Applied physical pharmacy 10. Rheology Sungkyunkwan University, School of Pharmacy Physical Pharmacy Lab Gyoung Won Kim
CONTENTS Introduction Newtonian system Non - Newtonian system Thixotropy Viscoelasticity Determination of viscosity Rheology of biological system Rheology of pharmaceutical system Viscosity modifiers
Introduction
Rheology Rheology is the science of the flow and deformation of matter under the effect of an applied force Matter : solid, liquid, gas Focus primarily on liquids and semisolids (e.g., creams, ointment, and gels) in this chapter Deformation : change of the shape and the size of a matter due to applied forces
Rheology Ideal solid Body that deforms in an elastic manner For an ideal solid, the energy of deformation is fully recovered when the stress is removed. Reversible deformation : Elasticity
Rheology Ideal liquid or gas Body that deforms irreversibly. It flows. Energy of deformation is converted to heat and it cannot be recovered when stress is removed. Irreversible deformation : Flow
Rheology In reality, we have neither ideal solids nor ideal fluids. Real solid can be deformed irreversibly when subjected to certain forces. This deformation is called creep. Very few liquids show ideal behavior. For most liquids, their behavior is between a sold and a liquid. We call them viscoelastic.
Stress Force that results in deforming a body divided by the area over which the force is applied Stress = F F : Force (dynes) A : Area (cm 2 ) A
Shear stress In case of fluids, we use shear stress
Strain Measure of how much a body deforms relative to its original dimensions tanγ = d h For small deformation, tanγ = γ γ = d h Shear strain
Shear rate In fluids, we are interested in the rate at which strain is produced when shear stress is applied γ = δγ δt = δd h δt = ν h Strain rate, commonly called Shear rate, Rate of Shear (G)
Newtonian system
Newtonian system Newtonian systems follow Newton s Law of Flow The relationship between shear stress (F) and rate of shear (G) is linear Rheogram G = 1 η F F A = η dν dr F = ηg slope = 1 η = φ = fluidity η: coefficient of viscosity, simply as viscosity
Viscosity A parameter that measures resistance to flow - the higher the magnitude of the viscosity, the more resistant the material will be to deformation and flow. The unit of viscosity is the poise (P) - Since many liquids, such as water, have relatively low viscosity, centipoise (cps) is also a frequently used unit. dynes cm 2 = η cm sec cm ( F A = η dν dr ) η = dynes sec cm 2 = g cm/sec2 sec cm 2 = g cm sec = poise 1 cps = 1 100 poise
Viscosity Viscosity of a system will change with temperature. - With increasing temperature, η will ln η = ln A + E v A: constant Ev: activation energy R: universal gas constant T: temperature RT (Arrhenius equation)
Viscosity
Non - Newtonian system
Non - Newtonian system Non-Newtonian flow is observed in complex heterogeneous systems in which the relationship between shear stress (F) and the rate of shear (G) is nonlinear Most liquids in pharmacies are non-newtonian systems e.g. emulsions, creams, suspensions, ointments Plastic flow Pseudoplastic flow Dilatant flow
Plastic flow
Plastic flow Bingham body Plastic flow describes a system in which no flow occurs until shear stress (F) reaches a critical transition point (yield value) - At stresses below the yield value, the system acts like a elastic material - At stresses above the yield value, the relationship between shear stress and rate of shear becomes linear U = F f G U: plastic viscosity f: yield value Yield value
Plastic flow Concentrated suspensions with flocculated particles are a good example of systems with plastic flow - held together with relatively week van der Waals forces Before the system can flow, the floccules must be redispersed. - week van der Waals forces must be broken The force required to break these bonds is the yield value
Pseudoplastic flow
Pseudoplastic flow Pseudoplastic system decrease in viscosity with increasing shear stress (shear-thinning system) - They become thinner with increasing shear / agitation - Apparent viscosity is 1/slope at any point along the curve. Slope A < Slope B Viscosity A > Viscosity B
Apparent viscosity There is an apparent viscosity for each value of shear rate or shear stress, which can be expressed in two different ways. tanφ Slope of the tangent to the flow curve at P tanθ Slope of the secant to the flow curve at P
Pseudoplastic flow Aqueous solutions of polymers (polysaccharides) are a good example of systems with pseudoplastic flow - At rest polymers within the solution become coiled up in their globular form - When shear stress (e.g. agitation or shaking) is applied, the polymer chains untangle. - With increased agitation, the polymers align themselves in the direction of flow internal resistance viscosity
