Definition of Rheology Rheology TX UTA [Greek rheos-"to flow"]is the study of deformation and flow of matter Name was coined by Dr. Marcus Reiner instead of the more obscure “continuum mechanics” Motto of the Society of ☒ Rheology:"Panta Rhei"or “everything flows'" -after Heraclitus THE VISCOSITY OF LIQUIDS -SOME SIMPLE EVERYDAY IDEAS _ryhing osimple色es地t motsmper.Ens时e电 English rheology words:viscosity,consistency,and texture Thick,creamy,watery,runny Gluey,gelatinous,sticky,tacky,goocy,gummy,cohesive laundry liquids,surface cleaning liquids om cabinet onal products tool shed paints.glues,mastics 1
1 Definition of Rheology • Rheology [Greek rheos - “to flow”] is the study of deformation and flow of matter • Name was coined by Dr. Marcus Reiner instead of the more obscure “continuum mechanics” • Motto of the Society of Rheology:“Panta Rhei” or “everything flows” - after Heraclitus English rheology words: viscosity, consistency, and texture Thick, creamy, watery, runny Gluey, gelatinous, sticky, tacky, gooey, gummy, cohesive
WHAT IS FLOW AND DEFORMATION? 'Insufficient facts aluays inite danger,Captain',Mr Spock o。8 velocity A Force dx y For solids dx is constant and is a function of F/A and y For liquids dx changes with time and a resulting velocity of The upper plane is a result. The velocity is constant and is a function F/A and y 2
2 y Force A dx velocity For solids dx is constant and is a function of F/A and y For liquids dx changes with time and a resulting velocity of The upper plane is a result. The velocity is constant and is a function F/A and y
Terms and Units Flow shear stress=F A velocity dx shear straln=y y Foree Ares=A shear rate=y==y 3 Modulus(solids)=G= 么 )=刀=g Extensional Viscosity a,=4 Force → Velocity cdhy =% w. w.p 10.1 3
3 Flow y v y dt dx shear rate y dx shear strain A F shear stress = = = = = = = γ γ σ & γ σ η γ σ & = = = = cos ( ) ( ) Vis ity liquids Modulus solids G Terms and Units y Area = A Force velocity dx Extensional Viscosity Force Velocity ε σ η ε ε σ & & e e e h V h dh A F = = = = h dh
Newtonian Fluids "The beginning of wisdom is to call things by their right names" A Chinese proverb O slope=n 0=7形 Newtonian Viscosity of Common Foods Viscosity mPa s Temp C Water 0.89 25 Milk 1.45 25 Coconut oil 26 40 Cocoa butter 41 4 Cream 40% 210 48 Glycerine 954 Honey 10.000 25 Newtonian Fluids Honey Glycerine O Cream 40% Coconut 4
4 Newtonian Fluids σ =ηγ& σ γ& slope =η “ The beginning of wisdom is to call things by their right names” A Chinese proverb Newtonian Viscosity of Common Foods Viscosity mPa s Temp °C Water 0.89 25 Milk 1.45 25 Coconut oil 26 40 Cocoa butter 41 40 Cream 40% 210 48 Glycerine 954 25 Honey 10,000 25 Newtonian Fluids σ γ& Water Coconut Oil Cream 40% Glycerine Honey
Viscous M女ous Intermediate Mobile Mobile Shear rate Shear rate y Liquid or gas Approx viscosity in Pas Hydrogen 105 Air 2x103 Petrol 3x10 Water 10 Lubricating oil 101 Glycerol 10e.1) Com syrup Bitumen Approximate viscosities of some common ewtonian fluids. the viscosity of the solvent or continuous phase.Pa.s dimensionless relative viscosity,n which is the ratio of the viscosity of a suspension to its continuous phase viscosity.n/n: the dimensionless specific viscosity,n,given byn-1: ·the intrinsic viscosity.【nl(with dime )which is the specific ity divided by the dis the kinematic viscosity,pwhich in pre e(你-1/c: centi-Stokes,c5,for thin liquids,with water at 20C-1 cS. The effect of temperature on viscosity The most widely-used expression is that due to Andrade logis n =A+B/T where T is the temperature in degrees absolute (C+273.15).i.e.K.Note that this equation is also known by other names for instance the Arrhenius law where B is replaced by E/R where E is an activation energy for viscous flow and R is the universal gas constant.The activation energy E is said to be a measure of the height of a potential energy barrier associated with the force needed to produce elemental quantum steps in the movement of molecules. Arrhenius =4eh) 5
5 The effect of temperature on viscosity Arrhenius η = A exp −Ea RT ⎛ ⎝ ⎜ ⎞ ⎠ ⎟
