SOPH 231 Rheology 2 PDF

Viscosity and Rheology Hilda Amekyeh, PhD UNIVERSITY OF HEALTH A N...

Viscosity and Rheology Hilda Amekyeh, PhD UNIVERSITY OF HEALTH A N D A L L IE D S C IE N C E S 1 School of Pharmacy 1 Outline Introduction/Definitions Importance of studying rheology Newton’s law of flow Viscosity Types of flow Measurement of viscosity Pharmaceutical applications Recommended Reference Books Pharmaceutics: The Science of Dosage Form Design Martin’s Physical Pharmacy and Pharmaceutical Sciences Remington: Essentials of Pharmaceutics UNIVERSITY OF HEALTH 2 A N D A L L IE D S C IE N C E S School of Pharmacy 2  Introduction/Definitions Rheology – Greek term coined by Eugene C. Bingham “rheo” means “to flow” “logos” is from the Greek word “logia”, which means “study of” Rheology is the study of the flow and deformation of matter under stress. Deformation describes the change of matter in terms of shape and/or volume. Studying the flow properties of liquids is important for the pharmacist. For instance The flow behaviours of formulations (e.g., suspensions, simple liquids, gels, creams, and pastes) can change when exposed to different stress conditions. UNIVERSITY OF HEALTH 3 A N D A L L IE D S C IE N C E S School of Pharmacy 3 Importance of Studying Rheology The rheological properties of pharmaceutical products can affect the following: Formulation of various dosage forms Drug absorption and bioavailability Patient acceptability of products and patient compliance. E.g., Stiff creams are difficult to use or could cause pain; hence, the patient might be reluctant to use such a product. Suspensions and emulsions should easily flow out of their bottles to allow for easy dosing. A paste should be easily squeezed out of a tube, but should form a string without fluid leakage. UNIVERSITY OF HEALTH 4 A N D A L L IE D S C IE N C E S School of Pharmacy 4  Fluidity of solutions to be injected Passage of the liquid through a syringe needle Tablet coating Choice of processing equipment during the manufacture of pharmaceuticals Mixing and flow of materials, their packaging into containers, their removal prior to use, and their pouring from the container UNIVERSITY OF HEALTH 5 A N D A L L IE D S C IE N C E S School of Pharmacy 5 Proper understanding of rheology is essential for the development/preparation evaluation performance of pharmaceutical dosage forms. The ability of a material to flow depends on: its viscosity the magnitude of stress applied temperature its composition/molecular chain characteristics and arrangements UNIVERSITY OF HEALTH 6 A N D A L L IE D S C IE N C E S School of Pharmacy 6  Viscosity The flow property of simple liquids is usually expressed in terms of viscosity. Viscosity of a fluid may be described as the resistance of the fluid to flow or movement. The higher the viscosity of a liquid is, the greater is its resistance to flow. E.g., castor oil, honey, and syrups resist flow more than water or alcohol does. UNIVERSITY OF HEALTH 7 A N D A L L IE D S C IE N C E S School of Pharmacy 7 More viscous materials require larger amounts of energy during mixing. Viscosity can be modified to improve products. However, this must be done cautiously. E.g., Decreasing the viscosity of a suspension could increase the sedimentation rate of the solids suspended in it. UNIVERSITY OF HEALTH 8 A N D A L L IE D S C IE N C E S School of Pharmacy 8  Viscosity Coefficients Dynamic viscosity Kinematic viscosity Relative viscosity Specific viscosity Intrinsic viscosity UNIVERSITY OF HEALTH 9 A N D A L L IE D S C IE N C E S School of Pharmacy 9 Viscosity was quantitatively defined by Sir Isaac Newton. He first realised that rate of flow (symbol, γ; unit, 1/s) is directly related to applied stress (symbol, τ or σ; unit, mPa). τ∝γ Rate of flow is also referred to as rate of shear. The constant of proportionality is the coefficient of dynamic viscosity (η), more usually referred to as viscosity (absolute viscosity). i.e., τ = ηγ (Newton’s Law of Viscosity) The SI unit for η is Pascal-second (Pa·s) or Poise (P). 