Definition of rheology 。Rheology T UTC [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'” t after Heraclitus
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
Terms and Units F Flow shear stress =o A dx velocity dx shear strain y y Force Area=A dx shear rate y dt y y y Moduls(solids)≤Gso Vis cosity(liquids)
Flow y v y dt dx shear rate y dx shear strain A F shear stress cos ( ) ( ) Vis ity liquids Modulus solids G Terms and Units y Area = A Force velocity dx
Situation Shear Rate Examples Range/s1 Sedimentation of fine 10-6-103 Medicines,paints,salad powders in liquids dressing Levelling due to surface 10-2-101 Paints,printing inks tension Draining off surfaces 101-101 Toilet bleaches,paints,coatings under gravity Extruders 100-102 Polymers,foods soft solids Chewing and 101-102 Foods swallowing Dip coating 101-102 Paints,confectionery Mixing and stirring 101-103 Liquids manufacturing Pipe flow 100-103 Pumping liquids,blood flow Brushing 103.104 Painting Rubbing 104.105 Skin creams,lotions High-speed coating 104-106 Paper manufacture Spraying 105-106 Atomisation,spray drying Lubrication 103-107 Bearings,engines
Newtonian fluids "The beginning of wisdom is to call things by their right names" A Chinese proverb O slope h 07y
Newtonian Fluids slope = h “ The beginning of wisdom is to call things by their right names” A Chinese proverb
VISCOMETRY 'It is a capital mistake to theorise before one has data',Arthur Conan Doyle Introduction Viscometry is the science of the measurement of viscosity'.Such viscometric measurements generally have to do with applying either a force F or a velocity V at a surface in contact with a contained test liquid.The response of this liquid to either the velocity or the force is measured at that surface or at some other nearby surface which is also in contact with the liquid.Examples of the geometries used for this purpose include tubes,parallel plates,cone-and-plate arrangements,and concentric cylinders.Sometimes artefacts arise whereby the presence of these surfaces interferes with the local liquid microstructure,giving apparent slip effects-these will be discussed in detail later
a Parallel Plates Cone Plate (variable gap) (fixed gap)
a Parallel Plates (variable gap) Cone & Plate (fixed gap)
CONE AND PLATE Shear rate Y- a C Shear stress 3T O 2πR3 Newtonian fluids h=s 3Ta T Torque /8 2pR32
CONE AND PLATE W R a Shear stress T Torque R T Shear rate . = W a W 3 2 3 Newtonian fluids R T p a g s h
PARALLEL PLATES Shear stress 2+n R Shear rate R YR= h Newtonian fluids SR 2T 2Th and h= pR3 PR W
PARALLEL PLATES W R h Shear rate h R R W Shear stress ln ln 3 2 3 d d T R T R Newtonian fluids s R = 2T pR 3 and h = 2Th pR 4W
CONCENTRIC CYLINDERS T 01= 2pR2h “For narrow gaps'” R where R2≈Rl R 。。+ R R2-R
W CONCENTRIC CYLINDERS 1 = T 2pR1 2h h R1 R2 2 1 1 R2 R1 R R R where W “For narrow gaps
Tube Flow (- du(r) shear dr shear rate stress profile profile u(r） parabolic velocity profile The physical parameters relating to flow in a tube:flow rate pressure drop P along the pipe of length L and radius a
Newtonian Fluids gú w = 4Q pa 3 w = Pa 2L gú = Ppa 4 8LQ gú w and s w are values or shear rate and stress at the wall of the tube. At the center of the tube : gú o and s o = 0 Tube Flow u(r) = P 4hL a 2 - r 2 ( )