Rheology - MOD-15-RHEOLOGY-FINALS PDF

RHEOLOGY Pharmaceutics-I (Physical Pharmacy) CONTENTS Definition & basic concepts Newtonian systems Non-Newtonian systems Thixotropy/ Anti-thixotropy/Rheopexy Rheology of emulsions & suspensions Determination of rheological properties- Viscometers Application of rheology...

RHEOLOGY Pharmaceutics-I (Physical Pharmacy) CONTENTS Definition & basic concepts Newtonian systems Non-Newtonian systems Thixotropy/ Anti-thixotropy/Rheopexy Rheology of emulsions & suspensions Determination of rheological properties- Viscometers Application of rheology INTRODUCTION It is derived from Greek word rheo means “to flow” and logos means “science” as suggested by Eugene C. Bingham (who proposed the mathematical form of the Bingham plastic - a viscoplastic material that behaves as a rigid body at low stresses but flows as a viscous fluid at high stress.). Scientifically, it is defined as: “the study of flow of fluids under applied stress (deformation forces)” Oil and water flow in familiar, normal ways, whereas honey, mayonnaise, peanut butter flow in complex and unusual ways. In rheology, we study the flows of unusual or interesting materials. The two-plates model mathematically describes this definition.  All materials range on an imaginary scale from solid to liquid. In scientific terms, solid materials are specified as elastic (*, while liquids are viscous. However, most materials are not purely elastic, nor entirely viscous, but viscoelastic. Depending on their properties, substances can be classified as viscoelastic solids (like e.g. gels) or viscoelastic liquids (like e.g. hair shampoo).  Elasticity is the tendency of solid materials to return to their original shape after forces are applied on them. When the forces are removed, the object will return to its initial shape and size if the material is elastic. Viscosity is a measure of a fluid’s resistance to flow. A fluid with large viscosity resists motion. A fluid with low viscosity flows. For example, water flows more easily than syrup because it has a lower viscosity. High viscosity materials might include honey, syrups, or gels – generally things that resist flow. Water is a low viscosity material, as it flows readily. Viscous materials are thick or sticky or adhesive. Since heating reduces viscosity, these materials don't flow easily. For example, warm syrup flows more easily than cold. Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation.  Viscometry deals with ideally viscous fluids, and - with certain limitations - also with viscoelastic liquids, i.e. viscous substances with an elastic portion. If a fluid flows easily, its resistance to deformation is low. It is a low-viscosity fluid. Fluids with greater resistance to deformation do not flow easily. They are highly viscous. At the same temperature high-viscosity fluids flow more slowly than low-viscosity fluids But how the flow of liquids is affected by stress or deformation forces????? A body may deform as a result of force applied to it:  Tensile (PULLING) force= Pulling apart Compressive (PUSHING) force= Pressing of a substance Shear Force= Pushing 1 part in 1 direction and the other in opposite direction Shearing (physics), the deformation of a material substance in which parallel internal surfaces slide past one another. The stress may be: Tensile stress If the stress is applied perpendicular to the body Shear stress If the force is applied tangentially (at any other angle) to the body The deformations that result from the application of stress may be: REVERSIBLE or ELASTIC deformations: The work used in producing this deformation is recoverable when the body returns to its original shape after removal of the applied stress IRREVERSIBLE or PERMANENT deformations: These are referred as flow and are exhibited by viscous bodies. The work used in producing this deformation is dissipated as heat and is non-recoverable when the stress is removed The Two-plates Model This model consists of two imaginary plates with the fluid in-between. Two conditions must be met to allow for accurate calculation of the viscosity-related variables. The fluid adheres to both plates and does not slip or slide along them. There are laminar flow conditions. That means the flow takes the shape of infinitesimally thin layers, no turbulence occurs. A stack of beer mats gives a good idea of how laminar flow works.  Shear Stress (F) While the lower plate stands still, the upper plate very slowly moves along. Even the slow movement causes stress that is parallel to the fluid's surface and which is called shear stress. The shear stress is defined as the force (F) applied to the upper plate divided by this plate's area (A). The force is measured in Newton, the area in square meters. The shear stress tau is force divided by area. This calculation results in the unit N/m2, which is called pascal [Pa] after Blaise Pascal.  