1 mPa·s is equivalent to 1 centipoise (cP) UNIVERSITY OF HEALTH 10 A N D A L L IE D S C IE N C E S School of Pharmacy 10  Viscosities of Some Fluids of Pharmaceutical Interest Fluid Dynamic Viscosity at 20 °C (cP) Chloroform 0.58 Water 1.002 Ethanol 1.20 Olive oil 84.0 Glycerol 1490 UNIVERSITY OF HEALTH 11 A N D A L L IE D S C IE N C E S School of Pharmacy 11 Kinematic Viscosity Kinematic viscosity is another coefficient that can be used to characterise a fluid. Kinematic viscosity (v) is defined as dynamic viscosity (η) divided by the density of the fluid (ρ). η i.e., v = ρ Its SI unit is m2s-1 [or the Stoke (St). NB: 1 St = 10-4 m2 s-1 ] Kinematic viscosity is also referred to as momentum diffusivity of a fluid. UNIVERSITY OF HEALTH 12 A N D A L L IE D S C IE N C E S School of Pharmacy 12  Relative and Specific Viscosities Relative viscosity (ηr) or viscosity ratio of a solution is the ratio of the solution’s viscosity (ηsol) to the viscosity of the solvent (ηs). i.e., ηr = ηsol ηs NB: Relative viscosity has no units. Specific viscosity (ηsp) = ηr - 1 UNIVERSITY OF HEALTH 13 A N D A L L IE D S C IE N C E S School of Pharmacy 13 Intrinsic Viscosity A colloidal dispersion is a dispersion of finely divided, insoluble solid particles (disperse phase) with a mean particle diameter of up to 1 µm in a fluid (dispersion medium or continuous phase). E.g., Al hydroxide and Mg hydroxide suspensions Albert Einstein derived the following equation, which can be used to estimate the viscosity of a colloidal dispersion: η = ηs(1 + 2.5Ø) where Ø is the volume fraction of the colloidal phase (the volume of the dispersed phase divided by the total volume of the dispersion) UNIVERSITY OF HEALTH 14 A N D A L L IE D S C IE N C E S School of Pharmacy 14  η = ηs(1 + 2.5Ø) η η = 1 + 2.5Ø (but s!" = ηr ) ηs ηs ηr = 1 + 2.5Ø ηr − 1 = 2.5Ø (but ηsp = ηr - 1) ηsp = 2.5Ø η sp = 2.5 Ø NB: The volume fraction (Ø) is directly related to concentration (C) η sp = k C η sp is referred to as viscosity number or reduced viscosity C UNIVERSITY OF HEALTH 15 A N D A L L IE D S C IE N C E S School of Pharmacy 15 ηsp A plot of as a function of concentration gives a linear relationship. C ηsp C [η] Concentration (g/dL) The intercept produced on extrapolation of the line to the y-axis will yield the constant referred to as limiting viscosity number or intrinsic viscosity [η]. The unit for [η] is dL/g, which is also known as inverse concentration. UNIVERSITY OF HEALTH 16 A N D A L L IE D S C IE N C E S School of Pharmacy 16  Types of Flow Systems UNIVERSITY OF HEALTH 17 A N D A L L IE D S C IE N C E S School of Pharmacy 17 Newtonian Newtonian fluids are simple fluids. They obey Newton’s law of viscosity (τ = ηγ) Non-Newtonian This includes the following: Plastic Pseudoplastic Dilatant UNIVERSITY OF HEALTH 18 A N D A L L IE D S C IE N C E S School of Pharmacy 18  When a Newtonian fluid is subjected to increasing rate of shear (γ), a plot of γ against the corresponding shear stress (τ) will produce a linear relationship. 𝟏 Shear rate Slope = η Shear stress Such a plot is referred to as a flow curve or rheogram. The slope of this plot gives the viscosity of the fluid. UNIVERSITY OF HEALTH 19 A N D A L L IE D S C IE N C E S School of Pharmacy 19 τ = ηγ y = mx + c τ=γ η γ= τ η y = mx + c UNIVERSITY OF HEALTH 20 A N D A L L IE D S C IE N C E S School of Pharmacy 20  Non-Newtonian Flow Most pharmaceutical fluids do not follow Newton’s law because their viscosities vary as shear stress is varied. The reason for this deviation is that such fluids are not simple fluids such as water and syrup. They are usually disperse or colloidal systems such as emulsions, suspensions, and gels. These materials are known as non-Newtonian fluids. UNIVERSITY OF HEALTH 21 A N D A L L IE D S C IE N C E S School of Pharmacy 21 Plastic Flow Plastic (or Bingham) flow is exhibited by concentrated suspensions, particularly if the continuous phase is of high viscosity or if the particles are flocculated. A plastic material does not flow until a certain value of shear stress (yield value) sufficient to overcome the van der Waals forces of attraction in the fluid is exceeded. The yield value is an indication of the degree of flocculation The more flocculated the suspension is, the higher the yield value will be. UNIVERSITY OF HEALTH 22 A N D A L L IE D S C IE N C E S School of Pharmacy 22  Deflocculated Flocculated UNIVERSITY OF HEALTH 23 A N D A L L IE D S C IE N C E S School of Pharmacy 23 Viscosity determined = Plastic viscosity Shear rate yield value Shear stress The yield value is obtained by extrapolating the linear portion of the curve to the shear stress axis. In practice, flow occurs at a lower shear stress than yield value. A plastic system resembles a Newtonian system at shear stresses greater than the yield value. UNIVERSITY OF HEALTH 24 A N D A L L IE D S C IE N C E S School of Pharmacy 24  Pseudoplastic Flow Pseudoplastic materials flow as soon as shear stress is applied. Their viscosities decrease as shear rate is increased. They are referred to as “shear thinning” systems. No single value of viscosity can be used to characterise such fluids. Materials