Rheology

The term rheology from the Greek rheo ( to flow ) and logos ( science ) was suggested to describe the flow of liquids and the deformation of solids.

The importance of rheology in pharmacy and its’ applications : Rheology is important for the formulation and analysis of pharmaceutical products as emulsions, suppositories, cosmetic creams, lotions and tablet coatings. Rheology is involved in the mixing and flow of materials, their packaging into containers and their removal prior to use, whether this is achieved by pouring from bottle, extrusion from a tube or passage through a syringe needle.

3. The rheology of particular product, which can range in consistency from fluid to semisolid to solid, can effect its patient acceptability, physical stability, and even biologic availability, for example, viscosity has been shown to affect absorption rates of drugs from the gastrointestinal tract.

Viscosity : is an expression of the resistance of a fluid to flow, the higher the viscosity the greater the resistance to flow. FACTORS INFLUENCING THE VISCOSITY Intrinsic Factors 1. Molecular size or molecular weight: the heavier the molecule of the given liquid, the greater will be the viscosity. 2. Shape: Liquids with large and irregularly shaped molecules are generally known to be viscous compared to small and symmetric molecules. 3. intermolecular forces : as the intermolecular interactions are stronger the molecules tend to stick to each other thereby increasing the viscosity of the liquid. The higher the intermolecular forces, the higher is the viscosity.

Pressure: An increase in pressure enhances the Extrinsic Factors Pressure: An increase in pressure enhances the cohesive forces of interaction leading to an increase in the viscosity. 2. Added substances: In general, small quantities of non electrolytes like sucrose, glycerin and alcohol when added to the water, the solution exhibits increased viscosity. Similarly, polymers and other macromolecules enhance the viscosity of solvents such as water. On the other hand, small amounts of strong electrolytes decrease the viscosity.

As the temperature increases, the system acquires thermal energy which facilitates the breaking of the cohesive forces. The viscosity of liquid decreases. In case of gases, an increase in temperature increases the viscosity owing to the increased molecular collisions and interactions . for many substances is expressed by Arrhenius equation of chemical kinetics η = A e A :is constant depend on the M.WT and molar volume of liquid. Ev: is the activation energy required to initiate flow between molecules. Ev 1 lnη = lnA + R T EvRT

The activation energy = 1/3 energy of vaporization. The energy of vaporization: is the energy required to remove a molecule from a liquid, leaving a hole behind equal in size to that of the molecule that has been departed. A hole must also be made available in a liquid if one molecule is to flow pas another. So it can be concluded that the free space needed for the flow is about one-third the volume of the molecule.

Centipoise (cp) = 0.01 poise The unit of viscosity is the Poise : which is the shearing force required to produce a velocity of 1cm/sec between two parallel planes of liquid each 1 cm² in area separated by a distance of 1 cm. Centipoise (cp) = 0.01 poise Fluidity (Φ) : is the reciprocal of the viscosity Φ = 1 η

Kinematic viscosity: is the absolute viscosity divided by the density of the liquid at a specific temperature. η Kinematic viscosity = P The units of kinematic viscosity are the stoke (s) and the centistoke(cs)

Acetone viscosity was found to be 0 Acetone viscosity was found to be 0.313 cp at 25 Cº, its density at this temperature is o.788 g/ml, what is the kinematic viscosity of acetone at this temp. η Kinematic viscosity = P

Substances, such as hydrocolloids and polymers, are dispersed in water and utilised as vehicles in the formulation of several dosage forms. These substances are termed as suspending agents or bodying agents. Such as methylcellulose and bentonite. Substances, such as glucose, fructose and sucrose, in water increase the viscosity of water to an appreciable extent. Honey is highly viscous and contains a large proportion of fructose. Simple syrup (sucrose in water) is also viscous.

Polymer solutions are still more viscous, the viscosity of polymer solutions increases almost many folds with concentration, i.e., the increase in viscosity is exponential with concentration. For example, methylcellulose USP in the concentration of 2.0 % w/w in water shows an apparent viscosity of 80 poise at room temperature. The viscosity of water is 0.01 poise. In other words, the increase in viscosity of water is 8000 fold. Normally, such polymers are used in low concentrations.

