Rheology - unideb.hukolloid.unideb.hu/en/files/2010/11/12-rheology.pdf · Applications of rheology...
Transcript of Rheology - unideb.hukolloid.unideb.hu/en/files/2010/11/12-rheology.pdf · Applications of rheology...
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Rheology
Levente NovákIstván
Zoltán NagyDepartment of Physical Chemistry
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Rheology
● Rheology is the science of the flow and deforma-tion of mater (liquid or “soft solid) under the ef -fect of an applied force
● Deformation → change of the shape and the size of a body due to applied forces (external forces and internal forces)– Flow → irreversible deformation (mater is not reverted
to the original state when the force is removed)– Elasticity → reversible deformation (mater is reverted
to the original form afer stress is removed)
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Applications of rheology
● Understanding the fundamental nature of a system (basic science)
● Qality control (raw materials and products, processes)● Study of the efect of diferent parameters on the quality of
a product● Tuning rheological properties of a system has many
applications in every day's life• Pharmaceutics• Cosmetics• Chemical industry• Oil-drilling
etc
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Deformation
● Solids or liquids in rest keep their shape (=form) unchanged
● When forces act on these bodies, deformation can occur if the force exerted is larger than the internal forces holding the body in its original form
● Deformation is the transient or permanent shape change of a given body– transient or reversible deformation (elasticity): when the force
acting upon the body ends, the shape reverts to its original state and the deformation work (=energy) is recovered
– permanent or irreversible deformation (flow): shape does not re-vert to its original state, the deformation energy can not be re-covered
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Deformation forces
● The deformation forces (also ofen called load or loading) which act on a solid body or a liquid can be– Static: the force is acting constantly and its direction
and magnitude are constant (constant loading)– Dynamic: the magnitude and/or direction of the force(s)
are variable as a function of time (variable loading)• cyclic or periodic• acyclic
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Deformation forces
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Definitions
● Strain: deformation in term of relative displace-ment of the particles composing the body
● Stress: measure of internal forces acting within a (deformable) body
● Shear: deformation of a body in one direction only (resulting from the action of a force per unit area τ=shear stress) and having a given perpendicular gradient (γ=shear strain)
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Ideal and real bodies
● Ideal bodies
1. Ideally elastic: Hookean body (only reversible deforma-tion, linear relation between stress and strain) → spring
2. Ideally viscous: Newtonian fluids (continuous irre-versible deformation, flow) → water
3. Ideally plastic: (no permanent deformation below the yield stress, and continuous shear rate at and above the yield stress.)
● Real bodies (combination of the properties above)– 1+2: viscoelastic materials– 2+3: viscoplastic materials
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Elastic deformation, ideally elastic bodies
For ideally elastic bodies, there is a linear relationship between the relative deformation and the applied force (observation of R. Hooke on springs)
Relative deformation (=strain): ε = Δ ll 0
(without unit)
Hooke's law:τ = εE
Shear stress:
τ = F
Ayz
(in N/m2 = Pa)
E is Young's modulus (in Pa), the measure of the stifness of an isotropic elastic material.For e.g. rubber: E = 0.01 GPa = 1·104 Pa steel: E = 200 GPa = 2·108 Pa
l0
l0
Δl
FA
yz
x
yzhh
0
h = h0
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Shearing deformation of solids
If a tangential force is acting on the upper plane of a body fixed at its base a shearing deformation will result
γ = dxdy
= dx max
h (without unit)
Shear stress:
τ = F
Axz
(in N/m2 = Pa)l0
l0
dxmax
F
hx
yz
Axz
h0
dxy
h < h0
The deformation will vary perpendicularly to the force with the distance from the base to the maximal shear plane: dx = f (y) and dxmax= f (h)
The gradient of the shear in this perpendicular direction is called shear strain:
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Shearing deformation of liquids
● In liquids, a constant shear will cause the liquid to flow (viscous de-formation).
● If the flow is laminar (there are no turbulences) the liquid flows as layers parallel to the wall of the vessel.
● The velocity of these layers is decreasing from a maximal value to zero in the direction perpendicular to the wall (the layer adsorbed at the wall does not move).
● The gradient of the shear in this perpendicular direction is also called shear strain:
● But as the layers of liquid are constantly moving (dx is not constant) we can define a velocity gradient from the bulk to the wall called shear rate:
γ = dxdy
(without unit)
D = dx /dt
dy =
dv x
dy (unit:
1s
= s−1 )
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Newtonian liquids
● In Newtonian liquids shear rate (D) is linearly proportional to shear stress (τ ):
● The proportionality coeficient η (called viscosity) is constant in the case of Newtonian liquids: η = const.
● Viscosity is the measure of resistance against flow.
τ = ηD
τ(Pa)
D (s-1)
α
η(Pa·s)
τ (Pa)
Viscosity curve Flow curve
η = tg α = τ/D
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Ideally plastic bodies
● Ideally plastic bodies would behave as rigid bodies until a yield value of shear and flow as Newtonian liquids above the yield value:
● These bodies are termed ideal Bingham bodies. They are practically non-existent.
τ = τ0+ ηD
τ(Pa)
D (s-1)
α
τ0
No flow untilthe yield stress
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.