Shear Rate (G) A second variable that can be derived from the two-plates model is the shear rate gamma-dot. In older literature the shear rate is sometimes given as D. To obtain the shear rate OR velocity gradient, the velocity v (or dv) of the upper plate, in meters per second, is divided by the distance h (or dr) between the two plates in meters. This gives the unit [1/s] or reciprocal second [s-1]. Or G = dv/dr Slope= dy/dx = y2-y1/x2-x1  When we talk about liquid flow, concept of viscosity comes in our mind….. VISCOSITY (η) The term 'viscosity' simply means fluid's thickness. A measure of fluid’s resistance to flow by an applied stress or deformation force. It describes the internal friction of moving liquids and therefore its thickness. Fluids with high viscosity resist motion because its structure and morphology results in lot of internal friction between neighboring molecules that are moving with different velocities. E.g Honey In case of less viscous liquids, there is very little internal friction (between layers) when the liquid is in motion. E.g. Water Relationship between shear stress (F) is shear rate (G) is the basis of viscosity.i.e. η= F/G where η is the coefficient of viscosity, usually referred to simply as viscosity.  Viscosity is 1 aspect of rheology. Intercept may refer to: X-intercept, the point where a line crosses the x-axis; Y-intercept, the point where a line crosses the y-axis Fluidity, φ, a term sometimes used, is defined as the reciprocal of viscosity: φ = 1/η The shear rate is an important parameter in defining viscosity (refer to the two-plates model) and also in specifying a substance's flow behavior. The vital question is whether a change of shear rate does or does not change a fluid's viscosity. This question draws the line between Newtonian and non-Newtonian fluids. TYPES OF RHEOLOGICAL SYSTEMS: 1) Newtonian systems 2) Non- Newtonian systems a. Plastic systems b. Pseudoplastic systems c. Dilatant systems Newtonian Liquids If a fluid's internal flow resistance is independent of the shear rate acting upon the fluid, it is ideally viscous. Such fluids are named Newtonian liquids after Sir Isaac Newton, Newtonian fluids are the simplest type of fluid. A Newtonian fluid is a fluid or dispersion whose rheological behaviour is described by Newton’s law of viscosity. He recognized that 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. Newtonian flow is characterized by constant viscosity, regardless of the shear rates applied. In an Newtonian fluid, such as water or oil, the shear stress is directly proportional to the shear rate, while the fluid is in laminar flow. A viscosity function means plotting the viscosity over the shear rate. The viscosity function of a Newtonian liquid is a straight line. Examples: water or salad oil. Non-Newtonian Liquids If a substance is not ideally viscous, its viscosity changes with the shear rate. Such substances are called Non-Newtonian Liquids Non-Newtonian flow is characterized by a change in viscosity characteristics with increasing shear rates. Non-Newtonian substances are those that fail to follow Newton’s equation of flow. Example: materials include colloidal solutions, emulsions, liquid suspensions, and ointments. There are three general types of Non-Newtonian materials: a. Plastic b. Pseudoplastic c. Dilatant RHEOGRAM A rheogram is a plot of shear rate (G) as a function of shear stress (F). Rheograms are also known as consistency curves or flow curves. The rheologic properties of a given material are most completely described by its unique rheogram. The simplest form of a rheogram is produced by Newtonian systems, G=fF The slope, f, is known as fluidity and is the reciprocal of viscosity, η: f = 1/η Therefore, the greater the slope of the line, the greater is the fluidity or, conversely, the lower is the viscosity.  Less difference of velocity between layers → less resistance/ friction to flow → less viscosity  The rheogram of Newtonian systems can easily be obtained with a single-point determination. A non-Newtonian system can only be fully characterized by generating its complete rheogram, which requires use of a multipoint rheometer.  The majority of fluid pharmaceutical products are not simple liquids and do not follow Newton’s law of flow. These systems are referred to as non-Newtonian. Non-Newtonian behavior is generally exhibited by liquid and solid heterogeneous dispersions such as colloidal solutions, emulsions, liquid suspensions, and ointments. When non-Newtonian materials are analyzed and results are plotted, various consistency curves, representing three classes of flow, are recognized: a. Plastic b. Pseudoplastic c. Dilatant  a. Plastic Flow In Figure, the curve represents a body that exhibits plastic flow. Such materials are known as Bingham bodies. Plastic flow curves do NOT pass through the origin but rather intersect the shearing stress axis at a particular point referred to as the yield value. IMPORTANT → A Bingham body requires certain amount of shear stress (Yield value) before it begins to flow. Bingham bodies= in honor of the pioneer of modern rheology and the first investigator to study plastic substances in a systematic manner.  