1 blood diseases hematocrit – measure of % rbc –males: 47% ± 5% –females: 42% ± 5% rule of...

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3 Definition of Rheology Rheology is the science of flow and deformation of matter We use rheology to study flow behavior of ceramics loaded slurries for preparation, casting and gelling.

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1 Blood Diseases Hematocrit measure of % RBC Males: 47% 5% Females: 42% 5% Rule of 3's: Hgb should be 3 times the Hematocrit (Hct) (i.e. Hgb of 9 gm/dl should make Hct 27%). The Hgb should increase 1 gm/dl & 3% Hct for each unit of PRBC's if you need a transfusion. The hematocrit, also known as packed cell volume (PCV) or erythrocyte volume fraction (EVF), is the volume percentage (%) of red blood cells in blood. It is normally 45% for men and 40% for women. It is considered an integral part of a person's complete blood count results, along with hemoglobin concentration, white blood cell count, and platelet count. Polycythemia Dengue fever Sickle Cell Anemia Malaria Hemoglobin/Hematocrit Value 2 Introduction To Rheology Santanu Dhara School of Medical Science and Technology Indian Institute of Technology Kharagpur 3 Definition of Rheology Rheology is the science of flow and deformation of matter We use rheology to study flow behavior of ceramics loaded slurries for preparation, casting and gelling. 4 Flow and Deformation Parameters: Shear Stress, Shear Strain, & Shear Rate Stress: Force per unit area. Symbol : Units: Pa (SI) or dyn/cm (cgs) Shear Strain: Relative deformation in shear. Symbol : Units: None Shear Rate: Change of shear strain per unit time. Symbol: Units: s -1 5 Range of Rheological Material Behavior Rheology: The study of flow and deformation of matter. Range of material behavior Solid Like Liquid Like Ideal Solid Ideal Fluid Classical Extremes 6 Classical Extremes: Elasticity 1678: Robert Hooke develops his True Theory of Elasticity The power of any spring is in the same proportion with the tension therof. Hookes Law: = G or (stress = G x strain) where G is the RIGIDITY MODULUS Hookes law describes ideal mechanical behavior using a constitutive equation in which stress and strain are related through a proportionality constant called the modulus G. If you double the stress, you double the strain. 7 Classical Extremes: Viscosity 1687: Isaac Newton addresses liquids and steady simple shearing flow in his Principia The resistance which arises from the lack of slipperiness of the parts of the liquid, other things being equal, is proportional to the velocity with which the parts of the liquid are separated from one another. Newtons Law: = where is the Coefficient of Viscosity Newtonss law describes idea flow behavior using a constitutive equation in which stress and rate of strain are related through a proportionality constant called the viscosity. If you double the stress, you double the shear rate. 8 Viscosity and Steady Shear Testing 9 Viscosity: Definition Viscosity is.... lack of slipperiness. synonymous with internal friction. resistance to flow. A measure of the resistance of flow due to internal friction when one layer of fluid is caused to move in relationship to another layer. 10 Viscosity: Units The Units of Viscosity are..... SI unit is the Pascal. second (Pa. s) cgs unit is the Poise Poise is > Pa. s by a factor of 10 10 Poise =1 Pa. s 1 cP (centipoise) = 1 m Pa. s (mili-pascal-second) 11 Typical Viscosities (Pa. s) Asphalt Binder Polymer Melt Molasses Liquid Honey Glycerol Olive Oil Water Air ,000 1, 12 Typical Shear Rates (1/s) Sedimentation10 -4 Molecular Structure Leveling/Sagging10 -3 to 10 0 Compression Molding Pouring10 0 to 10 1 Extrusion Pumping10 1 to 10 3 Blow Molding Rubbing10 3 to 10 4 Injection Molding Spraying10 5 Bearing lubrication10 6 13 Variables that Affect Viscosity Shear Rate Time of Shearing Temperature Pressure 14 Newtonian Vs. Non-Newtonian Behavior