Viscosity curve
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Real materials
● In practice only a few materials have an ideal flow behav-ior
● Usually rheological properties are a combination of vis-cous, elastic, and plastic properties
● Moreover these properties change most ofen non-linearly● Sometimes the sample is subject to breakdown if sheared,
in this case small dynamic strain or stress is applied dur-ing rheological measurements– Oscillation: small oscillating τ is applied and observe strain in-
crease– Creep: small constant τ is applied and observe strain increase– Relaxation: small strain is applied and observe the decay of τ
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Non-newtonian viscosity
● If the relation between shear stress and shear rate is not linear: non-newtonian viscosity
● Viscosity varies with the shear: η = f (τ) or η = f (D)● Most viscous materials are non-newtonian● Non-newtonian behavior depends on the micro- or nanostructure of
the material (breakdown, arrangement, or entanglement)
τ(Pa)
D (s-1)
η(Pa·s)
D (s-1)
τ(Pa)
D (s-1)
η(Pa·s)
D (s-1)
SHEAR-THINNING SHEAR-THICKENING
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The Weissenberg efect
● A spinning rod is placed in a polymer solution composed of long chains
● Polymer chains are drawn towards the rod → Weissenberg efect
– Long polymers get wrapped around the rod
– Entanglement of the polymer chains make the wrapped chains to stretch
– The stretched chains pull the free polymers and the liquid towards the rod
Newtonian liquid Viscoelastic liquid
Low viscosity High viscosity
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Influences on the viscosity
η (c ,T , p , t ) = τD
Viscosity can depend on:● concentration (c)● temperature (T)● pressure (p)● time (t)● shear rate (D)
If the shear rate changes during an ap-plication, the internal structure of the sample will change and the change in stress or vis-cosity can then be seen.
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Apparent viscosity
η = ( τ−τ0)
n
D
The ratio of stress to rate of strain, calculated from measure-ments of forces and velocities as though the liquid were Newto-nian.
(IUPAC definition)
This is a general equation valid also for systems having a yield stress value (τ0).
Nonlinearity factor
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Shear-thinning behavior
Structural changes due to the forces – changes in viscosity: ordering of molecules or particles
η =τ
n
Dn<1
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Shear-thickening behavior
Structural changes due to the forces – changes in viscosity, disordering of the particles or molecules
htp://video.google.com/videoplayddocid=-4688434842d588168d444eei=4&fVStqgI868z-AbYhtGrCgehl=hu#
E.g. wet sand or mixture of water and corn starch
η =τ
n
Dn>1
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Example of shear-thickening system
Very strong force, rigid solid
htp://www.youtube.com/watchdv=f2X=Q97dX=HjVwefeature=related
PVA hydrogel: 5% PVA + 5% sodium borate
Force≈0 : viscous fluid
weak force : plastic
medium force, : elastic
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Yield stress
Everyday's example: a cardhouse
● Below the yield value the sample keeps its shape and 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.
τ(Pa)
D (s-1)
τ0
η = ( τ−τ0)
n
D
η(Pa·s)
τ (Pa)τ0
Viscosity curve Flow curve
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Explanation of the yield value
Vsec ≈ yield value
In a “secondary minimumt a much weaker and potentially reversible adhesion between particles exists in a gel structure. These weak flocs are suficiently stable not to be broken up by Brownian motion, but may dissociate under an externally applied force such as vigorous agitation.
gel
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Time-dependent efects
● When viscosity at a given shear depends on time, the system can be:– Thixotropic: constant shear causes a decrease in viscosity• very common property (e.g. ketchup, yoghurt, paints, etc.)
– Rheopectic: constant shear causes an increase in viscosity• few materials are rheopectic (gypsum paste, printer ink)
● If time-dependent efects are significant, flow and vis-cosity curves present a hysteresis loop (curves mea-sured by increasing shear do not coincide with curves measured by decreasing shear).
● These efects are caused by the breakdown or buildup of ordered structures within the flowing mater.
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Hysteresis loop
Flow curve of thixotropic systems with and without yield stress
Hysteresis loops
Viscoplastic
Viscous
τ(Pa)
D (s-1)
τ0
Red: with increasing shear rate, sys-tem is breaking down
Blue: with decreasing shear rate, system is building up
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Flow curves
τ(Pa)
D (s-1)
τ0 Newtonian
Shear thickening
Shear thinning
Bingham (newtonian with yield)
Shear thickening with yield
Shear thinning with yield
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Viscosity curves
η(Pa·s)
τ (Pa)τ0
Newtonian
Shear thickening
Shear thinning
Bingham (newtonian with yield)
Shear thickening with yield
Shear thinning with yield
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Polymer solutions
● Dilute polymer solutions have generally shear-thinning properties → under load, the polymer molecules orient in the direction of the shear
● Viscosity of these solutions increases with increas-ing molar weight– hydrodynamic radius of the polymer coil increases with
molar weight– larger radius means more pronounced interaction with
solvent molecules (=tfrictiont) → increase in viscosity● Empirical relation between (intrinsic) viscosity and
molecular weight: the Mark-Houwink equation
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Molar weight determination by viscosity
[η] : intrinsic viscosityK : empirical constantM : molar massa : solvent-polymer interaction
parameter
Mark-Houwink equation
[η ] = K Ma
ηsp = ηr−1 = ηsolutionηsolvent
−1
Specific viscosity
ηr = ηsolutionηsolvent
Relative viscosity
Graphical determination of [η]
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Stress relaxation (stress applied → stress released → strain relaxes)
D
Advantages:
Small oscillation stress and strain → sensitive systems (e.g. gels) can also be measured
Oscillation measurements
● Elastic term in phase (δ=0)
● Viscous term out of phase (δ=970°)
● Viscoelastic materials: δ~45°
phase shif (δ )
Dynamic measurements