RHEOLOGY Part 2
Link for Video Demonstration of the topic on my YouTube channel πππ
https://youtu.be/f7kF6z07DdI
NEWTONIAN AND NON- NEWTONIAN FLOW
Liquids which follow Newton’s law of viscous flow are known as Newtonian liquids and those which do not follow it are known as non-Newtonian fluids.
While viscosity of Newtonian fluids remains constant, that of non-Newtonian fluids changes with change in applied shear force. While sample liquids like water, true solutions and dilute suspensions are example of Newtonian fluids, most of the pharmaceutical formulations like colloidal dispersions, emulsions, ointments or gels are examples of non-Newtonian fluids.
NEWTONIAN FLOW
Newton was the first to study the flow properties of liquid in quantitative terms. Liquids that obey Newton’s law of flow i.e. equation 1
F = ΕG
are called Newtonian fluids. The rheological properties of liquids are usually expressed in the form of flow diagrams or rheograms which consist of graphs showing the variation of shear rate with shear stress.
The plot for Newtonian liquid like water, simple organic liquids, true solutions and dilute suspensions and emulsions is a straight line, the slope of which is equal to the reciprocal of viscosity, a value referred to as the fluidity,
ΙΈ=1/Ε ____eq.3
NON NEWTONIAN FLOW
Rheology of heterogeneous dispersion such as concentrated emulsions, suspensions and semisolids are more complex form of liquids which don not obey Newton’s equation of flow. Based of the pattern of curves, non- Newtonian fluids are:
1. Plastic fluid
2. Pseudoplastic fluid
3. Dilatant fluid
PLASTIC FLOW
The consistency of curve for plastic fluid is given below:
The curve doesn’t pass through the origin. The substance initially behaves like an elastic body and fails to flow when less amount of stress is applied. When sufficient stress is applied with further increase in shear stress, leads to non-linear increase in the shear rate which progressively gets linearized after which it behaves like a Newtonian fluid. The linear portion when extrapolated intersects the x-axis at a point called yield value or Bingham yield value, FB or f.
The slope of the rheogram is termed as mobility, and it’s reciprocal is known as plastic viscosity, U.
U= F – f ___eq.4
G
Cause of plastic flow:
Plastic flow is considered to be the result of presence of flocculated particles in a concentrated suspension, butter, certain ointment, paste, gel or emulsion. The mechanistic explanation for the observed behaviour is as Floccules are the aggregation of particles with inter-particle contacts. This structure is maintained when the system is at rest .
Yield value represents the stress required to break the inter-particle contacts so that particles behave individually. Therefore, yield value is indicative of the forces of flocculation. More the degree of flocculation, more is the force required to bring the flow, i.e. more shear stress required. Frictional forces between moving particles also contribute to the yield value. Once the yield value exceeds, further increase in shearing stress (F-f) will bring about a proportional increase in the rate of shear.
PSEUDOPLASTIC FLOW
The consistency curve for a pseudoplastic flow begins at the origin (nearly zero at lower shear stress conditions).
As the shear stress increases progressively, shear rate also increases, but the trend is not linear . Therefore, the viscosity of a pseudoplastic system cannot be expressed by a single value. The entire curve is the most satisfactory representation of the pseudoplastic material.
FN = Ε'G ____eq.5
where
N is a number given to the exponent
Ε' is the viscosity coefficient
In case of pseudoplastic fluids, N is higher than 1 and rises as the flow becomes increasingly non-Newtonian. When N = 1, equation (5) becomes equation (1), i.e., Newtonian flow. The greater the value of N above unity, the greater is the pseudoplastic behaviour of the material. Taking logarithms of both sides, equation (5) can be written as:
N log F= log Ε' + log G ___eq.6
On rearrangement,
log G= N log F - log Ε' ____eq.7
In general, pseudoplastic flow is exhibited by polymer dispersions such as:
• Tragacanth in water
• Sodium alginate in water
• Methylcellulose in water
• Sodium carboxymethylcellulose in water
Cause of pseudoplastic flow:
Under normal storage conditions, the long chain molecules of the polymers are randomly arranged in the dispersion at rest. On applying a shear stress, these molecules begin to arrange their long axes or align in the direction of force applied. In addition, the solvent molecules which were earlier associated with the polymer molecules will also gets released as the polymer molecules align which reduces effectively the resistance to flow. Thus, the material becomes less viscous. Now, the material allows greater shear rate on progressive increase in the shearing stress.
DILATANT FLOW
The system exhibits enhanced resistance to flow with increasing rate of shear. When shear stress is applied, these systems increase their volume and hence are known as dilatant. Dilatant materials are also often termed as shear thickening systems because of increased apparent viscosity at higher rates of shear. When the stress is removed, the system returns to its initial state of fluidity. Dilatant flow is exhibited by:
• Highly concentrated suspensions containing solids (>50 per cent) of small, deflocculated particles.
• Suspension of starch in water.
• Inorganic pigments in water.
e.g. Kaolin 12% in water or Zinc oxide 30% in water
Cause of dilatant flow:
Dilatant flow is exhibited by suspensions containing a high concentration of very fine particles. The particles, although in close packed arrangement are in a state of deflocculation. Flocculated suspensions on the other hand tend to show plastic flow rather than dilatancy.
When the deflocculated particles of a suspension settle, they pack into a mass of minimum volume. Only a small quantity of vehicle is needed to fill the voids between the particles but it is sufficient to allow the suspension to flow like a liquid. When the undisturbed mass is vigorously agitated, the bulk is increased as the particles force past one another. This expansion results in a larger volume between the particles and an insufficiency of vehicle to fill the voids. Thus the unlubricated particles show an increased resistance to flow and a rigid paste results.
Dilatancy does not occur in a dilute suspension where the vehicle is in great excess.
Dilatancy may prove to be troublesome during processing of dispersions and granulation of tablet masses when high speed mixers and mills are employed. If the material being processed becomes dilatant, the resulting solidification can cause overload and damage to the motor.
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