of press machine will used in the manufacturing process.
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6.2 SINGLE STATION TABLET PRESS MACHINE:
The simplest tableting apparatus is a single station press machine, commonly referred to as a single
punch or eccentric press. The single punch tablet press typically produces 60 to 85 tablets per minute.
Figure 9: Schematic diagram of single station press machine
The single punch machine is mainly consisting the step as following, filling, weight adjustment,
compression and ejection. This is easy to operate, space saving small structure & operate it with lower
the noise [18].
6.2. MULTI-STATION ROTARY PRESS MACHINE:
Multi-Station rotary press machine have the great production capacity, multi-station presses, also known
as rotary machines, are one of the most often used pieces of machinery in the pharmaceutical business.
The multi-station press machine is used to produce about 8,000 to 200,000 tablets per hour.
Figure 10. Schematic diagram of multi-station press machine
The rotary tablet press machine is consisting the three major steps: Filling, Compression and Ejection.
This is cost efficient than single punch tablet press, guarantee independent control of both hardness and
weight and automated system [19].
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The different types of steps involving to explaining the compression as a major role in pharmaceutical
dosage form especially tablet or capsule formulation with the help of different equipment during the
complete formulations [20].
Events involving in the processing of compression-
- Transitional repacking and particle rearrangement.
- Deformation at the point of contact.
- Fragmentation
- Binding
- Deformation of solid body (Solid bonding)
- Decompression
- Ejection
The tablet compression process includes all of the aforementioned phases, including tablet formulation.
The steps are clearly laid out in the example (Fig. 11) for a clearer explanation.
Figure 11: Processing of Tablet Compression of Formulation as defined in Physics
01. Transitional Repacking and Particle Rearrangement: Initial repacking is determined by
particle size distribution. Smaller particles fill holes between larger particles during the early
stages of compression, when there is minimal pressure and particles move relative to one
another. As resulting volume decreases and density increase spherical particle undergoes lesser
rearrangement than the irregular particle.
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The granules flow with regards to one other with the fine particles in between the void of the
larger particles and the bulk density of the granulation increased. To get a fast flow rate that is
required for high speed presses the granules is generally processed to give spherical or oval
granules, thus particles gets rearrangement and energy is expended in rearrangement are minor
consideration I the total process of compression [21].
02. Deformation at point of contact: When a force is applied on a material deformation occur. It is
referred to as "elastic deformation" if the distortion totally vanishes (returns to its original shape)
when the stress is released. A deformation that not recover completely after removal of stress
known as ‘plastic deformation’. The Deformation is explained within the give (Fig. 12)
Figure 12: Deformation of Tablet Compression
The force required initial plastic deformation is known as ‘yield stress’. As the granule particles are
packed tightly together, there is no more space left for filling gaps, so any additional compression force
may result in deformation at the point of contact. Generally, deformation consists elastic, plastic and
yield stress deformation [23].
Figure 13: plastic and elastic deformation
Both plastic and elastic deformation may occur although only one type predominates for a given
materials.
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03. Fragmentation: Compression pressures induce a particle to fragment as a result of the high
load, which creates a new bonding area by breaking the particle into smaller fragments.
Fragmentation undergoes densification & infiltration of small fragment into voids.
When the particle's internal tension reaches a certain level, it fractures. Fragmentation causes
further densification with the infiltration of the smaller fragments into the void space [24]. With
some materials fragmentation does not occur because the stress is released by the plastic
deformation.
Table 6: Different fragmentation and deformation with material
Sr.
No.
Major deformation mechanism(s) Material
01. Fragmentation Ascorbic acid, Dicalcium phosphate,
Maltose, Phenacetin, Sodium Citrate,
Sucrose
02. Fragmentation and elastic
deformation
Ibuprofen, Paracetamol,
03. Fragmentation and plastic
deformation
Lactose monohydrate, Microcrystalline
cellulose
04. Plastic deformation Sodium bicarbonate, Sodium chloride, Pre
gelatinized starch
05. Elastic deformation Starch [25]
04. BONDING OF PARTICLES: After fragmentation as the pressure increased formation of new
bonds between the particles at the contact area occurs. There are three theories are about the
bonding of different particles in the tablet by compression-
a) The Mechanical theory: The total energy of compression is the sum of the energy of
deformation, heat, and energy absorbed for each constituent if there is simply the
mechanical link. It majorly occurred between asymmetric shaped particles.