Pseudoplastic flow Shear thinning is a useful property for suspensions - High viscosity at rest prevents particle sedimenting and aggregating stability of suspension stability of suspension - High viscosity easily overcome by shaking bottle As suspension passes through needle, it undergoes high shear stress as A is very small. - Shear thinning systems : viscosity through needle - Easier to push through needle High shear Stress = F A
Dilatant flow
Dilatant flow Opposite to Pseudoplastic flow (shear-thickening system) - Increased viscosity with increased shear stress - Apparent viscosity is 1/slope at any point along the curve. Systems are called dilatant because they also increase in volume with agitation Slope A > Slope B Viscosity A < Viscosity B
Dilatant flow The system are usually made up of high percentage of dispersed deflocculated particles (usually > 50%) After shaking, the particle become open packed void volume Closed packed particle Minimum void volume Sufficient vehicle Relatively low viscosity Open packed particle Increased void volume Insufficient vehicle Relatively high viscosity
Power law equation F N = η G N indicates the type of flow - N=1 : Newtonian flow - N>1 : Pseudoplastic flow - N<1 : Dilatant flow η consistency coefficient log G = NlogF logη
Thixotropy
Thixotropy When left to rest, Newtonian systems will revert back to their original form. That is, they have identical downward curves. When left to rest, non-newtonian systems do slowly revert back to something close to their original form, BUT they do not have identical downward curves. This phenomenon is known as thixotropy
Thixotropy Thixotropy can be defined as an isothermal and comparatively slow recovery, on standing of a material, of a consistency lost through shearing. B A Slope A < Slope B Viscosity A > Viscosity B
Thixotropy
Negative Thixotropy Negative Thixotropy or antithixotropy represents an increase rather than a decrease in consistency on the downcurve Slope A > Slope B Viscosity A < Viscosity B A B
Degree of Hysteresis The difference between the upward and downward curve in thixotropic systems is known as the degree of hysteresis - As products with high molecular weight take longer to recover, their degree of hysteresis will be larger than systems with low molecular weight particles
When is thixotropy useful Shear thinning is useful for suspension/creams - Increased viscosity at rest Increased stability - Thinning with agitation easy administration Thixotropy is useful as the delay in reversion to original viscosity ensure product is administered before it thickens up again
Intramuscular depot injection High shear stress through the needle thinning allows easy admin. At relative rest in muscle viscous depot which can release the drug slowly over a long period of time If the suspension was not thixotropic it could be too thin in the muscle to form a depot
Viscoelasticity
Viscoelasticity Mechanical properties of materials that exhibit both viscous properties of liquids and elastic properties of solids (e.g. semisolid) η = F G E = F γ η : viscosity F : shear stress V : shear rate E : elastic modulus F : stress γ : strain Hooke s law
Mechanical representation Viscous fluid Elastic solid
Viscoelasticity
Viscoelasticity One of several Voigt units can be combined with Maxwell elements to represent the changes that a pharmaceutical solid, such as an ointment or a cream. Behavior of wool fat https://www.youtube.com/watc h?v=q9emsmcg8cc
Determination of viscosity
Viscometer Capillary viscometer Falling-sphere viscometer - Single-shear-rate instrument - Use only with Newtonian material Cup-and-bob viscometer Cone-and-plate viscometer - Multipoint, rotational instrument - Use with both Newtonian and non-newtonian systems
Capillary Viscometer Known as Ostwald viscometer The time of flow of test liquid is compared with the time required for a liquid of known viscosity (usually water) Poiseuille s law η = πr4 tδp 8lV η = KtΔP Pressure difference ΔP depend on density ρ η 1 = K t 1 ρ 1 η 2 = K t 2 ρ 2 η 1 η 2 = t 1ρ 1 t 2 ρ 2 t: time of flow ρ: density of fluid
Falling Sphere Viscometer A glass or steel ball rolls down an almost vertical glass tube containing the test liquid at a known constant temperature The viscosity of fluid of liquid is directly related to the time taken by the ball to move between the two points η = t S b S f B t: time taken by the ball between two points S b : specific gravity of ball S f : specific gravity of fluid B: constant for a particular ball
Cup-and-Bob Viscometer Rotational viscometer Stormer viscometer η = K V W V K v : constant for instrument W : weight placed on hanger V: rpm shear rate
Cone and Plate Viscometer The sample is sheared in the narrow gap between the stationary plate and the rotating cone η = C T ν C : Instrument constant T : Torque reading ν : speed of cone in rpm η = C T T f ν yield value f = C f T f
Rheology of biological system (Biorheology)
Blood viscosity Blood is a complex suspension of cells in plasma Blood is a non-newtonian fluid with viscoelastic property Apparent blood viscosity depends on shear rate (Shear-thinning) - Low shear rate Rouleaux formation and sedimantation high apparent viscosity - High shear rate the stack break down Newtonian behavior low apparent viscosity Rouleaux formation (aggregate of erythrocyte)