Strict definition of Newtonian Behavior is only stress generated in simple shear flow (no normal stress difference). Shear viscosity does not vary with shear rate. is constant with time of shearing. in fluid falls immediately to zero when shearing is stopped. When sheared again, the is as was previously measured (regardless of delay between measurements). measured in different types of deformation are in proportion to one another. measured in uniaxial extension is three times shear (Troutons Ratio) A Liquid showing any deviation from Newtonian is said to be non-Newtonian 15 Characteristic Diagrams for Newtonian Fluids , Pa s Pa.s s 16 Non-Newtonian Fluids Non-Newtonian Time Independent Liquids, = ( ) Viscosity of fluid is dependent on shear rate but independent of the time of shearing. The viscosity is presented at a specific shear rate and referred to as the apparent viscosity, shear viscosity or shear dependent viscosity. Non-Newtonian Time Dependent Liquids, = ( t) Viscosity of fluid is dependent on shear rate and the time during which shear rate is applied. 17 Non-Newtonian, Time Independent Fluids Shear-Thinning A decrease in viscosity with increasing shear rate. Also referred to as Pseudoplasticity. Shear-Thickening An increase in viscosity with increasing shear rate. Also referred to as Dilatancy. 18 Characteristic Diagrams for Shear Thinning Fluids Pa.s s , Pa Pa.s , Pa 19 Shear Thinning Behavior Shear thinning behavior is often a result of: Orientation of non-sherical particles in the direction of flow. An example of this phenomenon is the pumping of fiber slurries. Orientation of polymer chains in the direction of flow and breaking of polymer chains during flow. An example is polymer melt extrusion Deformation of spherical droplets to elliptical droplets in an emulsion. An industrial application where this phenomenon can occur is in the production of low fat margarine. Breaking of particle aggregates in suspensions. An example would be stiring paint. 20 Non-Newtonian, Time Dependent Fluids Thixotropy A decrease in apparent viscosity with time under constant shear rate or shear stress, followed by a gradual recovery, when the stress or shear rate is removed. Rheopexy An increase in apparent viscosity with time under constant shear rate or shear stress, followed by a gradual recovery when the stress or shear rate is removed. Also called Anti-thixotropy or negative thixotropy. Reference:Barnes, H.A., Hutton, J.F., and Walters, K., An Introduction to Rheology, Elsevier Science B.V., ISBN 21 Non-Newtonian, Time Dependent Fluids time Viscosity Thixotropic Rheopectic Shear Rate = Constant 22 Linearity vs. Non-Linearity Hookes and Newtons laws are linear laws. They assume direct proportionality between stress and strain, or shear rate no matter what the stress. Most materials we work with obey these laws over a limited range of stresses. Beyond this limited range a material behaves non-linearly. 23 Newtonian and Non-Newtonian Behavior of Fluids Newtonian Region Independent of Non-Newtonian Region = f( ) 24 Linear and Non-Linear Stress- Strain Behavior of Solids Non-Linear Region G = f( ) Linear Region G is constant G % strain G' (Pa) osc. stress (Pa) 25 Types Of Flow Bingham Plastic Pseudoplastic Newtonian Dilatant Shear Thinning Shear Thickening "Yield" y Yield Stres s 26 Model Fitting Newtonian Pseudoplastic Dilatant Bingham Casson Herschel-Bulkley 27 Steady Shear Test Modes Stepped Ramp - Equilibrium Flow Continuous Ramp Temperature Ramp 28 Stress Ramp Test - Continuous Ramp l Stress is applied to material at a constant rate. Resultant strain is monitored with time. Stress (Pa) time (min.) m =Stress rate (Pa/min) Deformation l USES Yield stress Scouting Viscosity Run 29 Idealized Full Flow Curve (1) Sedimentation (2) Leveling (3) Pouring (4) Pumping (5) Rubbing (6) Spraying. Log 10 E E 1 10 E 4 Asphalt Binder Molasse s Glycerol Castor Oil Olive Oil Water (1) (2) (3) (4) (5)(6) Log 