The mechanical interlocking is not a major mechanism of bonding in pharmaceutical
tableting.
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b) The inter molecular theory: The surface molecules or ions of solids possess untapped
potential energy, which they unleash through interactions with neighboring particles in
physical proximity. The primary bonding process for tablet compression is thought to be
a combination of this theory and the liquid surface film theory.
c) The liquid surface film theory: The adhesion of a slender fluid on the surface of a
particle can occur due to either fusion or solution, brought about by the compression
energy. This is the major bonding mechanism involved in the tablet compression.
It may be classified into the two ways- Hot Welding & Cold Welding.
- Cold Bonding: Unsatisfied forces on a particle's surface cause the production of powerfully
attracting forces known as "cold-welding" when the particle approaches another.
- Fusion bonding: Particle irregular in shape het transmission leads increase mechanical
strength. A few of them calculate influencing holding: chemical nature of fabric, accessible
surface and nearness of surface contaminant [26].
05. DEFORMATION OF THE SOLID BODY: Bonded solids consolidate towards a limiting density
by plastic or elastic deformation as applied pressure is increased.
06. DECOMPRESSION: The success or failure of intact depends on stress induced by ‘elastic
rebounds and the associating deformation produced during decompression and ejection. Capping occurs
as a result of uniaxial relaxation on the die cavity. Removing the exerted force induces elastic recovery
that generates a series of tensions within the tablet. If the tablet is not sturdy enough to handle the
pressure, it could potentially result in the collapse of its structure. In the event that the degree and rate of
flexible recuperation are tall, the tablet may cap or cover. In the event that tablet breaks, compact may
come up short. Capless/laminate-free tablets can twist and soothe push through misshapening. *The
tablet failure is affected by rate of decompression (machine speed).
07. EJECTION: The last stage in compression cycle is ejection from die. Ejection phase also requires
force to break the adhesion between die wall and compact surface and other forces needed to complete
ejection of tablet.
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Ejecting a tablet involves a particular level of force that is crucial to begin the process of breaking the
bond between the die wall and the tablet. The second phase necessitates an exertion of energy to move
the tablet up the die wall, while the ultimate exertion of force is necessary for ejection. When there is
insufficient lubrication, the process can experience fluctuations and a slip-stick scenario can arise
between the tablets and the die wall. This leads to the continuous formation and breakage of adhesion
between the tablet and die wall.
Lubricants minimize stress patterns so; they reduce the tendency for materials to cap or laminate. When
the punch is lifted and pushes against the table, there is an ongoing presence of pressure from the die
wall, which may lead to the expenditure of energy resulting from friction against the die wall. The forces
are necessary to eject the finished tablets;
i. Peak force required to initiate ejection.
j. Small force required to push tablet up to die wall.
k. Decline force as tablet emerges from die [27].
FORCES APPLIED IN PHYSICS COMPRESSION OF TABLET: During the compression of
tablet here lots of forces will apply in the tablet manufacturing and formulation, it includes the different
forces such as, Frictional forces, forces distribution, radial forces and ejection forces.
FRICTIONAL FORCES: It takes into account inter-particulate force and die wall friction. Glidants
such as colloidal silica, in general, reduce inter-particulate. Die-wall friction is reduced by adding of
lubricants it including magnesium stearate.
- Inter-particulate Friction: Friction between particle/particle and expressed as coefficients or
‘interarticular friction’. This arises at the particle/particle contacts & expressed as coefficients of
inter-particulate friction. It expressed as µi.
