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Chapter Rheology

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**Contents Introduction Newtonian Systems Non-Newtonian Systems**

Thixotropy Determination of Rheologic Properties Viscoelasticity Applications to Pharmacy

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INTRODUCTION

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**Rheology Definition: Science of**

deformation (solids) and flow (liquids) rheo (to flow) logos (science) Rheology

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Viscosity An expression of the resistance of a fluid to flow (unit : dyne cm/sec2 (=poise)) cf. Fluidity () :액체의 흐름의 경향 The reciprocal of viscosity

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**Rheology Newtonian systems Non-newtonian systems Plastic flow**

Pseudoplastic flow Dilatant flow

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NEWTONIAN SYSTEMS

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**Viscosity G : rate of shear (dv/dr velocity gradient)**

Fig. 19-1 G : rate of shear (dv/dr velocity gradient) F: srearing stress (F’/A)

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**Newtonian’s Law of Flow**

: coefficient of viscosity F = F’/A G = dv/dr

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**Newtonian Flow G vs F Rheogram (유동곡선) (F vs G) slope = 1/h**

Fig. 19-2(a) Rheogram (유동곡선) (F vs G) slope = 1/h

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**Unit of Viscosity poise**

The shearing force required to produce a velocity of 1 cm/sec between two parallel planes of liquid each 1cm2 in area and separated by a distance of 1cm cf. centipoise (cp)

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**Kinematic Viscosity The absolute viscosity**

Unit : stoke(s), centistoke(cs)

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**Temperature Dependence of Viscosity**

Arrehenius (like) equation (Andrade Eq.) Temperature á è viscosity â

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**Viscosity Viscosity (absolute) viscosity kinematic viscosity**

relative viscosity specific viscosity Symbol (unit) (poise) (stock) rel sp Relation =F/G = / rel= / 0 sp= rel-1 = (-0)/ 0

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**Viscosity Viscosity reduced viscosity inherent viscosity**

limiting(intrinsic) viscosity number Symbol (unit) red inh [] Relation red= sp/C inh=(ln rel)/C []=

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**NON-NEWTONIAN SYSTEMS**

Plastic flow (소성흐름) Pseudoplastic flow (유사소성흐름) Dilatant flow (팽창흐름)

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**Plastic Flow Mechanism:**

정지 상태에서는 응집인자가 van der Waals force에 의하여 엉성한 망상구조를 이루다가 stress가 가해지면 항복치에 도달할 때 까지는 고체로서 거동하고 항복치가 넘는 stress가 가해지면 구조가 파괴되고 newtonian flow의 거동을 나타냄. Example: 치약, 케찹, 버터 등

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Plastic Flow Fig. 19-2(b) h G

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**Plastic Flow Plastic viscosity (U)(소성점도) cf. Plasticity(소성)**

f : yield value (항복치) cf. Plasticity(소성) 일반적으로 어느 stress까지는 변화하지않고 이보다 클 때 유동하는 성질 cf. plastic

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**Pseudoplastic Flow h Mechanism : Example : natural & synthetic gum**

stress h Align in the direction of flow Example : natural & synthetic gum tragacanth, sod. Alginate, Methyl cellulose, Sod. CMC, etc.

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Pseudoplastic Flow The viscosity of a pseudoplastic substance decreases with increasing rate of shear. (shear thinning system) Application to suspensions (semisolids) 제제 보관시 : 높은 점성도 >> 제제 안정 제제 복용시 : 진탕 >> 점성도 저하 >> 취급용이

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**Pseudoplastic Flow slope: b>a viscosity: hb<ha**

Fig. 19-2(c) a b slope: b>a viscosity: hb<ha “shearing thinning” h G

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**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% 이상의 전분을 함유하는 수성 현탁액 산화아연의 paste (30% 이상)

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Dilatant Flow Fig. 19-2(d) h G

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**Explanation of Dilatant Flow Behavior**

Fig. 19-3

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THIXOTROPY

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Thixotrophy An isothermal and comparatively slow recovery, on standing of a material, of a consistency lost through shearing 스트레스를 가해 주로 낮아진 점도가 방치함에 따라 서서히 회복되는 성질 (요변성) - 등온 가역적인 sol-Gel 변형 Plastic and pseudoplastic systems exhibit thixotrophy

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Thixotrophy Fig. 19-4

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**Negative Thixotrophy Fig. 19-9**

An increase rather than a decrease in consistency on the down-curve

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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

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**DETERMINATION OF RHEOLOGIC PROPERTIES**

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**Choice of Viscometer Use of a “one point” instrument is**

Fig Use of a “one point” instrument is proper only in the case of the Newtonian systems

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Capillary viscometer Fig Ostwald-Cannon-Fenske viscometer

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**Falling Sphere Viscometer**

Fig Hoeppler falling ball viscometer

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Cup and Bob Viscometer Principle Fig

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**Cone and Plate Viscometer**

Fig Ferranti-Shirley viscometer

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VISCOELASTICITY

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Viscoelasticity The property that have both viscous properties of liquids and elastic properties of solids

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**Viscoelasticity Hooke의 법칙 탄성한계 내에서의 변형(g)은 작용하는 힘 (F)에 비례한다.**

힘 = 탄성률 x 변형 cf. Hookean body (완전탄성체) 변형의 종류 Elongation strain Shear strain (전단변형) Volume strain

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**Viscoelasticity Creep**

반고형제에 일정한 stress를 가했을 때 점탄성에 의하여 생기는 변형이 시간적으로 변하는 현상 Creep wave (Creep curve) A plot of time vs compliance (J) Compliance(J) = strain/stress

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**Viscoelasticity Methods to describe viscoelasticity**

Newton법칙 + Hooke의 법칙 (Dashpot) + (Spring) (1) Maxwell unit : dashpot and spring in series : 영구변형 (by dashpot) (2) Voigt unit : dashpot and spring in parallel : 느린 완전회복

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**Viscoelasticity (1) Maxwell unit : 점탄성 액체의 역학모델 (영구변형)**

(2) Voigt unit : 점탄성 고체의 역학모델 액체 vs 고체 (1) 일정한 변형을 준 상태를 유지할 때, 장시간 후에 응력이 일정한 값에 가까워 지는 물체를 고체, 제한없이 0에 가까워 지는 물체를 액체 (2) 일정한 응력을 준 상태를 유지할 때, 장시간 후에 변형이 일정한 값에 가까워 지는 물체를 고체, 무한하게 크게 되는 물체를 액체 (무마찰?)

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**Mechanical Model Elastic solid : spring Viscous fluid : dashpot**

Fig

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Voiqt Element Fig

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Creep Model Fig

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**APPLICATIONS TO PHARMACY**

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**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

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**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

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**Pharmaceutical Area in which Rheology is Significant**

Solids Flow of powders from hoppers and into die cavities in tabletting or into capsules during encapsulation Packagability of powdered or granular solids Processing Production capacity of the equipment Processing efficiency

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