Chapter 17. Rheology
Contents Introduction Newtonian Systems Non-Newtonian Systems Thixotropy Determination of Rheologic Properties Viscoelasticity Applications to Pharmacy
INTRODUCTION
Rheology Definition: Science of deformation (solids) and flow (liquids) rheo (to flow) logos (science) Rheology
Viscosity An expression of the resistance of a fluid to flow (unit : dyne cm/sec 2 (=poise)) cf. Fluidity (φ) : 액체의흐름의경향 The reciprocal of viscosity
Rheology Newtonian systems Non-newtonian systems Plastic flow Pseudoplastic flow Dilatant flow
NEWTONIAN SYSTEMS
Viscosity G : rate of shear (dv/dr velocity gradient) F: srearing stress (F /A) Fig. 17-1
Newtonian s s Law of Flow F A ' dv = η dr η : coefficient of viscosity η = F G F = F /A G = dv/dr
Newtonian Flow G vs F Rheogram ( 유동곡선 ) Slope = 1/η 1 G = η F F = η G (F vs G) Fig. 17-2(a)
Unit of Viscosity poise The shearing force required to produce a velocity of 1 cm/sec between two parallel planes of liquid each 1cm 2 in area and separated by a distance of 1cm cf. centipoise (cp) (0.01 poise = 1 cp)
Kinematic Viscosity The absolute viscosity kinematic viscosity = η ρ Unit : stroke(s), centistroke(cs) Absolute viscosity Newtonian fluids Apparent viscosity Non-Newtonian fluids
Temperature Dependence of Viscosity Arrehenius (like) equation (Andrade Eq.) η = Ae Ev / RT Temperature viscosity
Viscosity Viscosity Symbol (unit) Relation (absolute) viscosity η(poise) η=f/g kinematic viscosity ν(stock) ν= η/ρ relative viscosity specific viscosity η rel η sp η rel = η/ η 0 η sp = η rel -1 =(η-η 0 )/ η 0
Viscosity Viscosity Symbol (unit) Relation reduced viscosity η red η red = η sp /C inherent viscosity η inh η inh =(ln η rel )/C limiting(intrinsic) viscosity number [η] [η]= lim = c 0 η lim ( η c 0 red sp / C )
NON-NEWTONIAN NEWTONIAN SYSTEMS Plastic flow ( 소성흐름 ) Pseudoplastic flow ( 유사소성흐름 ) Dilatant flow ( 팽창흐름 )
Plastic Flow Mechanism: 정지상태에서는응집인자가 van der Waals force 에의하여엉성한망상구조를이루다가 stress 가가해지면항복치에도달할때까지는고체로서거동하고항복치가넘는 stress 가가해지면구조가파괴되고 newtonian flow 의거동을나타냄. Example: 치약, 케찹, 버터등
Plastic Flow η Fig. 17-2(b) G f : yield value ( 항복치 ) : minimum shear stress required to induce flow
Plastic Flow Plastic viscosity (U)( 소성점도 ) U = Plasticity( 소성 ) ( F f ) G cf. f : yield value ( 항복치 ) Mobility = G (F 일반적으로어느 stress 까지는변화하지않고이보다클때유동하는성질 cf. plastic f)
Pseudoplastic Flow Mechanism: Example: natural & synthetic gum tragacanth, sod. Alginate, Methyl cellulose, Sod. CMC, etc. (viscosity modifier, suspending agents, etc.)
Pseudoplastic Flow The viscosity of a pseudoplastic substance decreases with increasing rate of shear. (shear thinning system) Application to suspensions (semisolids) 제제보관시 : 높은점성도 >> 제제안정 제제복용시 : 진탕 >> 점성도저하 >> 취급용이
Pseudoplastic Flow slope: b>a b viscosity: η b <η a shearing thinning a η Fig. 17-2(c) G
Dilatant Flow Inverse of pseudoplastic flow As the shear stress is increased, the bulk of system expands or dilates Increase the viscosity (shear thickening system) Examples : 50% 이상의전분을함유하는수성현탁액산화아연의 paste (30% 이상 )
Dilatant Flow η G Fig. 17-2(d)
Explanation of Dilatant Flow Behavior Fig. 17-3
THIXOTROPY
Thixotrophy An isothermal and comparatively slow recovery, on standing of a material, of a consistency lost through shearing 스트레스를가해주로낮아진점도가방치함에따라서서히회복되는성질 ( 요변성 ) - 등온가역적인 sol-gel 변형 Plastic and pseudoplastic systems exhibit thixotrophy
Thixotrophy 기준 : Gel η = F G G 1 < G 2 2 1 η 1 > η 2 Fig. 17-4
Negative Thixotrophy An increase rather than a decrease in consistency on the down-curve Fig. 17-9
Rheopexy A phenomenon in which a solid forms gel more readily when gently shaken or otherwise sheared that when allowed to form the gel while the material is kept at rest
DETERMINATION OF RHEOLOGIC PROPERTIES
Choice of Viscometer Use of a one point instrument is proper only in the case of the Newtonian systems Fig. 17-10 10
