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**Pharmaceutics II - Rheology**

Definitions Importance of Viscosity in Pharmacy 2.1 Liquids 2.2 Semi-Solids 2.3 Processing 3. Measurement of Rheologic Properties 3.1 Capillary Viscometer 3.2 Cup and Bob/Disk Viscometer 3.3 Cone and Plate Viscometer 4. Newtonian Systems 4.1 Newton’s Law of Flow 4.2 Fluid Flow and Reynolds Apparatus 4.3 Boundary Layers 5. Non-Newtonian Systems 5.1 Plastic or Bingham Bodies 5.2 Pseudo-plastic Flow 5.3 Dilatant Flow 6. Thixotrophy 6.1 Description 6.2 Measurement of Thixotropy 6.3 Rheopexy 6.4 Thixotropy in Formulation Dr M. Skinner

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**Pharmaceutics II - Rheology**

FLUID FLOW 7.1 Boundary Layers 7.2 Reynold’s Apparatus 8. Determination of Rheologic Properties 8.1 Why measure viscosity? 9. Applications of Rheology to Pharmacy Course Outcomes: Describe the importance of rheology in the formulation, manufacture, stability and quality assurance of pharmaceutical dosage forms. Describe the rheological properties of Newtonian, non-Newtonian and thixoptropic systems and to ascribe these characteristics to various pharmaceutical systems. Describe methods of determining the viscosity of pharmaceutical formulations. Dr M. Skinner

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**Pharmaceutics II - Rheology**

Texts Physical Pharmacy, 4th Edition, Alfred Martin, Chapter 17, Rheology. Pharmaceutics – The Science of Dosage Form Design, 2nd Edition, ME Aulton, Chapter 4, Rheology. Dr M. Skinner

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**Pharmaceutics II - Rheology**

DEFINITIONS Rheology is the science concerned with the deformation of matter under the influence of a stress. Viscosity is an expression of the resistance of a fluid to flow, the higher the viscosity, the greater the resistance. When stress is applied, it causes strain in the system which leads to deformations which can be either: elastic and spontaneously reversible permanently irreversible viscoelastic Dr M. Skinner

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**Pharmaceutics II - Rheology**

2. IMPORTANCE OF VISCOSITY IN PHARMACY 2.1 Fluids Mixing Particle size reduction of disperse systems with shear (e.g. creams) Passage through orifices Fluid transfer Physical stability of disperse systems 2.2 Semi-Solids Emulsions, pastes, suppositories and tablet coatings – semi-solid entities which can flow or deform. Spreading and adherence on skin Removal from jars or extrusion from tubes Capacity of solids to mix with immiscible liquids Release of the drug from the base Dr M. Skinner

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**Pharmaceutics II - Rheology**

2.3 Processing Production capacity and power requirements of equipment Manufacturing equipment fitted with strain gauges to permit monitoring of torque measurements Units of viscosity – centipoise (η) – coefficient of viscosity - complex unit 1 centipoise = 1 mPa-s. (1 millipascal*s). 1 Pa = (kg.m/s²)/m² = kg/m.s² = N/m² Dr M. Skinner

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**Pharmaceutics II - Rheology**

3. MEASUREMENT OF RHEOLOGICAL PROPERTIES 3.1 Capillary (Ostwald) viscometer The viscosity of a Newtonian liquid determined by Ostwald viscometer. Reference is usually water (at 25°C – ρ = 0.997g/cm3, η = centipoise) The absolute viscosity of the unknown liquid η1 : η1 = ρ1 t1 η ρ2 t2 This equation is based on Poiseuille's law for a liquid flowing through a capillary tube. η1 and η2 = viscosities of unknown and standard liquids ρ1 and ρ2 = densities of unknown and standard liquids t1 and t2 = respective flow times in seconds Assuming a linear relationship Dr M. Skinner

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**Pharmaceutics II - Rheology**

3.2 Cup and Bob/Disk Viscometer A cylindrical bob or flat circular disk Sample shear Variable rate of shear (revs/min) - Shearing stress is read on the indicator scale. Quick and easy to use but: - The rate of shear is not constant across the diameter of the disk – average value - interpretation - Requires a relatively large volume of sample (e.g. 100ml +) dv dx ? Dr M. Skinner

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**Brookfield Viscometer with RV Spindle**

Dr M. Skinner

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**Brookfield Viscometer with RV Spindle**

Dr M. Skinner

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**Range of RV Viscometer Spindles (RV1 to RV7)**

Dr M. Skinner

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**Range of HA Viscometer Spindles (HA1 to HA7)**

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**Range of T Viscometer Spindles (T-A to T-F)**