Example: Colloidal silica (fumed silica)
- Die-Wall Friction: Arises as material being pressed to die wall and moved down it, can be
expressed as “coefficients of die wall friction”, addition of lubricants. This is due to material
being pressed against the die wall & moves down it. it expressed as µw.
Example: Magnesium Stearate [28].
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DISTRIBUTION FORCE: The Most of the investigational of fundamental of tableting have been
carried out on single punch presses with hydraulic press. A force is applied on top of cylinder of powder
mass consider single isolated punch.
These must be an axial balance of forces; a force is applied on cylinder on top of cylinder of powder of
mass.
FA = FL + FD
Where, FA= Is the force applied to the upper punch, FL = Proportional applied force transmitted to lower
punch and FD = Is the reaction at the die wall [29].
RADIAL FORCE: The radial force applied by a radial compression mechanism (or a “crimping head”)
to a product (such as a stent) is usually measured by a linear force transducer that senses the force
applied by an actuator.
Classical friction theory can be applied to obtain a relationship between axial frictional force FD and
radial force FR as:
FD = µw. FR
Where, µw, is coefficients of die wall friction.
It approaches 1 for perfect lubrication and in practice, as high as 0.98 can be achieved, value is below
0.8 indicate poor lubricants.
POISSON’S RATIO OF MATERIAL: When force is applied on vertical direction which result in
decrease in height (H) for unconfirmed solid body, the expansion is in horizontal direction (D).
This ration of two dimensional (2D) changes is known as Poisson’s ratio:
λD = (ΔD)/(ΔH)
The Poisson’s ratio is a character constant for each tablet.
EJECTION FORCES: Radial die wall forces and die wall friction also affects ejection of the
compressed tablet from die. The force necessary to eject a finished tablet is known as ejection force.
Variation occurs in ejection force when lubrication is inadequate. Force necessary to eject a finished
tablet. Ejection force for a finished tablets consists of 3 stages:
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- Stage- 01: Peak force required to initiate ejection by breaking tablet/die wall adhesion.
- Stage- 02: Small force, that required to push the tablets up the die wall.
- Stage- 03: declining force of ejection as the tablet emerges from the die.
The variation in this pattern also occurs is ejection force when lubrication is inadequate and or slip-stick
conditions occurs between tablet and die wall. A smaller force usually follows, this is required to push
the tablet up the die wall [30].
In the engineering and pharmaceutical sciences, the relationship between volume and applied pressure
during the compression is the main approach to deriving the mathematical representation of the
compression process. The latter approaches are more common as it can be performed rapidly with the
limited amount of powder. Among these, the recognized expression in both engineering and
pharmaceutical science is the tablet porosity-applied pressure functions according to the different types
of equation for the better explanation. Here the different equations mentioned in the below data shown is
the give (Fig. 05) for the explaining the data on compression of tablets:
The compaction equation typically establishes a connection between various indicators of powder
consolidation, including but not limited to porosity, volume (or relative volume), density, or voids ratio.
This relationship is dependent on the amount of pressure applied during the compaction process. These
are mentioned in the above (Fig. 14).
Figure 14: Equations involving in the compaction of tablet
a. HECKEL EQUATION: The Heckel equation is one of the most useful equations for
describing the compaction properties of pharmaceutical powders. Important material
properties (e.g., yield strength) of powders can be derived using Heckel analysis. Two
types of Heckel analysis are in common use. One is the "out-of-die," or "zero-pressure"
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method, the other is the "in-die" or "at-pressure" method. The Heckel equation is based
on the assumption that densification of the bulk powder under force follows first order
kinetics. The Heckel equation is expressed as,
In (1/1-D) = Kp +A
Where, D represents the relative density of the tablet, which is the ratio of the tablet
density to the true powder density. P stands for the applied pressure, while K denotes the
slope of the straight-line section of the Heckel Plot. Lastly, A represents the intercept
[31].
b. WALKER EQUATION: The Walker equation is a differential equation that assumes
the pressure's rate of alteration relative to volume is proportionate to the pressure itself
which mainly denoted with the formula:
where, V0 is the volume at zero porosity. The relative volume is V′/V0 = V = 1/D, C1
is constant. The coefficient L is referred to as the pressing modulus.
c. KAWAKITA EQUATION: The Kawakita equation for powder compression is
founded on the concept that particles experience a consistent compressive load during all
phases of compression, resulting in a steady product of pressure and volume.