Capillary viscometer Measurement the time required for the liquid to pass between two marks η 2 = ( t 2 ρ 2 / t 1 ρ 1 ) η 1 Fig. 17-11 11 Ostwald-Cannon-Fenske viscometer
Falling Sphere Viscometer Measurement the terminal velocity of a falling or sliding sphere η = 2 {[ 2R ( d d ) g]9v} 2 1 based on Stoke s law Fig. 17-13 13 Hoeppler falling ball viscometer
Cup and Bob Viscometer Principle Fig. 17-14 14
Cone and Plate Viscometer Fig. 17 Fig. 17-18 18 Ferranti-Shirley viscometer
VISCOELASTICITY
Viscoelasticity The property that have both viscous properties of liquids and elastic properties of solids
Viscoelasticity Hooke의법칙탄성한계내에서의변형 (γ) 은작용하는힘 (F) 에비례한다. 힘 = 탄성률 x 변형 cf. Hookean body ( 완전탄성체 ) 변형의종류 Elongation strain Shear strain ( 전단변형 ) Volume strain
Viscoelasticity Creep 반고형제에일정한 stress를가했을때점탄성에의하여생기는변형이시간적으로변하는현상 Creep wave (Creep curve) A plot of time vs compliance (J) Compliance(J) = strain/stress
Viscoelasticity Methods to describe viscoelasticity Newton법칙 + Hooke의법칙 (Dashpot) + (Spring) (1) Maxwell unit : dashpot and spring in series : 영구변형 (by dashpot) (2) Voigt unit : dashpot and spring in parallel : 느린완전회복
Viscoelasticity (1) Maxwell unit : 점탄성액체의역학모델 ( 영구변형 ) (2) Voigt unit : 점탄성고체의역학모델 액체 vs 고체 (1) 일정한변형을준상태를유지할때, 장시간후에응력이일정한값에가까워지는물체를고체, 제한없이 0에가까워지는물체를액체 (2) 일정한응력을준상태를유지할때, 장시간후에변형이일정한값에가까워지는물체를고체, 무한하게크게되는물체를액체 ( 무마찰?)
Mechanical Model Viscous fluid : dashpot Elastic solid : spring Fig. 17-20
Voiqt Element Fig. 17-21
Creep Model Maxwell-Voigt model Fig. 17-22
APPLICATIONS TO PHARMACY
Pharmaceutical Area in which Rheology is Significant Fluids Mixing Particle-size reduction of disperse systems with shear Fluid transfer, including pumping and flow through pipes Physical stability of disperse systems
Pharmaceutical Area in which Rheology is Significant Quasisolids Spreading and adherence on the skin Removal from jar or extrusion from tubes Capacity of solids to mix with miscible liquids Release of the drug from the base
Pharmaceutical Area in which Solids Rheology is Significant Flow of powders from hoppers and into die cavities in tabletting or into capsules during encapsulation Package-ability of powdered or granular solids Processing Production capacity of the equipment Processing efficiency
Viscosity Modifier Cellulose Derivatives Cellulose is insoluble Derivatives are soluble (hydrogen bonding interaction) Methylcellulose (MC) Sodium Carboxymethylcellulose (Sod. CMC) Hydroxyethyl cellulose Hydroxypropyl cellulose (HPC) Hydroxypropyl methylcellulose (HPMC)
Viscosity Modifier Poly(acrylic acid) resins Crossed-linked (Caropol ) resins Viscsity increasing and gel-formation agents Homopolymer resins Copolymer resins Sodium salt resins
Viscosity Modifier Polyvinylpyrrolidone BASF Corp. - Kollidon USP povidones, polyvidones, PVP Complexes with iodine (Povidone) serve slow releasing formulation for antibacterial or topical use
Viscosity Modifier Pluronic copolymers ABA-tyoe triblock copolymers of poly(ethylene oxide) and poly(propylene oxide) F-68, F-108, F-127; freely soluble in waqter Pluronic F-127; dissolve in cold water change to a gel consistency in room temperature Poloxamer series
Rheology of Biological Systems Rheologic property of blood Shear rate < 100 s -1 ; Non-Newtonian, high viscosity Shear rate > 100 s -1 ; Newtonian, constant viscosity (~3 cps) Effects of the rheologic profile of blood Disease states Concentration of plasma proteins A number of pharmacological agents: Aspirin, Pentoxifylline, Thrombolyc agents, Ca channel blockers
Rheology of Biological Systems Rheological properties of mucus Bronchial mucus GI tract Female Urinogenital Tract η Cilia movement, N-acetylcystein H.pylori, Aspirin, NSAIDs η Cystic fibrosis Misoprostol Contraceptive drugs, biguanides
Rheology of Biological Systems Rheological properties of synovial fluid All the skeletal joints Egg white consistency Decrease hyaluronic acid ㅡ > decrease viscosity of fluid