The slope of the rheogram is termed the Mobility, and its reciprocal is known as the plastic viscosity, U. The equation describing plastic flow is: Where: f = yield value, or intercept, on the shear stress axis (dynes/cm2), and F = Shear stress G = Shear rate  At stresses below the yield value, the substance acts as an elastic material. Those substances that exhibit a yield value (Bingham bodies) → Solids, Substances that begin to flow at the smallest shearing stress and show no yield value → Liquids. “A plastic system resembles a Newtonian system at shear stresses above the yield value.” Once the Yield value has been exceeded, any further increase in shearing stress (i.e., F − f ) brings about a directly proportional increase in G, rate of shear. Example: Plastic flow is associated with the presence of flocculated particles in concentrated suspensions. Yield value is an indication of → Force of flocculation: “The more flocculated the suspension, the higher will be the yield value.” A continuous structure is set up throughout the system. A yield value exists because of: ✓ The contacts between adjacent particles (brought about by Van der Waal’s forces), which must be broken down before flow can occur. ✓ Frictional forces between moving particles  An example of a plastic material is toothpaste. It is necessary that toothpaste will stay on the brush but it must be easily extrudable.  b. Pseudoplastic Flow As seen in Figure, the consistency curve for a pseudoplastic material begins at the origin therefore NO yield value. NO part of the curve is linear, therefore the viscosity of a pseudoplastic material cannot be expressed by any single value. (entire consistency curve is used) The viscosity of a pseudoplastic substance decreases with increasing rate of shear. (Shear THINNING systems) i.e. the more stress is applied, the more freely it flows As shearing stress is increased, normally disarranged molecules begin to align their long axes in the direction of flow. This orientation reduces internal resistance of the material. Some of the solvent associated with the molecules may be released, resulting in further decrease in viscosity.  The most frequently used exponential formula for pseudoplastics is given as: --------(1) Where; F = Shear stress G = Shear rate η = viscosity coefficient N = exponent/power ✓ N rises as flow becomes increasingly non-Newtonian. ✓ When N = 1, the above equation reduces to equation ( ) and flow is Newtonian.  Following rearrangement, we can write the previous equation in the logarithmic form: --------(1) Many pseudoplastic systems fit this equation when log G is plotted as a function of log F. Example: Pseudoplastic flow is typically exhibited by polymers in solution. Many pharmaceutical products, including liquid dispersions of natural and synthetic gums (e.g., tragacanth, sodium alginate, methylcellulose, and sodium carboxymethyl cellulose) exhibit pseudoplastic flow. Plastic and pseudoplastic behaviors can be explained as follows: The decrease in apparent viscosity is due to the disentangling of aggregates of dispersed particles of the systems.  Modern paints are examples of pseudoplastic materials. When modern paints are applied the shear created by the brush or roller will allow them to thin and wet out the surface evenly. Once applied the paints regain their higher viscosity which avoids drips and runs. Quick sand…….? Other examples= ketchup, whipped cream, blood, paint, and nail polish c. Dilatant Flow Certain suspensions with a high percentage of dispersed solids exhibit an increase in resistance to flow with increasing rates of shear. Such systems actually increase in volume when sheared and are hence termed dilatant or Shear THICKENING systems. Inverse of pseudoplastic systems. When stress is removed, a dilatant system returns to its original state of fluidity. Equation (1) can be used to describe dilatancy: In this case, ✓ N is always less than 1 and decreases as degree of dilatancy increases. ✓ As N approaches 1, the system becomes increasingly Newtonian in behavior.  In short, the value of n or N indicates the type of flow: N = 1 (Newtonian flow) N > 1 (Pseudoplastic flow) N < 1 (Dilatant flow) Dilatant behavior can be explained as follows: At rest; particles are closely packed with minimal interparticle volume (voids). The amount of vehicle in the suspension is sufficient, however, to fill voids and permits particles to move relative to one another at low rates of shear. Thus, a dilatant suspension can be poured from a bottle because under these conditions it is reasonably fluid. At increased shear stress; As shear stress is increased, the bulk of the system expands or dilates; hence the term dilatant. The particles, in an attempt to move quickly past each other, take on an open form of packing, as depicted in Figure 19–3.  