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**Pharmaceutics II - Rheology**

3.3 Cone and plate viscometer - A flat, circular plate - A wide-angled cone placed centrally above. - The tip of the cone just touches the plate. - Place sample at the centre of the plate. - Raise plate into position under the cone. - Cone is driven by a variable-speed motor . - Sample is sheared in the narrow gap between the stationary plate and the rotating cone. - The rate of shear (revs/min) 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. - Important advantages of this viscometer: - The rate of shear is constant throughout the entire sample . - Only a small sample volume of 0.1 to 0.2 ml is required. Dr M. Skinner

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**Pharmaceutics II - Rheology**

4. NEWTONIAN SYSTEMS 4.1 Newton's law of flow (dynamic viscosity) Dr M. Skinner

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**Pharmaceutics II - Rheology**

A velocity gradient exists and this will be equal to the velocity of the upper layer (m/s) dv divided by the height of the cube (m) dx rate of flow or velocity gradient, the rate of shear (s-1). Dr M. Skinner

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**Pharmaceutics II - Rheology**

Rate of shear = dv/dx (s-1) The applied stress of force per unit area (F/A) required to bring about flow is called the shear stress (S) and has units of N/m2. Increased viscosity = increased shear force or shear stress required to produce a certain rate of shear A certain shear stress with produce a certain rate of shear Rate of shear should be directly proportional to the shearing stress. Dr M. Skinner

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**Pharmaceutics II - Rheology**

F α dv Rate of shear directly proportional to A dx the shearing stress. F = k . dv Replace proportionality sign with a constant k . A dx F/A = η ● dv/dx where k = η = coefficient of viscosity if F/A = S then S = η dv/dx Newton's equation or rearranged dv/dx = 1/ η . S y = m . X C Dr M. Skinner

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**Pharmaceutics II - Rheology**

Newtonian fluids exhibit the least complex flow patterns e.g. true solutions and water. Viscosity here is a true constant unaffected by rate of shear Only a single determination of viscosity at any rate of shear or any shear stress is required to fully characterise the rheological properties Dr M. Skinner

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**Pharmaceutics II - Rheology**

Viscosity is constant – unaffected by rate of shear – linear so - 1/η (gradient) can be determined at any rate of sheer. Viscosity Diagram for a Newtonian Fluid dv/dx = 1/ η . S Unit for η the poise (complex unit) y = m x c (c=0) dv/dx (rate of shear s-1) Gradient = 1/η (1/coefficient of viscosity) S (Nm-2 ) (F/A) Dr M. Skinner

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**Pharmaceutics II - Rheology**

4.2 Measuring Viscosity of Newtonian systems Rate of shear is proportional to shearing stress Can us instruments that operate at a single rate of shear. Provide a single point on the rheogram. Extrapolation of a line through this point to the origin will result in the complete rheogram. Dr M. Skinner

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**Pharmaceutics II - Rheology**

VISCOSITIES OF SOME FLUIDS OF PHARMACEUTICAL INTEREST _______________________________ Fluid Dynamic viscosity at 20°C (mPa s) Chloroform 0.58 Water Ethanol 1.20 Glyceryl trinitrate 36.0 Olive oil 84.0 Castor oil Glycerol 1490 Dr M. Skinner

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**Pharmaceutics II - Rheology**

5. NON-NEWTONIAN SYSTEMS Most pharmaceutical fluids do not follow Newton's equation: - because the viscosity of fluid varies with the rate of shear. - therefore a single determination of viscosity at any one rate of shear cannot yield the entire rheological profile. - i. Plastic or Bingham flow ii. Pseudoplastic flow iii. Dilatant flow Dr M. Skinner

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**Pharmaceutics II - Rheology**

Rheograms for Newtonian and Non-Newtonian Flow Physical Pharmacy p.522 Dr M. Skinner

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**Pharmaceutics II - Rheology**

5.1 Plastic or Bingham flow The rheogram does not pass through the origin. Intersects with the shear stress (x) axis . (or will if the straight part of the curve is extrapolated to the axis) X - intercept is usually referred to as the yield value. Dr M. Skinner

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**Pharmaceutics II - Rheology**

A Bingham body does not begin to flow until a shearing stress, corresponding to the yield value, is exceeded. If stress is less than the yield value, the system behaves like a solid and exerts elastic deformations that are reversible. The quantitative behaviour of these bodies is best described by the Bingham Equation where fB is the Bingham yield value: Newtonian S = η . dv/dx η = S . dv/dx Non-Newtonian η pl = S - fB Dr M. Skinner

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**Pharmaceutics II - Rheology**