Blood viscosity Apparent blood viscosity depends on hematocrit level. (Normal range 40~45%) Hematocrit is the percentage of whole blood occupied by cellular elements
Blood viscosity Apparent blood viscosity depends on plasma viscosity which depends on the protein concentration of plasma (Normal range: albumin 45 to 50 mg/ml, fibrinogen 3~5 mg/ml) - Plasma is a Newtonian fluid - Plasma protein such as fibrinogen are thought to cause RBC aggregation by facilitating binding between RBCs
Mucus viscosity Mucus is gel-like material The mucus gel layer is a heterogeneous mixture of mucus glycoprotein, phospholipid, and enzyme with imbibed water to form a firm layer Rheological property of mucus change from viscoelastic gel-like matrix (infinite viscosity) to a fluid consistency (low viscosity) upon an increase in the shear rate More viscous : trap particle and microorganism Relatively low viscous because of rapid movement of cilia
Mucus viscosity Cystic Fibrosis The inhalation form of N-acetylcysteine, a mucolytic agent that break disulfide bonds in mucus, is effective in reducing the viscosity of mucus Helicobacter pylori- secreted phospholipase A2 may decrease the viscosity of stomach mucus enzyme and acid diffuse into tissue (ulcer formation) mucosal protective agent (prostaglandin E2, sucralfate) increase the production and viscosity of mucus
Synovial fluid viscosity Synovial fluid is a viscous liquid present in all the skeletal joint Composed mainly of hyaluronic acid, proteins such as albumin, and water The rheological property of synovial fluid is dependent on the structure of hyaluronic acid - In inflammatory conditions such as rheumatoid arthritis, the molecular weight and concentration of hyaluronic acid decrease sharply, and the viscous consistency of the fluid is lost
Rheology of pharmaceutical system
Suspension / Emulsion Non-Newtonian rheological profile Mixing process affect the viscosity of formulation - For shear-thickening system, high viscosity can have a significant effect on the content uniformity of drug. The settling and aggregation of solid particles in suspensions are viscosity-dependent. Emulsion stability is viscosity-dependent. - use polymeric emulsifier e.g. poly(acrylic acid) copolymer emulsification and viscosity enhancement
Ointment / Ophthalmic Drops The viscosity of the ointment increases upon the addition of the drug and excipients - More difficult to remove product from container problem to elderly patients - Does not spread well on skin surface less efficacious Very small volume (10 μl) of Ophthalmic drop remains after blinking, and is absorbed - Increase viscosity Retard drainage Increase contact time Increase bioavailability - use hydrophilic polymer e.g. polyvinyl alcohol (PVA), hydroxypropylmethyl cellulose (HPMC)
Polymer Gels Semisolid system made up of polymer interpenetrated by a solvent (water) - Gel is formed by physical cross-linking, chemically cross-linking, noncovalent forces (e.g. hydrogen bonding, hydrophobic interaction) Gel exhibit a viscoelastic property - Rigid material at rest - Flow when shear stress in induced
In situ gelling A process of gel formation at the site of application after the composition or formulation has been applied to the site - Gellan gum, alginic acid, xyloglucan, pectin, chitosan, poly(dl-lactic acid), poly(dl-lactide-co-glycolide) and poly-caprolactone
In-situ Gelling Temperature-sensitive polymeric formulations change from a liquid to gel consistency at critical transition temperature, sol-gel transition temperature (T sol-gel ) - 20%~25% (w/w) aqueous solution of Pluronic F-127 (poloxamer 407) : T sol-gel = 21 (69.8 )
In-situ Gelling Ploymeric system that change from a liquid to a gel consistency as a result of ionic interaction - Gellan gum change from a liquid to a gell consistency in the presence of monovalence cation ( e.g., Na +, K + )
Viscosity Modifiers
Viscosity Modifier Cellulose Derivatives Natural Gums Sodium Alginate Poly(Acrylic Acid) Resin Pluronic Copolymers Clays Methylcellulose Sodium Carboxymethylcellulose Hydroxyethyl Cellulose Hydroxypropyl Cellulose Hydroxypropyl Methylcellulose Acacia Tragacanth Xanthan Carrageenan Homopolymer Resins Copolymer Resins Sodium Salt Resins Poly(N-vinylpyrrolidone) Bentonite
Hydroxypropyl Methylcellulose (HPMC) Typical substitution is 15% to 30% methoxy groups and 4% to 30% hydroxypropyl groups - A factor which influences organic solubility, thermal gelation temperature of aqueous solutions Nonionic polymer does not have incompatibility issues with cationic compound
METHOCEL TM Cellulose METHOCEL TM cellulose ethers are water-soluble methylcellulose and hydroxypropyl methylcellulose polymers (Dow chemical) Molecular weight Concentration
METHOCEL TM Cellulose Pseudoplastic (shear thinning) Shear rate