Such an arrangement leads to a significant increase in interparticle void volume. The amount of vehicle remains constant and, at some point, becomes insufficient to fill the increased voids between particles.  Accordingly, resistance to flow (viscosity) increases because particles are no longer completely wetted, or lubricated, by the vehicle. Eventually, the suspension will set up as a firm paste. Behavior of this type suggests that appropriate precaution be used during processing of dilatant materials. IMPORTANT PRECAUTION → Processing of dispersions containing solid particles is facilitated by the use of high-speed mixers, blenders, or mills. Although this is advantageous with all other rheologic systems, dilatant materials may solidify under these conditions of high shear, thereby overloading and damaging processing equipment. Example: Substances possessing dilatant flow properties are suspensions containing a high concentration (about 50% or greater) of small, deflocculated particles. This can readily be seen with a mixture Oobleck……….????  cornstarch and water (sometimes called oobleck), which acts in counterintuitive ways when struck or thrown against a surface. Sand that is completely soaked with water also behaves as a dilatant material. This is the reason why when walking on wet sand, a dry area appears directly underfoot  Corn starch and water (oobleck) Cornstarch is a common thickening agent used in cooking. It is also a very good example of a shear thickening system. When a force is applied to a 1:1.25 mixture of water and cornstarch, the cornstarch acts as a solid and resists the force. Quicksand Quicksand is a natural case of a shear thinning, non-Newtonian fluid. This is the opposite of a dilatant. As its strain rate increases, its resistance to shear will decrease causing the system to act more like a liquid than a solid. Hence, as one thrashes about in quicksand one sinks faster as the mixture's resistance decreases. THIXOTROPY Viscosity of a system not only depends on shear rate but is also time dependent. It may have been assumed that if the rate of shear were reduced once the desired maximum had been reached, the down curve would be identical with, and superimposable on, the up curve. Although this is true for Newtonian systems, the down curve for non-Newtonian systems can be displaced relative to the up curve.  Typical rheograms for plastic and pseudoplastic systems exhibiting this behavior are shown in Figure. With shear-thinning systems (i.e., pseudoplastic), the down curve is frequently displaced to the left of the up curve (as in figure) This indicates a breakdown of structure (and hence shear thinning) that does not reform immediately when stress is removed or reduced.  The discussed phenomenon is known as thixotropy or shear duration thinning, and can be defined as: “an isothermal and comparatively slow recovery (on standing of a material) of a consistency lost through shearing.” As so defined, thixotropy can be applied only to shear-thinning systems.  At rest, such structure confers some degree of rigidity on the system, and it resembles a gel. As shear is applied and flow starts, this structure begins to break down. The material undergoes a gel-to-sol transformation and exhibits shear thinning. On removal of stress, the structure starts to reform. This process is NOT instantaneous; rather, it is a progressive restoration of consistency as asymmetric particles come into contact with one another by undergoing random Brownian movement.  Rheograms obtained with thixotropic materials (thixotropic curve or hysteresis loop) is not unique but are highly dependent on ✓Changes in rate of shear ✓Duration of time involved (at a particular rate of shear) In other words, the previous history of the sample has a significant effect on the rheologic properties of a thixotropic system.  For example, suppose that in Figure 19–5 the shear rate of a thixotropic material is increased in a constant manner from point a to point b and is then decreased at the same rate back to e. Typically, this would result in the so-called hysteresis loop abe. If, however, the sample was taken to point b and the shear rate held constant for a certain period of time (say, t1 seconds), shearing stress, and hence consistency, would decrease to an extent depending on time of shear, rate of shear, and degree of structure in the sample. Decreasing the shear rate would then result in the hysteresis loop abce and so on… Difference….. Rapid recovery of viscosity after disturbance →classic shear-thinning or pseudoplasticity. Measurable time taken for the viscosity to recover → thixotropic behavior. When describing the viscosity of liquids, however, it is therefore useful to distinguish shear-thinning (pseudoplastic) behaviour from thixotropic behaviour, where the viscosity at all shear rates is decreased for some duration after agitation: both of these effects can often be seen separately in the same liquid.  