RHEOLOGY
Roselyn Aperocho-Naranjo
Faculty, College of Pharmacy
USPF
Rheology
 rheo – to flow
 logos – science
 ology – the study of
 is the study of the flow of materials that behave
in an interesting or unusual manner.
 Unusual materials such as mayonnaise, peanut
butter, chocolate, bread dough, paints, inks,
road building aterials, cosmetics, dairy products,
etc.
Rheology
The study of viscosity is of true liquids,
solutions, dilute and concentrated colloidal
systems is of much importance in this
study
It is involved in the mixing and flow of
materials, their packaging into containers,
the pouring from the bottle, extrusion from
a tube or a passage of the liquid to a
syringe needle.
Rheology
Can affect the patient’s acceptability of the
product, physical stability, biologic
availability, absorption rate of drugs in the
gastrointestinal tract
Influence the choice of processing
equipments in the pharmaceutical system
Two Categories of
Flow & Deformation
Newtonian (Newtonian Law of Flow)
“the higher the viscosity of a liquid, the greater is the
force per unit area (shearing stress) required to
produce a certain rate of shear”
Shear – as a stress which is applied parallel or
tangential to a face of a material, as opposed to a
normal stress which is applied perpendicularly.
Shear stress
• Measured in (SI unit):
• Commonly used symbols:
• Expressed in other quantities:
pascal
τ
τ=F/A
A shear stress, is
applied to the top of
the square while the
bottom is held in place.
This stress results in a
strain, or deformation,
changing the square
into a parallelogram.
Two Categories of
Flow & Deformation
Newtonian (Newtonian Law of Flow)
A Newtonian fluid (named for Isaac Newton) is a fluid
whose stress versus rate of strain curve is linear and
passes through the origin. The constant of
proportionality is known as the viscosity.
A simple equation to describe Newtonian fluid
behavior is where
• τ is the shear stress exerted by the fluid ("drag") [Pa]
• μ is the fluid viscosity - a constant of proportionality [Pa·s]
• du is the velocity gradient perpendicular to the direction
dy of shear [s−1]
Two Categories of
Flow & Deformation
Newtonian (Newtonian Law of Flow)
In common terms, this means the fluid continues to
flow, regardless of the forces acting on it. For
example, water is Newtonian, because it continues to
exemplify fluid properties no matter how fast it is
stirred or mixed.
For a Newtonian fluid, the viscosity, by definition,
depends only on temperature and pressure (and also
the chemical composition of the fluid if the fluid is not
a pure substance), not on the forces acting upon it.
Two Categories of
Flow & Deformation
Newtonian (Newtonian Law of Flow)
For a Newtonian fluid, the viscosity, by definition,
depends only on temperature and pressure (and also
the chemical composition of the fluid if the fluid is not
a pure substance), not on the forces acting upon it.
If the fluid is incompressible and viscosity is constant
across the fluid, the equation governing the shear
stress is expressed in the Cartesian coordinate
system
Two Categories of
Flow & Deformation
Newtonian (Newtonian Law of Flow)
Cartesian coordinate system
where, by the convention of tensor notation,
• τij is the shear stress on the ith face of a fluid element in
the jth direction
• ui is the velocity in the ith direction
• xj is the jth direction coordinate
Two Categories of
Flow & Deformation
Newtonian (Newtonian Law of Flow)
Cartesian coordinate system
Tensor - are geometrical entities introduced into
mathematics and physics to extend the notion of
scalars, (geometric) vectors, and matrices
- Components of stress, a second-order tensor, in
three dimensions. The tensor in the image is the
row vector, of the forces acting on the X, Y, and
Z faces of the cube. Those forces are represented
by column vectors. The row and column vectors
that make up the tensor can be represented
together by a matrix.
Two Categories of
Flow & Deformation
Non-Newtonian
A non-Newtonian fluid is a fluid whose flow
properties are not described by a single constant
value of viscosity.
Many polymer solutions and molten polymers are
non-Newtonian fluids, as are many commonly found
substances such as ketchup, starch suspensions,
paint, blood and shampoo.