30 Viscosity: Temperature dependence 31 Type of Viscometer Ostwald viscometers named after Wilhelm Ostwald or glass capillary viscometers. Another type is the Ubbelohde viscometer. They basically consist of a glass tube in the shape of a U held vertically in a controlled temperature bath. In one arm of the U is a vertical section of precise narrow bore (the capillary). Above this is a bulb, there is another bulb lower down in the other arm. In use, liquid is drawn into the upper bulb by suction, then allowed to flow down through the capillary into the lower bulb. Two marks (one above and one below the upper bulb) indicate a known volume. The time taken for the level of the liquid to pass between these marks is proportional to the kinematic viscosity. Most commercial units are provided with a conversion factor, or can be calibrated by a fluid of known properties 32 Rotary Viscometer - Spring Brookfield Fungilab viscoelite Air bearing (Graphite bearing) Bohlin Rheometers and Viscometers TA instrument 33 CSL 2 CSL 100 Rheometer Air Bearing & Motor Optical Encoder Measuring System Temperature Control Cell Autogap Set 2 34 Cross-Section CSL Draw Rod Optical Encoder Air Bearing Controlled Torque Motor Peltier Temperature Control Plate Micrometer Wheel Measurement Geometry Auto Gap Set Motor Pneumatic Ram 35 Cross-Section of CSL Drive Air Jet Optical Encoder Drag Cup Non-Contact Motor Air Bearing 36 Controlled Stress Schematic t Ball Slide AR 1000 t Draw Rod l l Rheometer Head t air bearing t drag-cup motor t optical encoder l Sample Plate t Peltier (optional) t blank (optional) l Column t Geometry Normal Force Transducer t (optional) Rheometer Base t auto gap set motor t AGS encoder t communication ports l l l 37 AR 1000: Rheometer Head Schematic l Lower Radial Bearing Optical Encoder Thrust Bearing Drag-cup Motor Motor Housing l Drag Cup l Upper Radial Bearing 38 Parallel Plate Strain Constant: K = RHRH Stress Constant: K = 3 * G c (R/10) 3 Variable Gap (Sample Thickness) 500 to 2000 microns recommended. Assortment of Plate Diameters (2 cm, 4 cm, and 6 cm Standard) Easy to load. Able to use with a wide range of viscosities. Velocity gradient from center to edge of plate during steady shear testing. 39 Plate Gaps and Diameters 2cm 4cm 6cm Shear Stress Gap Shear Rate Decreases Increases 0 Infinity 40 l Set gap to be at least 10 x particle or droplet size [consider extremes of size distribution] l Minimum gap should be 1000 microns Gap Choice for Parallel Plate Geometry Plate & Plate 1) Set Gap & Trim Edge Plate & Plate 2) Close microns 41 Cone Angles and Diameters 2cm 4cm 6cm Shear Stress Angle Shear Rate Decreases Increases 42 Limitations of Cone & Plate for Dispersions - Fixed Gap! Cone & Plate Truncation Height = Gap Truncation Heights: 1 degree ~ microns 2 degrees ~ 60 microns 4 degrees ~ 120 microns Gap must be > or = 10 [particle size]!! 43 Concentric Cylinder Strain Constant: K = 2 1-(R 1 /R 2 ) 2 Stress Constant: K = 1,000 L(R 1 ) 2 Large surface area to obtain low stress measurements. Possibility of shear history effects from loading. Good for testing suspensions with limited stability. 44 l Reduces errors due to solvent evaporation l Available for cones, plates, and concentric cylinders Solvent Trap System 45 Edge Effects Under Filling Over Filling Correct Filling 46 Rheology of Dispersions 47 Dispersion - Definition DEFINITION: Discrete particles randomly distributed in a fluid medium. Dispersions can be broken into three categories Suspensions - solid particles in a liquid medium. Emulsions - liquid droplets in a liquid medium. Foam - a gas in a liquid medium. Reference:Macosko, C.W., Rheology: Principles, Measurements, and Applications, VCH Publishers Inc., ISBN 48 Dispersion + - Particle, Droplet, or Air Bubble Number, Size, Shape, Density Continuous Phase, c Modify Surface Liquid Medium 49 Factors Influencing Rheology of Dispersions High volume fractions, Particle