Mechanism of enhanced viscosity The lower sugars, such as glucose and sucrose contain many alcohol functional groups. These react with water molecules through hydrogen bonding. The higher numbers such as starch and other cellulose polymers also react with water. For example, methylcellulose has three to four ether groups and one to two hydroxyl groups. When water is added to it, the groups get easily hydrated in solution. When the polymer molecule moves, the hydrated solvent sheath also moves. As a result, the size of polymer unit increases and hence, increases the resistance to flow.

types of flow and deformation The classification of material according to types of flow and deformation This classification depends on whether or not their flow properties are in accord with Newton's Law of flow

Newton's Law of flow The difference of velocity dv between tow planes of liquids separated by an infinitesimal distance dr is the velocity gradient or the rate of shear G = dv/dr The force per unite area F`/ A , required to bring about a flow is called the shearing stress = F F’ A dv dr The higher the viscosity of the liquid the greater is the force per unit area ( shearing stress ) required to produce a certain rate of shear. Rate of shear Shearing stress

F` = η dv dv = G (rate of shear) A dr dr F` = F ( shearing stress ) A F = η G η = F G A representative flow curve or rheogram, obtained by plotting F versus G

For Newtonian system a straight line passing through the origin is obtained. Slope = fluidity F

Non Newtonian systems Most of pharmaceutical fluid products are not simple liquids and do not follows Newtonian law of flow . Example colloidal solutions, emulsions, suspensions and ointments. These systems can be classified into 3 classes of flow. Plastic flow. Pseudoplastic flow. Dilatant flow.

Plastic flow The substance that exhibits plastic flow are known as Bingham bodies. Plastic flow curves do not pass through the origin, but intersect the shearing stress axis at a particular point referred to as the yield value. The Bingham bodies does not begin to flow until a shearing stress exceed the yield value . At a stress below the yield value the substance act as an elastic material. Rate of shear Slop = mobility f = yield value Shearing stress Plastic flow

How the plastic flow is produced Plastic flow is associated with the presence of flocculated particles in concentrated suspensions, so in this case the yield value results from the contacts between adjacent particles which must be broken down before flow can occur . So the yield value indicate the force of flocculation in that the higher the flocculated suspension the higher the yield value. At a value of shearing stress above the yield value the plastic systems become resemble Newtonian systems in that there is a direct relation ship between the shearing rate and shearing stress.

F : is the shearing stress. G: is the shearing rate. The slop of the rheogram in plastic flow is termed as the mobility which analogous to the fluidity in Newtonian system, and its` reciprocal is known as plastic viscosity (u) F - f u = G F : is the shearing stress. G: is the shearing rate. f : is the yield value.

Example: A plastic material was found to have a yield value of 5200 dynes / cm². at shearing stress above the yield value, F was found to increase linearly with G, if the rate of shear was 150 sec -¹ when F was 8000 dynes / cm². calculate the plastic viscosity of the sample.

Pseudoplastic flow Pseudoplastic flow is typically exhibited by polymers in solution, example natural and synthetic gums as tragacanth, methyl cellulose and sodium carboxymethyl cellulose. The curve of the pseudoplastic flow begins at the origin therefore there is no yield value as there is in the plastic flow. The viscosity of the pseudoplastic material can not be expressed by any single value, in that it will be decreased with increasing the rate of shear. HOW? G F

As the shearing stress is increase , normally disarranged molecule begin to arrange their long axis 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 molecule may be released resulting in effective lowering of the conc. And size of dispersed molecules, this will lead to reduce the apparent viscosity. The viscosity of the pseudoplastic material cannot be expressed by any single value, it can be obtained at any rate of shear from the slop of the tangent to the curve at the specified point tangent

This flow is the inverse of the pseudoplastic flow in that there is an increase in the resistance to flow with increasing the rate of shear . These systems actually increase in volume when sheared and hence termed Dilatant. Dilatant flow So dilatant materials are referred to as shear thickening systems while pseudoplastic materials referred to as shear thinning systems. Why ?