‫܉۾‬
۱
ൌ ൤
૚
‫܊܉‬
൅
‫܉۾‬
‫܉‬
൨
C = ቂ‫܄‬૙ െ
‫܄‬
‫܄‬૙
ቃ
This equation involves three variables: Pa represents the pressure applied along the
axis, a refers to the amount of volume reduction in the particle bed, and b is directly
proportional to the particles' yield strength. The extent to which volume decreases is
measured by the degree of reduction denoted by C, while V represents the compact's
volume under pressure and V0 refers to the powder's starting apparent volume. This
formula is most suitable for delicate and light medicinal powders, and works
particularly well in scenarios with a low level of pressure and high level of porosity.
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These equations play a crucial role in the manufacturing process of tablets, as they are utilized for both
formulation and compaction purposes. The tablet formulation involves the utilization of various
parameters, which are enumerated in (Table 7), to enhance the compaction process:
Table 7: Mathematical Equations and Parameters to Study Compaction of tablet
Sr. No. Process Parameter
1. Compaction stages (Compressibility and
consolidation)
Heckel condition, Kawakita condition,
Leuenberger condition etc..
2. Elastic deformation,
Elastic recovery,
Capping/lamination tendency
Percentage elastic recovery.
Work on upper punch in recompression.
Elastic recovery index.
Plastic-elasticity index, Work of elastic
deformation.
Radial die-wall and axial pressure.
3. Interparticulate bonding Brittle fracture index and Bonding index.
4. Plastic flow,
Plastic deformation
Work of plastic deformation.
Surrender weight and Abdicate quality.
5. Lubrication efficiency R value and Force transmission ratio.
These are the other terms used in the compaction of tablet formulation as well as manufacturing of the
tablet in the under applying pressure.
The manufacture of compacted pills is a complicated procedure that necessitates a meticulous
understanding of multiple factors and engineering concepts, and acquiring a comprehensive grasp of
compression physics is an ongoing pursuit. The compression characteristics can be influenced by
various factors including the size and distribution of particles, crystal shape, degree of crystallization,
the presence of different crystal forms, false crystal forms, lack of crystal structure, and moisture content
[32]. Prior to delving into a study on the compression of tablet dosage form, it is crucial to elucidate the
diverse properties of this particular type of solid oral dosage form. Some of the properties explained in
the above the description such as –
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7. PROPERTIES OF TABLETS: The compressibility and overall performance of solid dosage forms,
such as tablets, are dependent on the physicochemical characteristics of the pharmaceutical solids. One
property has a consequential impact on the others, meaning modifications to one will impact the others
as well as including different properties such as:
I. SURFACE PROPERTIES: The surface characteristics of powdered materials significantly
impact their intermolecular attraction and flow properties. The way atoms or ions in a surface
are bonded to one another both internally and externally differs from how they are bonded
within a particle. The source of this occurrence is due to the unfulfilled attractive molecular
forces that protrude slightly past the surface of the solid. The presence of this phenomenon
creates a free surface energy in solid materials, which plays a significant part in the
interaction between particles.
Cohesion and adhesion are two types of particle attraction forces which are exist between
like and dissimilar particles. Attraction forces resist movement of particles under external
force. Other resistances include electrostatic forces, moisture, and solvent on solid particle
surfaces [33].
II. POROSITY: The measure of the openness or permeability of powder (E) can be explained
as the fraction obtained when dividing the total volume of empty space (Vv) by the overall
volume (Vb) of the powdered material. The total void volume, Vv is given by the above
equation. where, Vt is the true volume.
