Rheology MPharm Programme PHA114 PDF

MPharm Programme PHA114 Rheology Dr Paul Carter Slide 1 of 12 MPharm  Rheology * NEWTON The rheologist’s definition: the science of deformation an...

MPharm Programme PHA114 Rheology Dr Paul Carter Slide 1 of 12 MPharm  Rheology * NEWTON The rheologist’s definition: the science of deformation and flow From Greek rheos a stream, or anything that flows. Aulton’s Pharmaceutics Ch6 HAHAHA Slide 2  Viscometry Testing viscous pure watera ↓ sponge + viscoelastic solld Slide 3  The importance of rheology Characterisation & classification of materials – Rheological measurements describe the flow behaviour of liquids & semisolids. Insights into viscosity, elasticity, ex) creams , antments dispersion of solids in cream viscoelasticity, to understand structure Raw materials Finished products Quality control – Physical stability, consistency in quality, patient compatibility, drug bioavailability. Differences could indicate contamination, poor mixing, variability. – Adhesive performance of transdermal patches = solid-like ? Slide 4  The importance of rheology Process optimisation - by understanding how materials behave under stress and strain. Select suitable equipment. toothpaste ext Product development - optimise flow, spreading, firmness etc. Predict behaviour - under different conditions, e.g. temp, pressure Research & Development - explore molecular structure, interactions, new materials Slide 5  Learning outcomes Rheology & rheological testing Introduction to Viscometry * Thixotropy and yield stress = shear-thinning LsHAKE bottle-VISCOSIFy ↓. Stop shaking-thickens up again Oscillatory rheological testing Rheological viscoelasticity parameters Slide 7  Rheology as a Quality Control tool It can describe and quantify processing or application product characteristics or issues/problems: – “Is it spreadable on the skin?” – “How well does it pour from the container?” – “The formulation has particle sedimentation during storage on the shelf” – “The patch detached from the skin – how adhesive is it on the skin surface?” (Dodou & Ho, 2007) and so on.... Slide 6  Newton’s experiment DETAIL NO Imagine a cube of liquid, sandwiched between 2 parallel plates. Bottom plate is fixed whilst top plate slides horizontally. Liquid sticks to both plates – intermolecular forces. Force applied to top plate and it moves at constant velocity. Bottom plate stationary. Liquid layers move at different velocities from zero (bottom) to v (top) – giving velocity gradient. As liquid layers move relative to each other, experience an internal resistance to flow = Shear stress, proportional to velocity gradient. Slide 8  Newton’s experiment sposeds Shear stress = Force / Area σ = F/A (Nm-2 or Pa) Velocity of top layer = Displacement/time V = x/t (ms-1) Shear strain = displacement /height γ = x/H (unitless) Shear strain rate = Velocity of top layer/Height γ’ = V/H (s-1) Slide 9  Viscometry – Definition of Terms Shear Stress (σ) The torsional force per area. Strain (γ) The resultant displacement divided by the sample height. Shear (strain) rate (γ’) The change in strain in a certain time. Viscosity (η) Shear stress divided by shear rate. Slide 10  Shear Strain (γ) Displacement Strain = Gap Shear strain is normally abbreviated to strain Dimensionless: use “% strain” or “millistrain” terms Slide 11  Shear Stress (σ) Force N = Area m2 The applied force per unit area is the shearing stress or SHEAR STRESS 1 N/m2 = 1 Pa Slide 12  Shear rate (γ’) Shear Strain Shear Rate = Shear Time The rate of change of STRAIN is known as the shear strain rate or SHEAR RATE. Since strain has no units, the shear rate has units of reciprocal seconds (s-1). Slide 13  Shear Viscosity (η) Shear Stress Viscosity = Shear Rate Units: Pascal.second Pas (SI) Poise P (CGS) Remember: - 1 Pa.s = 10 P 1 mPa.s = 1 cps Slide 14  Viscosity * Dynamic viscosity η (Nm-2s or Pas) η = σ / γ’ – A measure of the resistance of a fluid to flow (or move) Kinematic viscosity ν (m2s-1) ν=η/ρ – Normalised value of viscosity – “Velocity” of flow The dynamic viscosity of a Newtonian liquid is 0.65 (Pa s) and its density is 650 kg m-3. What is the kinematic viscosity of this liquid? (0.001 m2 s-1) Slide 15  Newtonian Flow = normal (no surprises is constant L viscosity Water, simple fluids Liquids have constant viscosity, regardless of applied shear stress (force per unit area acting parallel to the surface (as opposed to normally)). So resistance to flow does not change with speed or force of flow. Shear stress (force per unit area) = dynamic viscosity x shear rate (rate of deformation) So, graph of shear stress vs shear rate is linear. Gradient = viscosity. sheard Unear I stress y = mx + c vm = Viscosity -near rate Equipment for measuring Newtonian flow Newtonian flow – Capillary viscometers – Falling sphere viscometer – Also called SINGLE POINT viscometers Slide 16  Newtonian Flow Ostwald U-tube viscometer Laminar flow of liquid under the influence of gravity Record time to flow from C to D. Dynamic viscosity: η = K ρ t (Instrument constant x density x time) Slide 17  Capillary viscometer question Calculate the dynamic viscosity of a Newtonian liquid after using a capillary viscometer. The density of the liquid is 800 Kg m-3 and the instrument constant is 1 x 10-7 m2 s-2. The mean time you have found using a stopwatch is 100 seconds. # Dynamic viscosity: η = K ρ t CrEck the units i.e. 