Usually dilatant flow are produced by suspension that contain a high conc. ( 50% or more ) of small deflocculated particles. G F

The dilatant flow can be explained as follows By increasing shear stress Closed – packed particles, minimum void volume, sufficient vehicle, relative low consistency Open packed ( dilated ) particles, Increased void volume, Relative high consistency

Particles are closely packed with minimal interparticle volume ( void ), the amount of vehicle in suspension is sufficient to fill the voids and permits particles to move relative to on another at low rate of shear. As shear stress is increased the particles is in an attempt to move quickly past each other, taking an open form of packing which leads to a significant increase in interparticle void volume.

The amount of vehicle remains constant and at some points becomes insufficient to fill the increased voids between particles, accordingly resistant to flow increases because particles are no longer completely wetted or lubricated by the vehicle, eventually the suspension will set up as a firm paste.

Thixotropy : it is an isothermal and comparatively slow recovery, on standing of a material, of a consistency lost through shearing. i.e. shear- thinning systems Thixotropy Plastic Pseudoplastic Thixotropy in Newtonian system Thixotropy in plastic and pseudoplastic systems

For Newtonian systems: When the shear stress were reduced once the desired maximum had been reached, the down curve would be identical with and super imposable on the up curve . For the non Newtonian systems (plastic and pseudoplastic ): The down curve is frequently displaced to the left of the up curve showing that the material has a lower consistency at any one rate of shear on the down curve than it hade on the up curve. This indicates the break down of structure that does not reform immediately when stress is removed or reduced. Gel Sol Gel

Thixotropy in Dilatant Systems In dilatant systems, an increase in the shearing stress causes an apparent increase in viscosity at a given temperature. On removal of the shearing stress, the viscosity decreases but after a lag time. This phenomenon is known as thixotropy in dilatant systems and may be described as a reversible isothermal transformation from sol to gel. Application of Removal of shear stress shear stress Sol Gel Sol

G F Thixotropy in dilatant system

Negative Thixotropy Antithixotropy or negative thixotropy represents an increase in consistency on the down curve. For example, magnesia gel exhibits an enhanced resistance to flow with increased time of shear compared to resting state. In the rheogram, the down-curve shifts to the right of the up-curve. When magnesia gel is sheared alternatively with increasing and then decreasing rates of shear, the gel thickens. As these cycles continue, the extent of increase in the thickening reduces gradually and finally reaches equilibrium state. There will be no change in the consistency curves on further cycles of shear rate.

D C A B G F Rheogram of antithixotropic behavior. Example is Magnesia gel

In the resting state, the system consists of a large number of individual particles and small floccules. When the product is sheared, the polymer molecular collisions are increased at a greater frequency. As a result, interparticle bonding increases. At equilibrium, large floccules are available in small numbers. However, the system exhibits sol form at equilibrium. When the product is allowed to rest, the large floccules breakup and gradually return to the original state of small floccules and individual particles.

Negative thixotropy should not be confused with the term 'dilatancy' Negative thixotropy should not be confused with the term 'dilatancy'. Dilatant systems are deflocculated and the volume of solids is high (more than 50%), whereas negative thixotropy is seen in a flocculated system containing low solid content (1 to 10%).

AT REST Individual particles are (On storage) in large number Small flocs (low viscosity) ON SHEAR Particle collisions (Equilibrium) particle contacts are more; Large flocs in small numbers (high consistency) SET ASIDE Flocs contacts break (Removal of stress) individual particles (low consistency) Particle-particle interactions in an antithixotropic material

Rheopexy is a phenomenon in which a sol transforms to a gel state more readily rather than keeping a sol at rest. A gentle shaking or low rate of shear is sufficient to transform a sol into a gel. At equilibrium, the system is in gel state, while antithixotropy exhibits sol form