Transcript RHEOLOGY
RHEOLOGY
Definition:
The branch of physics, which deals with deformation and flow of matter. Rheology governs the circulation of blood & lymph through capillaries and large vessels, flow of mucus, bending of bones, stretching of cartilage, contraction of muscles.
Fluidity of solutions to be injected with hypodermic syringes or infused intravenously, flexibility of tubing used in catheters, extensibility of gut.
From the rheological viewpoint systems are: Solid if they preserve shape & volume. Liquid if they preserve their volume. Gaseous if neither shape nor volume remains constant when forces are applied to them.
To the pharmacist: Flow of emulsions through colloid mills, Working of ointments on slabs or roller mills.
Trituration of suspensions in mortar and pestle.
Mechanical properties of glass or plastic containers & of rubber closures. To the consumer: Squeezing toothpaste from a collapsible tube. Spreading lotion on his skin. Spraying liquids from atomizers or aerosol cans.
Types of Flow:
The choice depends on whether or not their flow properties are in accordance to Newton's law of flow.
Newtonian Non - Newtonian
Representation of flow of liquid
Newton Law of Flow:
Laminar or Stream line
:
The bottom layer is considered to be fixed in place. If the top plane of liquid is moved at a constant velocity, each lower layer will move with a velocity ∞ to its distance from the stationary layer.
Velocity gradient
or
rate of shear
,
dv / dr
. The rate of shear indicates how fast the liquid flows when a shear stress is applied to it. Its unit is sec -1 . The force per unit area (
F'/A)
required to bring about flow is called the shearing stress and its unit is dyne/cm 2 .
F'/A = η dv / dr (1)
Where
η
is the viscosity .
Equation (1) is frequently written as:
η = F/G (2)
Where
F = F'/A
&
G = dv/dr. For Newtonian System straight line passing through the origin is obtained.
is shown in the figure. A
Units of Absolute Viscosity:
The Poise
(p), is the shearing force required to produce a velocity of 1 cm/sec. between two parallel planes of liquid each 1 cm 2 in area & separated by a distance of 1 cm.
The Centipois
(cp), 1 cp = 0.01 poise .
Fluidity
( ) is the reciprocal of viscosity:
(
) = 1/η (3)
Kinematic viscosity
: is the absolute viscosity divided by the density of the liquid
Kinematic viscosity
= η/ρ (4)
The units of kinematic viscosity are the
stoke
(
s
) & the
centistoke
(
cs
).
Effect of Temperature on Viscosity:
Viscosity of a gas increases with the increase of temperature.
Viscosity of liquid decreases as the temperature is raised & the fluidity of a liquid, increases with temperature.
Non-Newtonian Systems:
Non - Newtonian bodies are those substances, which fail to follow Newton's law i.e. liquid & solid , heterogeneous dispersions such as colloidal solutions, emulsions, liquid suspensions and ointments. They are classified into 3 types of flow: Plastic. Pseudoplastic. Dilatant.
Plastic Flow:
Materials exhibiting plastic flow are known as
Bingham bodies
.
The plastic flow curve does not pass through the origin & it intersects the shearing stress axis (or will if the straight part of the curve is extrapolated to the axis) at a particular point referred to as
yield value
.
(f) A Bingham body does not begin to flow until a shearing stress, corresponding to the yield value, is exceeded.
The slope of the rheogram =
mobility
, ( fluidity in Newtonian systems).
Its reciprocal is known as the
plastic viscosity
.
U = ( F-f ) / G (5)
where
f
is the yield value, or (intercept, on the shear stress axis in dynes cm -2 ).
U is the plastic viscosity.
Plastic flow is associated with the presence of flocculated particles in concentrated suspensions. continuous structure is set up.
The yield value is present due to contacts between adjacent particles (brought about by V
an der Waal's
forces).
Consequently, the yield value is an indication of the force of flocculation, the more flocculated the suspension, the higher will be the yield value. Frictional forces between moving particles can also contribute to the yield value. Once the yield value has been exceeded, any in shearing stress (i.e.
F-f
) brings about a directly proportional increase in
G
, the rate of shear. Aplastic system resembles a Newtonian system at shear stresses > the yield value.