E = (‫܄‬‫܊‬ െ ‫܄‬‫ܜ‬)/‫܊܄‬ ൌ ቂ૚ െ
‫ܜ܄‬
‫܊܄‬
ቃ
A technique employed to measure the compressibility of a powder layer is through assessing
the extent of reduction in volume that results from the application of pressure. This reduction
is linked to porosity and is believed to be a primary chemical reaction. The correlation
between porosity and pressure can be elucidated by the Heckel equation and is frequently
utilized as an indicator of compressibility.
III. FLOW PROPERTIES: A pharmaceutical powder's flow property is critical for ensuring
proper die fill during compression, especially in the direct compaction process. High fines
content, excess moisture, lubricants, and electrostatic charge can all contribute to poor
powder flow [34]. A pharmaceutical powder's flow property is critical for ensuring proper
die fill during compression, especially in the direct compaction process.
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The angle of repose serves as a conventional way of gauging the movement of powders,
indicating the greatest angle (θ) that may be obtained between the powder plane and a level
surface. It mainly given with the using formula such as:
‫܍ܔ܏ܖۯ‬ ‫܎ܗ‬ ‫܍ܛܗܘ܍܀‬ (ી) ൌ ‫ܖ܉ܜ‬ି૚
൜
ࢎ
࢘
ൠ
The height of the heap is denoted by h and can be measured by passing the powder through a
funnel, while the heap's radius, determined using graph paper, is represented by r.
The angle of repose is a common metric for gauging the movement of powdered substances,
representing the greatest angle (Φ) observed between the powder's plane and a flat, level
surface. When the value of Φ is below 30°, it typically signifies that the material is flowing
easily, while a value up to 40° suggests that there is some potential for flow. If Φ exceeds
50°, the flow becomes substantially more challenging. The interrelation between bulk density
and tap density serves as an additional method for assessing the flowability. Indices like the
Hausner Ratio (HR) and Carr's Index (CI) utilize tapped and bulk densities as foundational
measurements. The Hausner ratio, which is the relationship between the bulk density and the
tapped density, can range from 1.2 for powders that can move freely to 1.6 for powders with
stronger adhesive properties [35].
The Carr's Index, which measures the compressibility percentage, can be calculated by
dividing the difference between bulk density and tapped density by the tapped density and
multiplying the result by 100. The values of Carr’s record of around 5–12% show free-
flowing powder, 23–35% show destitute stream, and >40% an amazingly destitute stream
[36]. In determining the resistance of particles, particularly those with low cohesiveness like
granular powder, flow rate plays a critical role. A simple indication of the ease with which a
material can be induced to flow is given by compressibility index, I.
I = [1 - Vt / V0] × 100,
The volume after tapping, denoted as Vt, is distinguished from the volume before tapping,
represented by V0 [37]. A powder's flow properties are considered favorable when the value
of I is less than 15%, while a value exceeding 25% suggests poor flow properties [38].
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8. CONCLUSION
Understanding the physics behind the compression of tablets provides important insights into the
compatibility and flow characteristics of pharmaceutical powders, which are crucial factors to consider
in tablet formulation. Materials for plastic deformation, fragmentation, and elasticity can be compared
with various materials using technology. Studying bonding theories enhances tablet strength. Powder
parameters such as flow rates and moisture content are examined for their impact on tablet compression.
Compaction is key for tablet production, thus it's vital to comprehend its physics. Despite physics being
a complex field, several factors impact tablet attributes, including drug/excipient deformation, solid-state
properties, and process parameters. A pharmaceutical researcher can plan an ideal definition that's free
of issues such as capping, laminating, picking, and staying by carefully considering the factors of the
compaction prepare. The successful production of tablets largely depends on the compatibility of drugs
used, particularly in high dosage systems. An understanding of the commitment of tableting excipients
to the compaction conduct of the tablet network can lead to science-based excipient choice. The review
article aims to provide insight into the significance of physics in formulating tablets and dosage forms
within the industry. It highlights the vital role of various flows involved in conventional dosage forms
and fluids, including liquids and capsules.
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