Rheology The relationship between rheological response and material structure Márta Berka University of Debrecen Dept of Colloid and Environmental Chemistry http://dragon.unideb.hu/~kolloid/
Introduction The consistency of shower gels and the mouth-feel of yogurt and fruit juice are all controlled by their rheology - how these everyday colloidal products flow and deform when in use. Rheology plays a major role in manufacturing these products well before they reach supermarket shelves. The rheology of these colloids must be optimum during mixing, stirring, pumping, coating, spraying or extrusion processes. It follows that chemists and technologists working in areas as diverse as paints, inks, foods, agricultural chemicals, pharmaceuticals, electronics and petroleum recovery need to understand the relationship between the rheology of their products and their composition. In turn, the flow behaviour of these products is controlled by their microstructure - the way in which the constituent colloidal particles interact and self-assemble. Physicochemical principles of pharmacy, Alexander Taylor Florence,D. Attwood (internet)
Rheological measurements In general, rheological measurements on pharmaceutical and cosmetic materials are performed for the following reasons: 1) to understand the fundamental nature of a system; 2) for quality control of raw materials, final products, and manufacturing processes such as mixing, pumping, packaging, and filling; 3) to study the effect of different parameters such as formulation, storage time, and temperature on the quality and acceptance of a final product.
Principle Rheology (from the Greek, panta rhei = all things flows) is the science of the deformation and flow of matter. Different materials deform differently under the same state of stress. Deformation is defined as the relative displacement of points in a body and it can be divided into two types: 1. Flow is the irreversible part of the deformation: when the stress is removed the material does not revert into its original configuration. Hence, work is converted into heat. 2. Elasticity is the reversible part of deformation: removing the stress the applied work is largely recovered and the body retains its original configuration. 3 main concepts such as force, deformation and time. Irreversible flows, reversible elastic deformations or their combination (viscoelasticity) can describe a rheological phenomenon. Sometimes dynamic characterization such as creep, relaxation tests and the material response to sinusoidal oscillatory motion is needed.
States of matter Solids: keep their shape and do not flow. Elastic deformation. Liquids: it take the shape of the container. Flow if it forces are applied on it. (Shear deformation with constant speed on liquid flow) The states of matter is the question of time scale and the magnitude of exerted forces. Small forces during very short times elastic deformation. Large forces during very long times flow (mountains). Deborah number. Intermediate times and forces viscoelasticity (viscoelastic liquid -liquid like behaviour, viscoelastic solid - solid like behaviour)? Cream, butter, ketchup liquids or solids? Keep their shape if the forces are weaker than cohesive interaction, semisolids. relaxationtime 1 observationtime >> relaxationtime 1 relaxationtime observationtime << ~1 observationtime Viscous liquid Elastic solids Viscoelasticity removing the stress the applied work is largely recovered and the body retains its original configuration
Different forces and deformations If a material is subjected to a constant force, it is called static loading. If the loading of the material is not constant but instead fluctuates, it is called dynamic or cyclic loading. Different way as the forces are applied elongation Shear can be applied for any condition gaseous, liquid, solid
Ideal and complex rheological bodies 1. Ideal elastic: Hooke (only reversible deformation, linear relation: stress and strain) 2. Ideal viscous: Newtonian fluids (continuous irreversible deformation, flow) 3. Ideal plastic: (no permanent deformation below the yield stress, and continuous shear rate is at the yield stress.) Complex rheology (1 and 2) viscoelastic materials as: elastic fluids (macromolecular solution) and elastic solids (macromolecular solids) (2 and 3) real plastic materials
Elastic deformation, ideal elastic body A stress τ= force/unit area, N/m 2 Δ l = ε l 0 ε relative deformation or strain Linear relation: strain = constant stress τ = εe Hooke s law τ = E ε Young Modulus, E is a material property that describes the stiffness of an isotropic elastic material (N/m 2 ) ( rubber E: 0.01 GPa; steel: E 200 GPa) Elasticity is the reversible part of deformation: removing the stress the applied work is largely recovered and the body retains its original configuration. Giga 10 9
Shear deformation Force, deformation and time stress τ= tangential force/unit area Shear deformation with constant speed on liquid flow Linear relation: shear stress = constant shear rate τ ηγ& = Newtonian viscosity γ` (or D) shear rate s -1 x v dx/dt = v strain γ = dx dy dx / dy dx / dt dv γ `= = = dt dy dy y & γ D Symbol depends on the literature A shear stress, is applied to the top of the square while the bottom is held in place. This stress results in a strain, or deformation, changing the square into a parallelogram.