When the recovery of viscosity after disturbance is very rapid however, the observed behaviour is classic shear-thinning or pseudoplasticity, because as soon as the shear is removed, the viscosity returns to normal. When it takes a measurable time for the viscosity to recover, thixotropic behaviour is observed. When describing the viscosity of liquids, however, it is therefore useful to distinguish shear-thinning (pseudoplastic) behaviour from thixotropic behaviour, where the viscosity at all shear rates is decreased for some duration after agitation: both of these effects can often be seen separately in the same liquid. Measurement of thixotropy This area of hysteresis has been proposed as a measure of thixotropic breakdown. With plastic (Bingham) bodies, two approaches are frequently used to estimate degree of thixotropy: i. The first is to determine structural breakdown with time at a constant rate of shear. (Time is varied) ii. The second approach is to determine the structural breakdown due to increasing shear rate (Shear rate is varied) i) The first is to determine structural breakdown with time at a constant rate of shear. Where, B = Thixotropic coefficient (which indicates the rate of break down with time at constant shear rate) U1, U2 = Plastic viscosities t1, t2 = time duration ii) The second approach is to determine the structural breakdown due to increasing shear rate Where, M = Thixotropic coefficient U1, U2 = Plastic viscosities V1, V2 = shear rates Bulges & Spurs Dispersions employed in pharmacy may yield complex hysteresis loops when sheared in a viscometer. Two such complex structures Includes: Bulges A concentrated aqueous bentonite gel (10% to 15% by weight), produces a hysteresis loop with a characteristic bulge in the up-curve. It is presumed that the crystalline plates of bentonite form a “house-of-cards structure” that causes the swelling of bentonite magmas. This three-dimensional structure results in a bulged hysteresis loop as observed in Figure. Bulges & Spurs Spur In still more highly structured systems, such as a procaine penicillin gel, the bulged curve may actually develop into a spur-like protrusion. The structure demonstrates a high yield or spur value, ϒ, that traces out a bowed up-curve when the three dimensional structure breaks in the viscometer, as observed in Figure. The spur value represents a sharp point of structural breakdown at low shear rate. It is difficult to produce the spur, and it may not be observed unless a sample of the gel is allowed to age undisturbed in the cup-and-bob assembly for some time before the rheologic run is made. Negative thixotropy or Antithixotropy Generally, thixotropic systems are shear thinning i.e. with a decrease in consistency in the down curve. But some materials like magnesia magma (1-10%) shows deviation from suggested behavior. The down curve falls to the right of up-curve and it continuously thickened and finally reached equilibrium at which the up and down curves overlap each other. After reaching equilibrium, the system was found to have gel-like property and showing greater suspendability. When allowed to stand, however, the material returned to its sol-like properties.  It is believed that antithixotropy results from an increased collision frequency of dispersed particles or polymer molecules in suspension, resulting in increased interparticle bonding with time. This changes an original state consisting of a large number of individual particles and small floccules to an eventual equilibrium state consisting of a small number of relatively large floccules. At rest, the large floccules break up and gradually return to the original state of small floccules and individual particles. Rheopexy Rheopexy is: “a phenomenon in which a sol forms a gel more readily when gently shaken or sheared.” The system exists in gel state at equilibrium unlike antithixotropic substances which exists in sol form. Magnesia magma and clay suspensions may show a negative rheopexy, analogous to negative thixotropy. Thixotropy in formulations Various pharmaceutical dosage forms like suspensions, emulsions, creams, gels show thixotropic behavior, which helps in easy spreadability and pourability from containers. Example: Gel preparation stored in a tube; gel from the tube does not start flowing on opening the cap or inverting the tube. It only flows with application of pressure. The reason behind is nothing but thixotropy (i.e. shear thinning)  Same principle also apply for suspensions. At rest → high viscosity, with well suspended particles. Upon shaking → viscosity gets reduced which