Pseudoplastic Flow:
Polymers in solution, natural & synthetic gums, e.g. liquid dispersions of tragacanth, sodium alginate, methylcellulose. The curve for a pseudoplastic material begins at the origin (or at least approaches it at low rates of shear). The curved rheogram for pseudoplastic materials is due to shearing action on the long chain molecules of materials such as linear polymers.
In contrast to Bingham bodies, there is no yield value no part of the curve is linear, one cannot express the viscosity of a pseudoplastic material by any single value.
F N = η' G (6)
The exponent N rises as the flow becomes increasingly non Newtonian. When N = 1, equation (6) reduces to equation (2) & the flow is Newtonian.
F= η' G
The term
η'
is a viscosity coefficient. Following rearrangement, equation (6) may be written in the logarithmic form:
log G = N log F log η' (7)
This is an equation for a straight line. Many pseudoplastic systems fit this equation when
log G
is plotted as a function of
log F
.
Shearing stress Coiling & entanglement Alignment & disentanglement Due to Random & Brownian motion in fluids Shear stress applied to the fluid
As the shearing stress the normally disarranged molecules begin to align their long axes in the direction of flow. This orientation reduces the internal resistance of the material and allows a greater rate of shear at each successive shearing stress. In addition, some of the solvent associated with the molecules may be released, resulting in an effective lowering of the concentration and size of dispersed molecules. An equilibrium exists between the shear induced changes and random coiling tendency caused by stress.
Brownian motion
which entraps water inside the coils. The rate of entanglement and randomization by Brownian motion is constant, while the rate of disentanglement and alignment increases with increasing shear The viscosity diminishes as the shear is increased, so they known as “ shear thinning systems ” .
F N = η' G (6)
The exponent N rises as the flow becomes increasingly non-Newtonian. When N = 1, equation (6) reduces to equation (2) and the flow is Newtonian. The term η' is a viscosity coefficient. Following rearrangement, equation (6) may be written in the logarithmic form:
log G = N log F log η' (7)
This is an equation for a straight line. Many pseudoplastic systems fit this equation when log G is plotted as a function of log F.
Dilatant Flow:
Certain suspensions with a high percentage of dispersed solids exhibit an in resistance to flow with increasing rates of shear. Such systems actually increase in volume when sheared & are called dilatant. Dilatant materials "shear thickening systems." When the stress is removed, a dilatant system returns to its original state of fluidity.
F N = η' G (6)
N is always < 1 and decreases as the degree of dilatancy increases.
As N approaches 1, the system becomes increasingly Newtonian in behavior . Substances possessing dilatant flow properties are invariably suspensions containing a high concentration (about 50 % or greater) of small, deflocculated particles.
At rest: Particles are closely packed with small interparticle volume. The amount of vehicle in the suspension is enough to fill this volume. The particles move relative to one another at low rates of shear.
Applying shear stress Particle , s arrangement is expanded, particles take an open form of packing (dilate). The amount of vehicle in the suspension is constant & becomes insufficient to fill the inter-particles voids. The resistance to flow increases, the particles are no longer completely wetted or lubricated by the vehicle. Eventually, the suspension will set up as a firm paste.
Time-Dependent Behaviour: Thixotropy:
Newtonian systems
the up-curve. : If the rate of shear was reduced once the desired maximum rate had been reached, the down curve would be identical with & superimposed on Non Newtonian systems: With shear-thinning systems (i.e., plastic & pseudoplastic), the down - curve is frequently displaced to the left of the up-curve. This means that the material has a lower consistency at any one rate of shear on the down-curve than it had on the up curve. This phenomenon is known as
Thixotropy.
Definition: It is a comparatively slow recovery, on standing of a material which lost its consistency through shearing." Thixotropy is only applied to shear-thinning systems. This indicates a breakdown of structure (shear-thinning), which does not reform immediately when the stress is removed or reduced .
Gel structure Asymmetric particles, many points of contact , network structure & rigid structure.
Shearing stress
Sol structure Breakdown of structure, flow starts, particles are aligned and transform to sol (shear thinning)
Removal of Shearing stress
Gel structure Rebuild of the gel structure by brownian motion (time is not defined)
An aqueous dispersion of
8% w /w sodium bentonite
sets to gel within an hour or two after preparation when undisturbed, but flows & can be poured within many minutes after it had been stirred above the yield value. After prolonged rest it reverts to a gel. Thixotropic systems usually contain asymmetric particles which, possess numerous points of contact & set up a loose three-dimensional network. At rest , this structure confers some degree of rigidity on the system & it resembles a gel.