The everyday perception of Newtonian viscosity The normal perception of the level of viscosity of Newtonian liquids by untrained persons is described by Steven's gencral power-law of psycho-physical cognition For viscosity states,the estimates are approximately proportional to the square root of the real numerical value. e.g.n(water)=1 mPa.s,n(oil)=100 mPa.s,and n(comn syrup)=106 mPas Then oil would be preceive as 10 times more viscous than water and com syrup would be preceive as 1000 times more viscous than water. Stevens,S.S and Guiro,M,Science 144,1157-8 1964. The limit of Newtonian behaviour 10 103 1031010 102 Shear rate,/s Flow curves for a series of silicone oils Note the ian behaviour at a shear stress of around 2000 Pa VISCOMETRY 'It mistake to thcorise before one has data'Arthur Conan Doyle introduction Viscometry is the science of the measurement of viscosity.Such viscometric lly hav to do with g either a force F or a velocity Vat a with ained test i se of this liquid to either which is als m contact of the used for this purpose include tubes,parallel plates,cone-an plate arrangeme and co the presen interferes with the local lquid microstructure,giving apparent p will be discussed in detail later. 6
6 The everyday perception of Newtonian viscosity The normal perception of the level of viscosity of Newtonian liquids by untrained persons is described by Steven’s general power-law of psycho-physical cognition: For viscosity states, the estimates are approximately proportional to the square root of the real numerical value. e.g. η(water) = 1 mPa.s, η(oil) = 100 mPa.s, and η(corn syrup) = 106 mPa.s Then oil would be preceive as 10 times more viscous than water and corn syrup would be preceive as 1000 times more viscous than water. Stevens, S.S. and Guirao, M, Science 144, 1157-8. 1964. The limit of Newtonian behaviour
Fow in rotational viscometers 六亡 viscosity at a given shear rate or shear stress. +音 公岳 rate is approximately the same everywhere Parallel Plates Cone Plate (variable gap) (fixed gap) CONE AND PLATE Shear rate Shear stress 3T 0=2R Newtonian fluids 3Ta T=Torque n=%-2成n 7
7 Parallel Plates (variable gap) Cone & Plate (fixed gap) CONE AND PLATE Ω R α Shear stress T Torque R T = = 3 2 3 π σ Shear rate γ . = Ω α Ω = = 3 2 3 Newtonian fluids R T π α γ η σ &
PARALLEL PLATES Shear stress T dInT R OR= 3+ 2πR3 dIny Shear rate RO iR= h Newtonian fluids 2T and 2Th 0R= R 7= πR2 CONCENTRIC CYLINDERS T 01= 2πRh 'For narrow gaps'” R where R,≈R 少≈ RO R2-R How to measure the Torque measure dx T=kdx k=torsion bar constant 士 Angular Velocity 8
8 PARALLEL PLATES Ω R h Shear rate h R R Ω γ& = Shear stress ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = + π γ σ ln & ln 3 2 3 d d T R T R Newtonian fluids σ R = 2T πR3 and η = 2Th πR4 Ω Ω CONCENTRIC CYLINDERS σ1 = T 2πR1 2 h h R1 R2 2 1 1 R2 R1 R R R where − Ω ≈ ≈ γ& “For narrow gaps” T = k dx Angular Velocity =Ω dx k k = torsion bar constant How to measure the Torque measure dx
Viscometer Design Gravity is used © To generate a Torque (shear stress) And the angular Velocity (shear rate) is Measured Schematie diagram of the 1912 Searle controlled- stress,concentric-cylinder viscometer(D.Hopkins). Controlled Stress Rheometer Optical Encoder Air Bearing、 Induction Sample- Temperature Control Apply shear stress as a torque with the induction motor And measure the shear rate from the angular velocity Important things about viscometers Calibration ·Artifacts ·Wall effects ·Evaporation* Sedimentation/separation ·Chemical attack Mechanical damage ·Sampling ·High-speed testing* 公2 ·Suspended particles 9
9 Viscometer Design Gravity is used To generate a Torque (shear stress) And the angular Velocity (shear rate) is Measured Optical Encoder Air Bearing Induction Motor Sample Temperature Control Controlled Stress Rheometer Apply shear stress as a torque with the induction motor And measure the shear rate from the angular velocity Important things about viscometers • Calibration • Artifacts • Wall effects* • Evaporation* • Sedimentation/separation • Chemical attack • Mechanical damage • Sampling • High-speed testing* • Suspended particles
Tube Flow 0-） 点4 密 in a tube:flow -” g-49mn0 The parallel-plate plastometer (or squeeze-film)geometry F.v The rate of change of the separation h with respect to timet is dh2 dt3xn For a given volume with an initial radiusr and height h,then if it stays within the plates, F=3发 10
10 Newtonian Fluids γ Ý w = 4Q πa3 σ w = Pa 2L η = σ γ Ý = Pπa4 8LQ γ Ýw and σ w are values or shear rate and stress at the wall of the tube. At the center of the tube : γ Ý oand σ o = 0 Tube Flow u r( )= P 4ηL a2 − r2 ( ) F,v The rate of change of the separation h with respect to time t is dh dt = 2Fh3 3πηa4 For a given volume with an initial radius ro and height ho, then if it stays within the plates, F = 3πηvro 4 ho 2 h5 The parallel-plate plastometer (or squeeze-film) geometry