that exhibit this type of flow include aqueous dispersions of natural and chemically modified hydrocolloids or gums E.g., acacia, tragacanth, methylcellulose and carmellose, and synthetic polymers such as polyvinylpyrrolidone and polyacrylic acid. UNIVERSITY OF HEALTH 25 A N D A L L IE D S C IE N C E S School of Pharmacy 25 The presence of long, high-molecular-weight molecules in solution results in entanglement together with the association of immobilised solvent. Under the influence of shear, the molecules tend to become disentangled and align themselves in the direction of flow. They thus offer less resistance to flow and this, together with the release of some of the entrapped water, accounts for the lower viscosity. UNIVERSITY OF HEALTH 26 A N D A L L IE D S C IE N C E S School of Pharmacy 26  UNIVERSITY OF HEALTH 27 A N D A L L IE D S C IE N C E S School of Pharmacy 27 Shear rate Shear stress At higher shear stresses, the flow curve tends towards linearity, indicating that a minimum viscosity has been attained. This indicates that the orientation of the molecules is complete. The solution may then show a Newtonian flow at high shear stresses. UNIVERSITY OF HEALTH 28 A N D A L L IE D S C IE N C E S School of Pharmacy 28  Dilatant Flow This type of flow is the opposite of pseudoplasticity. The viscosity of a dilatant material increases with increase in shear rate. Such materials increase in volume during shearing. They exhibit “shear thickening”. When the stress is removed, a dilatant system returns to its original state of fluidity. This type of behaviour is less common than plastic or pseudoplastic flow. It may be exhibited by dispersions containing a high concentration (≈ 50%) of small, deflocculated particles. UNIVERSITY OF HEALTH 29 A N D A L L IE D S C IE N C E S School of Pharmacy 29 Under conditions of zero shear the particles are closely packed interparticulate voids are minimum particles are well lubricated by the dispersion medium At low shear rates, e.g., during pouring, fluid in the interparticulate voids can adequately lubricate the particles to ensure flow. As shear rate is increased, the particles come together this results in the creation of larger voids the vehicle drains into these voids consequently, the particles become less lubricated resistance to flow increases and viscosity increases UNIVERSITY OF HEALTH 30 A N D A L L IE D S C IE N C E S School of Pharmacy 30  Resting state Sheared state Pharmaceutics: the design and manufacture of medicines The effect is progressive with increase in shear rate until eventually the material may appear paste-like as flow ceases. Fortunately, the effect is reversible and removal of the shear stress results in the re-establishment of the fluid nature. UNIVERSITY OF HEALTH 31 A N D A L L IE D S C IE N C E S School of Pharmacy 31 Shear rate Shear stress During the processing of a material that exhibits dilatant flow High shearing (e.g., with high-speed blenders and mills) must be avoided. If the material becomes dilatant during processing, the resultant solidification could overload and damage the equipment. UNIVERSITY OF HEALTH 32 A N D A L L IE D S C IE N C E S School of Pharmacy 32  Thixotropy Thixotropy is the property of some non-Newtonian fluids (most often shear-thinning systems) to show a time-dependent change in viscosity. This occurs because the material experiences some structural breakdown when subjected to an increasing rate of shear. Thixotropy is defined as isothermal and comparatively slow recovery on standing of material that has lost its consistency through shearing. The common feature of all thixotropic materials is that if they are subjected to gradually increasing shear rate, followed immediately by decreasing shear rate to zero, then the down-curve will be displaced to the left of the up-curve (for τ – x-axis, γ – y-axis). As a result, the rheogram will exhibit a hysteresis loop UNIVERSITY OF HEALTH 33 A N D A L L IE D S C IE N C E S School of Pharmacy 33 Plastic Pseudoplastic hysteresis loop Shear rate Shear rate up-curve Shear stress Shear stress UNIVERSITY OF HEALTH 34 A N D A L L IE D S C IE N C E S School of Pharmacy 34  The presence of the hysteresis loop indicates that a breakdown in structure has occurred. The area within the loop may be used as an index of the degree of breakdown. A thixotropic suspension settles slowly after being agitated, which allows for accurate dosing, whereas a non-thixotropic one settles rapidly. Several gel and colloidal preparations exhibit thixotropy. UNIVERSITY OF HEALTH 35 A N D A L L IE D S C IE N C E S School of Pharmacy 35