As shear is applied & flow starts, this structure begins to break down. Points of contact are disrupted & the particles become aligned. The material a gel-to-sol transformation & exhibits shear thinning.
Upon removal of the stress, the structure starts to reform. This process is not immediate. It is a progressive restoration of consistency as the asymmetric particles come into contact with each other by undergoing random brownian movement. The rheograms obtained with thixotropic materials are dependent on: 1- The rate at which shear is increased or decreased.
2- The time for which a sample is subjected to any one rate of shear.
Choice of Viscometer
“ One point" instruments : provide a single point on the rheogram. Extrapolation of a line through this point to the origin will result in the complete rheogram. Used for Newtonian fluids. Since the rate of shear is directly proportional to the shearing stress.
The capillary and falling sphere are for use only with Newtonian materials
“Multi-point" instruments: Used with non-Newtonian systems The instrumentation used must be able to operate at a variety of rates of shear. Cup and Bob , Cone and Plate viscometers may be used with both types of flow system
:Falling Sphere Viscometer
The sample & ball are placed in the inner glass tube & allowed to reach temperature equilibrium with the water in the surrounding constant temperature jacket. The tube & jacket are then inverted, which effectively places the ball at the top of the inner glass tube. The time for the ball to fall between two marks is accurately measured & repeated several times. For newtonian liquids:
η = t ) Sb – Sf ( B
t
= the time interval in sec. Sb & Sf are the specific gravities of the ball & fluid under examination at the temperature being used. B is a constant for a particular ball and is supplied by the manufacturer. The instrument can be used over the range 0.5 to 200,000 poise.
:Cone and Plate Viscometer
The sample is placed at the center of the plate which is then raised into position under the cone.
The cone is driven by a variable speed motor & the sample is sheared in the narrow gap between the stationary plate and the rotating cone.
The rate of shear in rev. /min. is increased & decreased by a selector dial & the torque (shearing stress) produced on the cone is read on the indicator scale.
A plot of rpm or rate of shear versus scale reading or shearing stress may be plotted.
C is an instrumental constant . T is torque reading.
V is speed in revolution / η = minute.
C T / V U = C (T - T f ) / V f = T f x C f C f is constant Plastic materials
Advantages :
The rate of shear is constant throughout the entire sample being sheared. As a result, any change in plug flow is avoided. Time saved in cleaning & filling.
Temperature stabilization of the sample during a run. The cone and plate viscometer requires a sample volume of 0.l to 0.2 ml. This instrument could be used for the rheological evaluation of some pharmaceutical semisolids.
Factors Affecting Rheological Properties in Pharmaceutical Products:
Chemical Factors:
(a) Degree of Polymerization:
Suspending agents, and emulsion stabilizers act in low concentrations to produce viscous solutions (high molecular weight). Lower concentrations of the high molecular weight grades of synthetic & modified natural gums are used to obtain the desired viscosity.
(b) Extent of Polymer Hydration:
In hydrophilic polymer solution the molecules are completely surrounded by immobilized water molecules forming a solvent layer. Such hydration of hydrophilic polymers gives rise to an increased viscosity.
The solvate layer is strongly bound to the macromolecule viscosity will be insensitive to pH changes or low concentrations of electrolytes. Loose solvate around the macromolecules, pH & electrolytes will produce variations in viscosity.
( c) Impurities, Trace Ions and Electrolytes Changing the viscosity of natural polymers, e.g. in sodium alginate solution, the viscosity to the gelling point traces of calcium are present the formation of calcium alginate.
At concentrations, electrolytes do not change the viscosity of natural colloids in aqueous solution. concentrations, the salts compete for the adsorbed water molecules, surrounding the hydrated polymer, due to the affinity of the salt ions for water. As the polymer molecules become dehydrated, their dispersions decrease in viscosity & precipitation occurs
)
d) Effect of pH :
Changes in pH greatly affect the viscosity & stability of the hydrophilic natural & synthetic gums. The natural gums usually have a relatively stable viscosity plateau extending over 5 or 4 pH units. Above and below this stable pH range viscosity decreases sharply. Methyl cellulose has a stable pH range of 3 to 12. Sodium salts polymers are unstable in acid medium due to the separation of the acid form of the polymer, e.g. sodium alginate.