In practice, deformation and flow usually occurs at a lower shear stress value and this accounts for the curved portion of the curve. The viscosity decreases initially and then remains constant. In a highly flocculated system, there is interaction between flocs which results in a structured system and plastic flow is associated with these systems e.g highly flocculated suspensions. The yield value is present because of the contacts between adjacent particles (caused by van der Waals forces which may be capable of withstanding weak stresses) which must be broken down before flow can occur. Consequently, the yield value is an indication of the degree of flocculation; the more flocculated the suspension, the higher will be the yield value. This type of behaviour is also exhibited by creams and ointments. Dr M. Skinner

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**Pharmaceutics II - Rheology**

5.2 Pseudoplastic flow Many pharmaceutical products exhibit pseudoplastic flow include natural and synthetic gums e.g. liquid dispersions of tragacanth, sodium alginate, methylcellulose, sodium carboxymethylcellulose,. As a general rule: Pseudoplastic flow is exhibited by polymers in solution Plastic systems are composed of flocculated particles. Dr M. Skinner

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**Pharmaceutics II - Rheology**

The curve commences at the origin and there is no yield value. No part of the curve is linear, so viscosity cannot be expressed by any single value. The apparent viscosity may be obtained at any rate of shear from the slope of the tangent to the curve at the specified point. The viscosity decreases with an increasing rate of shear (shear-thinning systems). Dr M. Skinner

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**Pharmaceutics II - Rheology**

Pseudoplastic flow cannot be satisfactorily expressed by fundamental equations. The following empirical equation correlates most closely with experimentally observed flow not involving stress over vast ranges: Sn = η1 dv n > 1 ; the term η' is a viscosity coefficient. dx The exponent n rises as the flow becomes increasingly non-Newtonian. When n = 1, this equation reverts to the classic Newton equation and the flow is Newtonian. 1/η = gradient (changes with S) Dr M. Skinner

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**Pharmaceutics II - Rheology**

At the Particulate level: The curved rheogram for pseudoplastic materials results from a shearing action on the long-chain molecules which become entangled and associated with immobilized solvent. As the shearing stress is increased, the randomly arranged particles tend to become disentangled and align their long axes in the direction of flow. This orientation reduces the internal resistance of the material and offers less resistance to flow. Some of the entrapped water will also be released. Both of these account for the lower viscosity. Once stress is removed, the structures reform spontaneously. Dr M. Skinner

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**Pharmaceutics II - Rheology**

5.3 Dilatant flow Dilatant flow - usually suspensions containing a high concentration (>50%) of small, deflocculated particles. Exhibit an increase in resistance to flow with increasing rates of shear. Systems increase in volume when sheared - termed dilatant. The reverse of pseudoplastic systems. Pseudoplastic systems – shear-thinning systems, Dilatant materials - shear-thickening systems. Dr M. Skinner

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**Pharmaceutics II - Rheology**

The same equation can be used to describe dilatancy in quantitative terms: Sn = η1 dv n < 1 dx n is always less than 1 Decreases as the degree of dilatancy increases. As n approaches 1, the system becomes increasingly Newtonian in behaviour. Dr M. Skinner

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**Pharmaceutics II - Rheology**

At the particulate level: At rest: - particles closely packed - voids at a minimum. Vehicle: - sufficient to fill this volume - allows the particles to move relative to one another at low rates of shear. Can pour a dilatant suspension from a bottle without shaking as it is relatively fluid without shear stress applied. If the shear stress is increased by shaking, the bulk expands or dilates as the particles move quickly past each other and take an open form of packing. Dr M. Skinner

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**Pharmaceutics II - Rheology**

Such an arrangement results in a significant increase in the void volume, with the vehicle now being insufficient to fill the voids between the particles. The resistance to flow increases since the particles are no longer completely wetted or lubricated by the vehicle and eventually the suspension will set up as a firm paste. Caution must be taken in processing dilatant materials. - Usually, the processing of dispersions containing solid particles is facilitated by the use of high speed mixers, blenders or mills. - Dilatant materials may solidify under these conditions of high shear, thereby overloading and damaging the processing equipment. Dr M. Skinner

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**Pharmaceutics II - Rheology**

THIXOTROPY 6.1 Description So far for Newtonian and non-Newtonian behaviour: - observed behaviour when the rate of shear was progressively increased and plotted against the resultant shear stress. Assumed that if the rate of shear was reduced, the down-curve would be identical with and superimposed on the up-curve. This is so with - Newtonian systems - some non-Newtonian materials. For most non-Newtonian systems: - The flowing elements, whether particles or macromolecules, may not adapt immediately to the new shearing conditions. - When subjected to a particular shear rate, the shear stress and consequently the viscosity, will decrease with time. - Therefore the down-curve can be displaced with regard to the up-curve. Dr M. Skinner