Ideal viscous materials Definition of viscosity: Flow resistance to an external force applied to a fluid sample Shear rate is proportional to the stress (force) linear Newtonian liquid shear stress η = vis cosity = = shear rate Pas τ D η τ = ηd τ, D D tg alfa: η τ s -1 flow Pa resistance α β interchangeable plotting β α tg alfa: η τ Pa γ` or D shear rate D s -1
Ideal Plastic materials Ideal plastic material almost does not exist. Ideal viscosity with a yield value, τ 0 τ = τ0 + ηd A minimum shear stresses, τ 0 required to cause flow. A mechanical analogue to plastic deformation is the frictional resistance to sliding of a block on a plane. No displacement occurs until the applied stress reaches the frictional resistance. τ 0 sliding of a block on a plane τ τ 0 η = D
Real materials Combination of viscous, elastic and plastic properties Viscoelastic, real plastic materials If a sample is sheared it may start to break down, therefore we use tiny perturbation to measure the viscoelastic structure, so called dynamic measurements: τ oscillating small constant τ small single deformation
Non-Newtonian behaviour Most dispersion (also blood) Viscosity depends on the shear rate. Viscosity is a material function because of the complexity of the micro structure system. Structural changes due to the forces changes in viscosity. Rheology can be used to learn about the microstructure of dispersions. Rheology and viscosity curves Where τ shear stress, η viscosity, γ` or D shear rate Weissenberg hatás
Weissenberg effect High viscosity Newtonian fluid Low viscosity Viscoelastic fluid Shear thickening fluid? olaj, méz, tészta?
Influences on viscosity time Apparent viscosity concentration η* = τ τ ( ) D 0 n If the shear rate changes during an application, the internal structure of the sample will change and the change in stress or viscosity can then be seen. Shape, orientation, attraction between particles
Shear thinning behaviors Structural changes due to the forces changes in viscosity: order Effect of anisometry and time! ( τ ) n η = n<1 D
Shear thickening behaviours Structural changes due to the forces changes in viscosity, disorder η = ( τ ) n D n>1 Wet sand or mixture of water and cornstarch Corn starch is a shear thickening non-newtonian fluid meaning that it becomes more viscous when it is disturbed http://video.google.com/videoplay?docid=-4684348427588167444&ei=4jfvstqgi86z-abyhtgrcg&hl=hu#
Yield stress Thixotropy Where τ shear stress, η viscosity, γ` or D shear rate D, s -1 viscosity curve Rheology curve τ, Pa η* = τ τ ( ) D 0 n House of card Below the yield value the sample keeps its shape behaves as a solid body above the yield value the structure breaks down and sample start to flow. The yield value shows how strong the structure is.