(E) Sequestering Agents and Buffers:
Sequestering agents have a stabilizing effect on viscosity in some polymer solutions, which are decomposed by traces of metals.
Examples :
Calcium ions the viscosity of sodium alginate. Addition of sequestering agents i.e. EDTA or hexameta-phosphate will viscosity in sodium alginate solutions. Tragacanth solution also suffers a rapid loss in viscosity, regardless of the pH, in systems, which bind calcium ions, i.e citrate buffers.
Physical Factors:
(a) Aeration:
Aerated products usually result from high shear milling. Aerated samples are more viscous or have more viscous creamed layer than non-aerated samples. Some aerated emulsions will be less viscous & less stable than un-aerated samples due to concentration of the surfactant or emulsion stabilizer at the air liquid interface & thus deletion of the stabilizer at the oil - water interface. De-aeration is done: Mechanically by roll milling, which squeezes out the air. Heat the aerated system.
(b) Light:
Various hydrocolloids in aqueous solutions are reported to be sensitive to light. These colloids include carbopol, sodium alginate & sodium carboxymethyl cellulose. To protect photosensitive hydrocolloids from decomposition: The use of light-resistant containers, Screening agents, antioxidants.
In the case of carbopol, the use of sequestering agents.
(c) The Degree of Dispersion and Flocculation :
In concentrated suspensions
of 3% solids & higher , a decrease in particle size of the solid phase, produce an increase in the viscosity of the system. This viscosity increase to immobilization of the vehicle with an increase in the fraction of the suspension volume effectively occupied by the solid. The addition of insoluble solids to a Newtonian vehicle non-Newtonian flow properties in system. The smaller the particle size of the dispersed solid phase, the lower the concentration of the solids required to produce non-newtonian flow and thixotropy.
Flocculation
of a suspension system: Flocculation viscosity & thixotropy. The flocs or aggregates are held weakly together and are capable of forming extended networks which give the flocculated suspension its structural properties. Immobilization of a portion of the dispersing media in the network & between the flocs viscosity.
Pharmaceutical and Biological Applications of Rheology:
1- Prolongation of Drug Action: The rate of absorption of an ordinary suspension differs from thixotropic suspension .
Example:
procaine penicillin G, a form of penicillin, of relatively low water solubility. Aqueous suspensions containing between 40 and 70% w/v of milled or micronized procaine penicillin G + small amount of sodium citrate & polysorbate 80 are thixotropic pastes & are of depot effect when injected intramuscularly .
Ordinary suspension of pencillin G I.M injection Thixotropy suspension of pencillin G Forms no depot, fast dispersion & absorption so maintain therapeutic Level for short time Forms spherical deposits at site of injection which resists disintegration by tissue fluids& Small surface area ( absorption) so maintain therapeutic Level for longer time The formation of depot depends on: a- high yield value b-fast thixotropic recovery after injection.
) 2 ( Effect on Drug Absorption:
The viscosity of creams and lotions may affect the rate of absorption of the products by the skin. A greater release of active ingredients is generally possible from the softer, less viscous bases. The viscosity of semi-solid products may affect absorption of these topical products due to the effect of viscosity on the rate of diffusion of the active ingredients.
(3) Thixotropy in Suspension and Emulsion Formulation:
Thixotropy is useful in the formulation of pharmaceutical suspensions and emulsions. They must be poured easily from containers (low viscosity)
Disadvantages of Low viscosity:
Rapid settling of solid particles in suspensions and rapid creaming of emulsions. Solid particles, which have settled out stick together, producing sediment difficult to redisperse ("caking or claying"). Creaming in emulsions is a first step towards coalescence. (break down of emulsion)
A thixotropic agent such as sodium bentonite magma, colloidal silicon dioxide, is incorporated into the suspensions or emulsions to confer a high apparent viscosity or even a yield value .
At rest : High viscosities retard sedimentation & creaming . Yield values prevent them altogether; since there is no flow below the yield stress, the apparent viscosity at low shear becomes infinite
Pouring the suspension or emulsion from its container: Shaking at shear stresses above the yield value The agitation breaks down the thixotropic structure so reducing the yield value to zero & lowering the apparent viscosity. This facilitates pouring. Back on the shelf, the viscosity slowly increases again and the yield value is restored as Brownian motion rebuilds the house-of-cards structure of bentonite.