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**Pharmaceutics II - Rheology**

Thixotropic systems usually contain asymmetric particles and through numerous points of contact, these particles set up a loose 3-D network throughout the sample. At rest, this 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 as the points of contact are disrupted and the particles become aligned in the general direction of flow. The material undergoes a gel to sol transformation and exhibits shear thinning. Upon removal of the stress, the structure starts to reform. This is not instantaneous, but is a progressive restoration of consistency as the asymmetric particles come into contact with each other by undergoing random Brownian movement. Dr M. Skinner

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**Pharmaceutics II - Rheology**

Shear-thinning systems (plastic and pseudoplastic) - down-curve is frequently displaced to the left of the up-curve - rheogram exhibits a hysteresis loop. Dr M. Skinner

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**Pharmaceutics II - Rheology**

i.e. the material has a lower consistency at any one rate of shear on the down-curve than it had on the up-curve. Indicates a breakdown of structure that does not reform immediately when the stress is removed. This phenomenon is known as thixotropy and may be defined as: “An isothermal and comparatively slow recovery, on standing of a material whose consistency is lost through shearing". According to this definition, thixotropy can only be applied to shear-thinning systems. Dr M. Skinner

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**Pharmaceutics II - Rheology**

The rheograms obtained with thixotropic materials are: - highly dependent on the rate at which shear is increased or decreased - the length of time a sample is subjected to any one rate of shear. Dr M. Skinner

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**Pharmaceutics II - Rheology**

6.2 Measurement of thixotropy Main characteristic of a thixotropic system is the hysteresis loop. The area of hysteresis has been proposed as a measure of thixotropic breakdown. Two approaches: - determine the structural breakdown with time at a constant rate of shear. - determine the structural breakdown due to increasing shear rate. Limitations: - Does not taken into account the shape of the up- and down-curves. So - Two different materials may produce loops of similar area but which have completely different shapes representing totally different flow behaviour. Dr M. Skinner

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**Pharmaceutics II - Rheology**

Rheogram of white soft paraffin This is typical of a loop obtained with some samples of white soft paraffin where the up-curve exhibits a number of bulges. Lower shear rates - the bulges are thought to be associated with the initial loss of 3-D structure. Higher shear rates - the smoother deviations here are associated with molecular reorientation. Dr M. Skinner

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**Pharmaceutics II - Rheology**

6.3 Rheopexy This is a characteristic exhibited by some thixotropic systems. A phenomenon where a sol forms a gel more readily when gently shaken than when allowed to form the gel while the material is kept at rest. The rocking motion provides a mild turbulence which aids in returning de-randomised particles to a random orientation. The gel is the equilibrium form. Dr M. Skinner

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**Pharmaceutics II - Rheology**

6.4 Thixotropy in formulation Thixotropy is a desirable property in liquid pharmaceutical systems that ideally should have: A high consistency in the container yet pour or spread easily. e.g. - a well formulated suspension will not settle out readily in the container - will become fluid on shaking and will remain so long enough for a dose to be dispensed. - will regain consistency rapidly enough so as to maintain the particles in a suspended state. Also desirable with emulsions, lotions, creams, ointments and parenteral suspensions to be used for intramuscular depot therapy. Dr M. Skinner

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**Pharmaceutics II - Rheology**

6.5 Measuring Viscosity of Non-Newtonian systems The instrument used must be able to operate at a variety of rates of shear to obtain the complete rheogram. The use of a one-point instrument, even in quality control in industry, is erroneous if the system is non-Newtonian as the flow properties could vary significantly, but will appear to be unchanged. Dr M. Skinner

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**Pharmaceutics II - Rheology**

7 FLUID FLOW 7.1 Boundary Layers Consider flow between two surfaces. The rate of flow over an even surface will be dependent upon the distance from the surface. The velocity will be almost zero at the surface and increases towards the middle where it becomes constant. The region over which differences in velocity occur is called the boundary layer. Dr M. Skinner

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**Pharmaceutics II - Rheology**

Depth of the boundary layer is dependent i. viscosity of the fluid directly proportional ii. rate of flow in the bulk fluid. indirectly proportional High viscosity and low flow rate will result in a thick boundary layer. Boundary layers can never be eliminated entirely and represent an important barrier to mass (and heat) transfer. Dr M. Skinner

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**Pharmaceutics II - Rheology**