Explanation of Yield value. Gel structure The height of the barrier indicates how stable the system is. Vmax>>kT kinetically stabil sol sol V sec < 1~2 kt gel Thixotropic ~ yield value Week floc ~gel sol In a secondary minimum a much weaker and potentially reversible adhesion between particles exists in a gel structure. These weak flocs are sufficiently stable not to be broken up by Brownian motion, but may dissociate under an externally applied force such as vigorous agitation
Dynamic measurements: Thixotropy Time-dependent flow measures the increase or decrease in viscosity with time, while a constant shear is applied. The flow is called thixotropic if viscosity decreases with time, or rheopetic if it increases. Thixotropic behavior describes a degradation of the structure during the loaded phase, particles will change to align with the flow direction. Viscosity (or stress) during the ramp-down period will be lower than that in the ramp-up shearing period. In general, shear thinning measures how easily the structure can be broken and the loop area indicates the recovery extent of that broken structure during the experimental time. recovering degradation
Determination of Yield stress The concept of yield stress, the minimum shear stresses required to cause flow, is only an approximation since this stress value is experimental time dependent. Pseudoplastic or shear thinning fluids, The yield stress is crucial in determining not only their shelf life but also in application for the end user. Yield stresses Ketchup Salad Dressing Lithographic Ink Mayonnaise Skin Cream Hair Gel 15 Pa 30 Pa 40 Pa 100 Pa 110 Pa 135 Pa
Steady shear flow curves Pa τ 0 The structure breaks down while shear rate increases, displaying reduced viscosity (2, 5 curve). s -1 1. Newtonian fluids 2. shear thinning or pseudoplastic, 3. shear-thickening or dilatant, 4. Bingham type body, 5. Thixotropic. t 0 yield value. Pas Newtonian: water, low molecular oils Shear thinning: Polymer melts, emulsions, ceramics Shear thickening: wet sand, cornstarch and water mixture Typical shear viscosity curves D,s -1
Viscosity of dispersion of spherical particles Rheology behavior depends on the structure of the system and the external force as well, see starch suspension and silly putty
Hydrogel: 5% PVA + 5% sodium borate Force~0 : viscous fluid weak force : plastic medium force, : elastic Very strong force, rigid solid http://www.youtube.com/watch?v=f2xq97xhjvw&feature=related
Ideal (linear) behaviour if φ< 0.1 More example Macromolecular solutions, non-ideal ηr = + kφ+ k φ + 2 1 1 2... φ or concentration η spec = η 1 r η spec c 2 [ η] kc kc = + 1 + 2... 250 200 η spec /c ηspec 1 limc 0 = [ η] = 2.5 c ρ c 150 ρ c coil density 100 50 ln η rel /c a [ η ] = KM 0 0 0.02 0.04 0.06 c, g/ml K, a constants, M molar mass
Linear polymer solution A thixotropic loop, the region between curves for the increasing and decreasing shear rate ramps folyásgörbe 0.9 1400 0.8 D, s -1 1200 1000 800 600, Pas 0.7 0.6 0.5 0.4 0.3 viszkozitás görbe 400 0.2 200 0.1 0 0 20 40 60 80 100 120 140 τ, Pa 0.0 0 20 40 60 80 100 120 140 τ, Pa the orientation of the structure s molecules or particles will change to align with the flow direction. Its original orientation can be restored over a period of time after the external force is removed. There is a delay in time for the structure to recover completely -- loop
Creams Added water η = τ τ ( ) D 0 n η, Pas 0.3 0.2 0ml 5ml 10ml 15ml D, s - 1 140 120 100 80 60 +water,ml 0ml 5ml 10ml 15ml 0.1 40 20 0.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 τ, Pa 0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 τ, Pa Internal structure, concentration: the limits value of viscosity and the yield values of rheology curves decrease with the dilution of cream.
videos http://www.youtube.com/watch?v=npzzlgkjs0i (Weissenberg effect) http://www.youtube.com/watch?v=s5sgiws5l6i (cornstarch 1) http://www.youtube.com/watch?v=qfhw6i_ubqg&nr=1 (Liquid armor) http://www.youtube.com/watch?v=3zotkxxnqiu&nr=1&feature=fvwp Non-Newtonian Fluid on a Speaker Cone http://www.youtube.com/watch?v=f2xq97xhjvw A pool filled with non-newtonian fluid http://www.youtube.com/watch?v=uu7iuj98frq Cornstarch and vibrations If a sample is sheared it may start to break down, therefore we use tiny perturbation to measure the viscoelastic structure, so called dynamic measurements:
Dynamic measurements show the elastic and permanent deformation Irreversible macro Brown motion Elastic recoil, reversible micro Brown motion (flexibility) and orientation (rod shape)
Dynamic measurements Stress relaxation (recoil, loosen up, be tired out) Small oscillation stress and strain shift D Elastic term in phase (δ=0), viscous term out of phase (δ=90 ), viscoelastic (δ~45 )