In a Newtonian fluid, the relation between the shear
stress and the strain rate is linear (and if one were to
plot this relationship, it would pass through the
origin), the constant of proportionality being the
coefficient of viscosity.
Two Categories of
Flow & Deformation
Non-Newtonian
A In a non-Newtonian fluid, the relation between the
shear stress and the strain rate is nonlinear, and can
even be time-dependent. Therefore a constant
coefficient of viscosity cannot be defined.
A ratio between shear stress and rate of strain (or
shear-dependent viscosity) can be defined, this
concept being more useful for fluids without timedependent behavior.
Two Categories of
Flow & Deformation
 Non-Newtonian Examples
 An inexpensive, non-toxic example of a non-Newtonian
fluid is a suspension of starch (e.g. cornflour) in water,
sometimes called oobleck (uncooked imitation custard,
being a suspension of primarily cornflour, has the same
properties).
The sudden application of force — for example:
• by stabbing the surface with a finger, or rapidly inverting the
container holding it — leads to the fluid behaving like a solid
rather than a liquid.
• This is the "shear thickening" property of this non-Newtonian
fluid. More gentle treatment, such as slowly inserting a spoon,
will leave it in its liquid state.
• Trying to jerk the spoon back out again, however, will trigger the
return of the temporary solid state.
• A person moving quickly and applying sufficient force with their
feet can literally walk across such a liquid.
Two Categories of
Flow & Deformation
Non-Newtonian Examples
There are fluids which have a linear shear
stress/shear strain relationship which require a finite
yield stress before they begin to flow. That is the
shear stress, shear strain curve doesn't pass through
the origin.
These fluids are called
1. Bingham plastics.
• clay suspensions, drilling mud, toothpaste, mayonnaise,
chocolate, and mustard. The classic case is ketchup
which will not come out of the bottle until you stress it by
shaking.
Two Categories of
Flow & Deformation
Non-Newtonian Examples
These fluids are called
1. Pseudoplastic Flow
• Polymers in solutions such as tragacant, sodium
alginate, methylcellulose
• Viscosity decreases with an increase in shear thinning
• Caused by the re-alignment of polymer and/or the
release of solvents associated with the polymers
2. Dilatant Flow
• Volume increases when sheared
• Shear thickening
• Suspension containing high-concentration of small
deflocculated particles
Two Categories of
Flow & Deformation
Non-Newtonian Examples
There are also fluids whose strain rate is a function of
time. Fluids that require a gradually increasing shear
stress to maintain a constant strain rate are referred
to as rheopectic.
An opposite case of this, is a fluid that thins out with
time and requires a decreasing stress to maintain a
constant strain rate (thixotropic).
THIXOTROPY
 is the property of some non-Newtonian
pseudoplastic fluids to show a time-dependent
change in viscosity; the longer the fluid
undergoes shear stress, the lower its viscosity.
 A thixotropic fluid is a fluid which takes a finite
time to attain equilibrium viscosity when
introduced to a step change in shear rate.
 the term is sometimes applied to pseudoplastic
fluids without a viscosity/time component. Many
gels and colloids are thixotropic materials,
exhibiting a stable form at rest but becoming
fluid when agitated.
THIXOTROPY
 pseudoplastic fluids
 Shear thinning is an effect where viscosity decreases
with increasing rate of shear stress. Materials that exhibit
shear thinning are called pseudoplastic.
 This property is found in certain complex solutions, such
as lava, ketchup, whipped cream, blood, paint, and nail
polish.
 Pseudoplasticity can be demonstrated by the manner in
which shaking a bottle of ketchup causes the contents to
undergo an unpredictable change in viscosity. The force
causes it to go from being thick like honey to flowing like
water.
 thixotropic fluid viscosity decreases over time at a
constant shear rate.
THIXOTROPY
The distinction between a thixotropic fluid
and a shear thinning fluid:
A thixotropic fluid displays a decrease in viscosity
over time at a constant shear rate.
A shear thinning fluid displays decreasing viscosity
with increasing shear rate.
Some fluids are anti-thixotropic: constant shear
stress for a time causes an increase in viscosity or
even solidification. Constant shear stress can be
applied by shaking or mixing. Fluids which exhibit
this property are usually called rheopectic. They are
much less common.