1 x 10-7 x 800 x 100 = 0.008 Pa s Slide 18  Falling Sphere viscometer A falling-sphere viscometer is a device used to calculate the dynamic viscosity of a fluid by measuring the time required for a spherical ball (usually small 1 100 90 80 Shear stress (Pa) 70 60 50 40 30 20 10 0 0 1 2 3 4 5 6 7 8 Shear rate (s-1) Slide 29  Bingham flow Newtonian flow begins when yield stress σy is reached σ = σy + η γ’ 100 80 shear stress (Pa) 60 40 20 σy 0 0 2 4 6 8 10 shear rate (s-1) Slide 30  Thixotropic Behaviour Thixotropy is time dependent shear-thinning behaviour. when mixed up it becomes a liquid but re-sets after application Slide 31  Hysteresis Loop (Thixotropic Loop) Stress Up Ramp Area Measured area gives an indication of how thixotropic a Down Ramp material is. Shear Rate Slide 32  Yield Stress Shear Stress No flow until a certain shear stress is applied Shear Rate Slide 33  Viscoelasticity in products Many materials exhibit visco-elasticity, i.e. they behave like viscous liquids in some processes and like elastic solids in others. An example would be a concentrated suspension: During storage it needs to behave like a solid to prevent sedimentation During application it needs to behave like a fluid e.g. so that it flows in the bristles of the brush and can be evenly painted. Slide 34  Oscillation Principles Input Stress Measured Strain 0 Time δ Phase angle Slide 35  Phase Angle (8) For purely Elastic Material The stress and strain are exactly in phase. Therefore the phase angle is zero. For purely Viscous Material The stress and strain are 1/4 of a cycle out of phase. Therefore the phase angle is 90°. Phase Angle (δ) is a measure of Elasticity The higher the phase angle, the more viscous. The lower the phase angle, the more elastic. Slide 36  Complex Modulus (G*) Stress Complex Modulus (Pa) = Strain Mathematically derived σ γ from the ratio of the stress and strain amplitudes Measured Strain Input Stress Slide 37  Calculated Parameters in Oscillation Loss (Viscous) Modulus, G’’ (Pa) = Stress × Sin (8) Can indicate the liquid-like nature of the sample Strain Storage (Elastic) Modulus, G’ (Pa) = Stress × Cos (8) Can indicate the solid-like nature of the sample Strain Dynamic Viscosity, η’ (Pas) = G’’ Frequency Can be related to the shear viscosity if the sample obeys the Cox-Merz rule Slide 38  Test Modes Rotational rheometers have a range of test modes: Viscometry (shear) Oscillation Creep and Recovery ‘Wet sponge model’ Dry = elastic solid (Storage modulus), if add water (inelastic, viscous) (loss modulus) – complex viscoelastic behaviour (Complex modulus -vector sum of moduli). Soak with honey – higher complex modulus Slide 39  Rheological behaviour of cosmetic ingredients/ finished products Materials/Products Liquids Semisolids Solids viscous viscoelastic elastic Newtonian non-Newtonian Slide 40  Viscoelastic behaviour Viscoelastic behaviour = viscous + elastic – Viscous behaviour: materials that flow - liquids – Elastic behaviour: structured materials that deform reversibly- solids – Viscoelastic behaviour: structured liquids which exhibit both viscous & elastic properties - e.g. polymer melts, polymer gels, creams. Slide 41  Oscillation Measurement Types Amplitude sweep Frequency sweep Temperature sweep Time experiment (e.g. thixotropic measurement) Slide 42  Amplitude sweep LVR LVR Storage Modulus G’ (Pa) Strain γ Two suspensions - one sample remains as a continuous phase and the other produces a supernatant layer Identify Linear Viscoelastic Region A longer LVR enables the sample to ‘absorb’ a Measures inherent structure broader range of deformations before the structure breaks down. Dispersion/ suspension stability Note that the magnitude of storage modulus is not necessarily related to product stability Slide 43  Frequency Sweep G’ Unique fingerprint. Shows relative process G” time behaviour. 8 When G’ > G’’ – elastically dominated. Behaves like a solid. Low Frequency High When G’ < G’’ – viscously Long Timescale Short Timescale dominated. Behaves like a liquid. Slide 44  Frequency sweep (liquid soaps, gels, hydrogel films) 90 Liquid soap Phase Angle (°) For all samples the phase angle is relatively independent of frequency 45 Gel, hydrogel film 0 0.1 1.0 10.0 100.0 Frequency (rad/s) Wong et al, 2015 Slide 45  Frequency sweep (pressure sensitive adhesives) 90 G’’ > G’ Phase Angle (°) 45 G’ > G’’ 0 0.1 1.0 10.0 100.0 Frequency (rad/s) Dodou & Ho, 2007 Slide 46  Viscoelasticity measurements- Creep test Application of constant stress σ over extended period of time t, and monitoring of the resulting strain. Applied stress should be low so as not to destruct internal structure of material but high enough to cause movement. The viscoelastic material stores some of the energy and dissipates (loses) the rest in the form of viscous flow. When stress is removed, the stored energy is recovered, in an attempt to restore the “rest state”. Creep compliance J (Pa-1) = strain / stress J = γ /σ Creep compliance curve (Creep compliance versus time) can be described by Burgers combined model Slide 47  Creep curve AB: immediate elastic response, BC: viscoelastic response CD: steady state viscous (Newtonian) response, DE: elastic recovery = AB, EF: viscoelastic recovery = BC Part of the structure cannot be recovered due to the lost energy during the viscous flow CD Creep compliance J C D: removal of stress (Pa-1) E F B A Time t (s) Slide 48