size Particle size distribution Particle shape Electrostatic interactions Vs Steric Hindrance 50 Concentration of Particles Rheology depends greatly on the hydrodynamic forces that act on the surface of particles (aggregates) regardless of the density. Need to define concentration of suspension in terms of phase volume or volume-per- volume fraction as opposed to weight-per- weight fraction which is often used as a measure of concentration. Reference:Barnes, H.A., Hutton, J.F., and Walters, K., An Introduction to Rheology, Elsevier Science B.V., ISBN 51 Forces Acting on Particles Arise from interaction between particles and result in overall repulsion or attraction between particles. Repulsion Like electrostatic charges. Entropic repulsion of polymeric or surfactant material on the surface of the particle. Net repulsive Forces Particles remain separate (dispersed or deflocculated). Attraction London - Van der Walls attraction between particles. Electrostatic attraction between unlike charges on different parts of a particle (edge/face attraction between clay particles). Net attractive forces Particles flocculate. Reference:Barnes, H.A., Hutton, J.F., and Walters, K., An Introduction to Rheology, Elsevier Science B.V., ISBN 52 Forces Between Particles Van der Waals Forces lead to particle clumping In most dispersions, particles are kept apart (in suspension) by modifying the surface of the particle. Want to prevent particles from clumping There are generally two ways to modify the the surface of a particle to maintain a stable dispersion Electrostatics forces Steric forces 53 Mechanism of stabilization of the colloidal particle in suspending medium The repulsive force should be predominant over Vander Walls force of attraction U T = U A + (U Re + U Rs ) Where U Re and U Rs are the energy term due to electrostatic repulsion and steric stabilization For electro statically stabilized slurry, the zeta potential of the suspended powder should be higher than 25 mV Primary Maximum Interparticle Spacing Deep Primary Minimum Van der Waals Attraction Van der Waals Attraction + Electrostatic Repulsion Hydration Layer Repulsion+ Van der Waals Attraction Flocced State Touching & Cohesive Particle Network Dispersed State Nontouching Particle Network Coagulated State Nontouching & Cohesive Particle Network Shallow Hydration Minimum (a)(b)(c) 0 Different State of Dispersion of Slurry Flocculated Slurry Dispersed Slurry Coagulated Slurry 55 Forming of dense, defect free ceramic components via gelcasting requires use of highly loaded slurries. In addition to high solids loading, gelcasting slurries must be stable, Shear thinning Yield stress 50 Pa Viscosity 2 Pa.s at the shear rate 10 s -1 Slurry Characteristics 56 Dispersion Stability Two ways dispersed particles are stabilized. Electrostatically The existence of a net charge which causes particles to repel one another. Sterically by absorption of polymer molecules on the particles. film of absorbed surfactant which which prevents the particles from adhering to one another may be sufficient to keep dispersed particles in suspension. Ref: Rohn, C.L.,The Rheology of Coatings and Dispersions, Journal of Water Borne Coatings, Au gust, 1987. 57 Electrostatic Forces on Particles Electrostatic Repulsion Pseudo-Structure 58 Steric Hindrance of Particles Non-interacting Adsorbed Polymer Bridging Floc 59 Concentrated Suspensions In concentrated suspensions, particles may link to build a three- dimensional network structure which extends through the whole system. This structure in a suspension is a result of particle-particle interactions. These particle-particle interactions cause deviation from Newtonian behavior in a suspension. We need to recognize that the rheology of suspensions is measured macroscopically but the rheology depends very much on microscopic considerations. Measuring these particle-particle interactions or structure will yield valuable information about the microstructure of the suspension. Reference: Sato, T., Rheology of Suspensions, Journal of Coatings Technology, Vol. 67, No. 847, August 1995. 