supports easy pouring from the container. In case of Procaine penicillin G in water (40-70% w/v), structural breakdown occurs when it passes through the needle results in easy flowability. After injection, it restores its consistency and forms a depot at the site of injection which helps in maintaining the sustain levels of drug in the body. Determination of rheological properties Viscometer is an instrument used to measure the viscosity of a fluid. The selection of an appropriate viscometer is necessary for successful determination of viscosity. This selection depends upon the type of system whose viscosity is to be determined. Viscometers can be broadly classified as: 1) Single point viscometers 2) Multi point viscometers 1) Single point viscometers: In case of Newtonian systems, where F is directly proportional to G, a single point viscometer can be used. These equipment work at single rate of shear These viscometers provide a single point on rheogram; extrapolation of which gives a complete rheogram. It includes: a) Capillary viscometer b) Falling sphere viscometer 2) Multi point viscometers: In case of non-Newtonian systems, these types of viscometers are used. (may be used for Newtonian systems as well). These viscometers act at different shear rates to get the entire rheogram. These include: a) Cup and bob viscometer b) Cone and plate viscometer Single point viscometers: a) Capillary viscometer Viscosity determination → by measuring Time required by the liquid to pass between 2 marks under the influence of gravity through a vertical capillary tube known as an Ostwald viscometer. Principle: The liquid is made to flow between two points X and Y. The time of flow of liquid under test is noted and compared with the time of flow of known liquid (usually water). The equation that governs the flow of liquid through capillary tube is based on law known as Poiseuille’s law: Where, r = radius of the inside of the capillary (cm) t = time of flow, P = pressure head (dyne/cm2) l = length of the capillary V = volume of liquid flowing  The absolute viscosity of unknown liquid is obtained by using following equation: Where, η1 = viscosity of the unknown liquid η2 = viscosity of standard liquid ρ1 and ρ2 = respective densities of the liquids t1 and t2 = respective flow times (sec) This viscometer is most suitable for the liquids of low viscosity. Single point viscometers: b) Falling sphere viscometer In this type of viscometer, a glass or steel ball rolls down an almost vertical glass tube containing the test liquid at a known constant temperature. Rate at which a ball falls 1/α Viscosity of the sample Example: Hoeppler viscometer Principle: It consists of glass tube, which is positioned vertically. The glass tube is filled with test sample. A ball (steel or glass) is dropped in the tube as soon as temperature equilibrium is achieved (between inner tube and outer jacket). The tube and jacket assembly is then inverted, which places the ball at the top of inner tube. The time for the ball to fall between 2 marks is accurately measured.  The viscosity is then calculated as: Where, t = time interval taken by ball to fall between the two points (sec) Sb and Sf = specific gravities of the ball and fluid, respectively. B = constant for a particular ball Reliable viscosity values range: 0.5 – 20,000 poise For best results, a ball whose t > 30 seconds should be used. Multi point viscometers: a) Cup and bob viscometer In cup-and-bob viscometers, the sample is sheared in the space between the outer wall of a bob and the inner wall of a cup into which the bob fits. If the cup is rotated → Couette type (Example: MacMichael viscometer) If the bob is rotated → Searle type (Example: Rotovisco viscometer, Stormer viscometer, Brookfield viscometer)  The viscous drag on the bob due to the sample causes it to turn. The resultant torque is proportional to the viscosity of the sample. The torque resulting from the viscous drag of the system under examination is generally measured by a spring or sensor in the drive to the bob. Principle: In operation, the test system is placed in the space between the cup and the bob and allowed to reach temperature equilibrium. A weight is placed on the hanger, and the time required for the bob to make 100 revolutions is recorded. These data are then converted to revolutions per minute (rpm). The weight is increased and the whole procedure repeated. In this way, a rheogram can be constructed by plotting rpm versus weight added. Here, Number of revolutions (rpm) = rate of shear Torque (weights added) = shear stress  For pseudoplastic systems: For plastic viscosity: Where, Kv is a constant for the instrument W = weight placed on hanger (g) V = rpm or shear rate U = plastic viscosity (poise) Wf = yield value intercept (g) The yield value of a plastic system is obtained by use of the expression: Disadvantage → Plug flow Plug flow In a