Streamline flow The 2 boundary layers meet at the centre of the tube, resulting in a parabolic distribution. Turbulent flow There is movement at right angles to the direction of flow - promotes mixing - fluid layers tend to move at a more similar velocity - results in a rounded velocity profile. Dr M. Skinner

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**Pharmaceutics II - Rheology**

7.2 Reynolds’ Apparatus Consider the flow of fluid through the system below. Dr M. Skinner

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Low Velocity Dye thread Streamlined or Laminar Flow Critical Velocity High Velocity Dr M. Skinner

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**Pharmaceutics II - Rheology**

Reynolds found flow was affected by 4 factors i. Density ( ) ii. Velocity (v) iii. Diameter of pipe (d) iv. Viscosity ( ) All measurable so can calculate Re. If Re < streamline flow will occur If Re > turbulent flow will occur Distance Travelled after specific time Re > 4000 (Turbulent) High density High velocity High pipe dia. Low viscosity Re < 4000 (Streamlined) Lower density Lower velocity Lower pipe dia. Higher viscosity Ideal Direction of Flow Dr M. Skinner

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**Pharmaceutics II - Rheology**

If Re = 2000 to 4000 flow depends on nature of surface - smooth, straight pipe - streamline flow at Re >> 2000 -rough, bends, joints and fittings – turbulent flow Re << 4000. Important in fluid transfer during manufacturing processes e.g. piped water and steam, filling processes, mixing processes. Dr M. Skinner

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**Pharmaceutics II - Rheology**

DETERMINATION OF RHEOLOGIC PROPERTIES 8.1 Why measure viscosity? -Formulation development Quantities of ingredients Grades of ingredients Formulation requirements Production Methods - mixing rate - temperature Setting limits for production - Production Quality Assurance / Batch-to-batch uniformity ? Production methods - variability ? Adjustments to formulation - thicken ? Quality of ingredients – natural products vary Dr M. Skinner

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**Pharmaceutics II - Rheology**

Other rheologic properties: - tackiness or stickiness - "body” - "slip“ - "spreadability" Are difficult to measure by means of a conventional apparatus and do not have precise meanings. Dr M. Skinner

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**Pharmaceutics II - Rheology**

8.2 Pharmaceutical Considerations and Applications Problems in establishing meaningful shear rates Viscosity requirements often emperical, however, researchers have attempted to establish shear rates relating to the use of pharmaceuticals e.g. - topical application sec-1 - nasal spray in a plastic squeeze bottle sec-1 - pouring from a bottle - below 100 sec-1. However, think about the shear rate resulting from rubbing a cream into the skin. This can range from 100 to sec-1 depending on the degree of rubbing. The shear rate for individual use by a process therefore varies greatly. Another example is squeezing a product from a collapsible container - the shear rate depends on the squeezing force that the subject can exert easily. Dr M. Skinner

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**Pharmaceutics II - Rheology**

Visual perception The importance of viscosity in visual perception must be considered e.g. cream to hold its shape in a jar a lotion to pour a toothpaste to retain its ribbon shape on a brush. Here shear rate is determined by subjectively evaluating an acceptable rate of deformation or flow under the constant stress of gravity. Ease of use e.g. Toothpaste. - After applying a rate of shear in squeezing the tube, the toothpaste must flow onto the bristles. - It must then recover its viscosity sufficiently to maintain its ribbon shape on the brush. - With shear, it must thin rapidly for ease in brushing. Dr M. Skinner

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**Pharmaceutics II - Rheology**

Topical preparations must meet certain criteria for: - Desirable pharmaceutical properties feel, spreadability, colour, odour - Desirable pharmacological properties – drug release Other psychologic and sensory characteristics e.g. - Sensations in the mouth - Between the fingers - On the skin are important considerations for manufacturers of cosmetic products and dermatologic products. Dr M. Skinner

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**Pharmaceutics II - Rheology**

Cussler et al studied the texture of non-Newtonian liquids of widely different rheologic properties applied to the skin. Found that the consistency of the material could be accurately assessed by a panel of untrained subjects by the use of only 3 attributes: - thinness - related to non-Newtonian viscous parameters that could be measured with appropriate instrumentation - smoothness - related to the coefficient of friction - warmth - complex concept that requires further study. Only 1 of these can be reliably measured – the rest are largely subjective. Dr M. Skinner

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**Pharmaceutics II - Rheology**

It can therefore be seen why statement defining a suitable viscosity for products are meaningless unless they are framed within a specific judgement of use. Product development In product development it is vitally important that all trial formulations be tested: - against assumed stresses and shear rates likely to be experienced in manufacturing, product movement, filling and use. - These values must be calibrated, preferably with products characteristically used and under the normal operating parameters of that facility. Dr M. Skinner

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