60 Particle-Particle Interactions Cause Structure 61 The Maximum Packing Fraction, m The maximum packing fraction m is the volume fraction of particles at which a three-dimensional continuous contacting network is formed. At m the suspension is jammed up and flow is impossible. At m the suspension the viscosity goes to infinity. m ranges form 0.5 to (FCC m = 0.74) 62 The Maximum Packing Fraction, m m depends on particle arrangement, particle size distribution, and particle shape. Broader particle size distributions tend to have higher m. the suspension is jammed up and flow is impossible. Non-spherical particles have lower m (poor space fitting). Particle flocculation leads to a low m (in general flocs are not close packed). Good to normalize concentration as the ration / m. Packing Fraction: The ratio of the total volume of a set of objects packed into a space to the volume of that space. 63 Limited Cases for the Viscosity Flow Curve for Suspensions log log Low shear viscosity limit often disappears with higher concentration Yield stress develops below which there is no real macroscopic flow 64 Ink Flow Curves: vs. Shear Stress shear stress (Pa) viscosity (Pa.s) Low shear viscosity limit often disappears with higher concentration Yield stress develops below which there is no real macroscopic flow 65 Ink Flow Curve: vs. Shear Stress 66 "Yield" Curve for Grease shear stress (Pa) 1.0E E2 1.0E4 1.0E6 viscosity (Pa.s) 400 Pa 600 Pa 800 Pa 1.0E3 1.0E5 1.0E7 Six Decade Drop in 67 The yield strength or yield point of a material is defined in engineering and materials science as the stress at which a material begins to deform plastically. Prior to the yield point the material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed some fraction of the deformation will be permanent and non-reversible.material engineeringmaterials sciencestressdeform plasticallyelastically How do you measure? 68 Yield Stress of Alumina-Zirconia Suspensions The yield stress of concentrated suspensions of alumina, zirconia, and mixed alumina-zirconia powders was measured by the vane technique as a function of solids loading, relative amounts of alumina and zirconia, and pH. At the isoelectric point (IEP), the yield stress varied as the fourth power of the solids loading. Vijay Ramakrishnan, Pradip S. G. Malghan using Vane geometry. J. Am. Ceram. Soc, 1996. 69 = 10.5 Pa = 11.5 Pa Ink Flow Curves: vs. Shear Rate 70 Concentrated Suspensions Exhibit Elasticity Concentrated suspensions typically show some degree of elasticity. If the material has a yield stress then it behaves as an elastic gel under small stresses or strains. The storage modulus, G, is a measure of the elasticity of the material and is a direct measure of the particle- particle interactions. Hence, G is a measure of the structural characteristics of a material. We can therefore use Dynamic Mechanical Testing to characterize the structure of a concentrated suspension. The mechanical response is extremely sensitive to the amplitude of the applied deformation, or . 71 Gel Structure in Suspensions 72 Gel Structure in Suspensions Unbroken Gel Structure Increasing Amplitude of Shear Deformation Structure begins to Breakdown Broken Structure 73 Stability is Related to Structure in Inks 74 Time-Dependent Gellation Time Break Structure under high shear Gel Structure rebuilds with time 75 The optimized dispersant amounts mg and 1.9 mg Darvan and DBAC respectively per gm of alumina powder 55 vol% alumina loading slurry showed shear thinning behaviour Optimization of the dispersant DarvanDBAC 76 Effect of nature and dispersant amount on non-Newtonian index Slurry Zeta Potential (mV) Darvan 821 ADBAC 3.2 mg 4.6 mg 6.3 mg 1.4 mg 1.9 mg 4.2 mg Fresh Aged All slurries were pseudoplastic in nature (n