viscometer of the Searle type: Shear stress close to the rotating bob = sufficiently high so as to exceed the yield value. Shear stress at the inner wall of the cup = lie below the yield value. Material in this zone would therefore remain as a solid plug and the measured viscosity would be in error. Major contributing factor → the gap between the cup and the bob. (use largest bob possible with a cup of a definite circumference) Multi point viscometers: b) Cone and plate viscometer In this type of viscometer, the sample is placed at the center of the plate, which is then raised into position under the cone. Example: Ferranti–Shirley viscometer, Brookfield viscometer Principle: the sample is sheared in the narrow gap between the stationary plate and the rotating cone. The speed of cone can be varied using variable - speed motor. The rate of shear in rpm is increased and decreased by a selector dial and the viscous traction or torque (shearing stress) produced on the cone is read on the indicator scale. A plot of rpm (rate of shear) versus scale reading (shearing stress) can thus be constructed.  For Newtonian liquids: Where, C = instrumental constant, T = torque reading, v = speed of the cone in rpm For plastic systems: Where, Tf = torque at the shearing stress axis (extrapolated from the linear portion of the curve) Cf = instrumental constant. f = Yield value = ………Types of Viscosity Absolute Viscosity (Shear/ Dynamic Viscosity) η= F/G Units: Poise, Centipoise (1P= 100cP or 0.01P= 1cP) The cgs units for poise= dyne. sec/cm2 or g/cm. sec Poise → the shearing force required to produce a velocity of 1 cm/sec between two parallel planes of liquid each 1 cm2 in area and separated by a distance of 1 cm. Kinematic Viscosity When Newtonian (absolute) viscosity is divided by density, it gives kinematic viscosity. ν = η/ρ Units: Stoke (S), Centistoke (CS) ,nu (ν)  Relative Viscosity It is the ratio of viscosity of dispersion to that of solvent. ηr = η / ηo  Temperature dependence and the theory of Viscosity A fluid's viscosity strongly depends on its temperature. Along with the shear rate, temperature really is the dominating influence. Viscosity of a liquid decreases as temperature is raised, and the fluidity of a liquid (the reciprocal of viscosity) increases with temperature. Factors influencing a substance's flow behavio  For some fluids a decrease of 1°C causes a 10 % increase in viscosity. The dependence of the viscosity of a liquid on temperature is expressed by an equation analogous to the Arrhenius equation of chemical kinetics: -1°C in temperature => +10 % in viscosity Where, A = constant depending on the molecular weight and molar volume of the liquid Ev = activation energy required to initiate flow between molecules. R = Gas constant T = Temperature (K)  RHEOLOGY OF SUSPENSIONS The flow property of suspension depend upon their rheological characters The rheological properties of suspension decide the pourability, easy of injection, sedimentation, its redispersibility. The viscosity of flocculated suspension is greater than deflocculated particles in same suspension. The flocculated suspension has yield value and behave like a plastic or pseudo plastic system. Example: conc.parenteral suspension contain 40- 70 % w/v of procain pencillin G RHEOLOGY OF EMULSIONS Dilute emulsions → Newtonian type flow Highly concentrated emulsions → Plastic flow The important properties influencing the emulsions : Aggregation of particles Viscosity of continuous phase Globule size and size distribution Nature and proportion of emulsifying agent Applications of Rheology Understanding the fundamental nature of a system (basic science) Quality control (raw materials and products, processes) Tuning rheological properties of a system has many applications in every day's life Pharmaceutics Cosmetics Chemical industry Oil-drilling etc  SUMMARY Rheology Shear stress (F/A) Shear rate (dv/dx) Viscosity (η= F/G) Yogurt= shear thinning  Types of Viscometers 1. Single point 2. Multi point viscometer viscometer Capillary Cup and bob viscometer viscometer Falling Cone and sphere plate viscometer viscometer  Interesting Fact → (Rheology) World’s Longest Running Laboratory Experiment – The Pitch Drop Experiment ⚫ 1927 – Prof Parnell in University of Queensland Australia heated a sample of pitch and poured it into a glass funnel with a sealed stem. Three years where allowed for it to settle, after which the stem was cut. ⚫ Examine the viscosity of the pitch by the speed at which it flows from a funnel into a jar. ⚫ Only eight drops has fallen in 80 years. ⚫ The viscosity is approximated as 100 billion times that of water. Dr. Aldo Acevedo - ERC SOPS REFERENCES Martin’s Physical Pharmacy And Pharmaceutical Sciences, (6th Edition) Cooper and Gunn’s Tutorial Pharmacy (6th Edition) World of Rheology (http://www.world-of-rheology.com) Viscopedia (http://www.viscopedia.com)