Summary Food Physics FPH 20306
Chapter 2 Rheology
rheology: studies relation between forces (stress) applied on a material and its
(rate) of deformation
Applied force F or stress σ deformation γ, important in processing, sensory
perception, chewing
Viscous liquids and elastic solids, viscous: needs time, deforms slowly, elastic:
deforms instantaneous
Viscous liquids
shear rate γxy = δVx(y)/δy [s-1] Vx changing in y-direction
extensional γxx = δVx(x)/δy [s-1] uniaxial -> ---> ------>
x direction stress, y direction of velocity gradient
Shear = extensional + rotational
Relation between shear/extensional rate and stress [Pa]:
σxy = η · γxy η: shear viscosity [Pa s]
σxx = ηE · γxx ηE: extensional viscosity [Pa s]
Fluids are Newtonian if the viscosity stays constant, independent of shear rate
and time.
Newtonian fluid: ηE = η, no rotational shear, examples: water, glycerol
For most dispersions and macromolecular solutions: ηE ≠ η, the rotational
viscosity is nonzero, the large structures resist to rotation
Newtonian behaviour
linear model, η constant with deformation, stress linear to deformation
Some only show linear behaviour at very low shear rates (η 0: zero shear viscosity)
Types of Non-Newtonian behaviour
Shear thinning: shear will disentangle the chains, on its path through the chain
will form new entanglements, rate of disentanglement > rate of formation new
entanglements
Δtγ < Δte : only a few entanglements formed, number of entanglements decreases
for increasing shear rate, and as a result η decreases for increasing shear rate.
Mechanism for dispersions & emulsions : large clusters high friction, layered
structure less friction,
Shear thickening: At high shear rates, the layer structure becomes unstable
and the particles will start to form clusters again, increase in viscosity
Bingham and plastic flow: have a yield stress, below this stress this material
behaves solid like (deformation but no viscous flow), above it it starts to flow,
For Bingham viscosity is a constant, in plastic flow shear thinning
, Elastic solids
Solids do not flow and will deform, not γ shear rate in s-1, but γ displacement,
strain [no unit]
Ideal elastic solid, σxy = G · γxy γxy = δux(y)/δy ux = x - x 0
G: elastic or storage modulus [Pa], γxy: deformation [-]
Ideally the solid material stores all the energy applied to the system by a
deformation reversibly,
called a Hookean solid, then the modulus G is independent of deformation and
time
For small deformations: γxy = δux/δy = tanϑ
σxy = E · γxx γxx = δux(x)/δx = ΔL/L E: extensional modulus
Uni axial extension, does not conserve volume For most materials: E ≠ G
Bi axial extension: volume is conversed, E = 3G γ xx = δux(x)/δx and γxy = δux-
(y)/δx
Non-Hookean behaviour
strain thinning: entangled (not cross linked) macromolecules)
strain hardening: in chemically covalently crosslinked rubber like materials,
when there is a limit of stretching the network, disruption of strong bonds costing
energy (after disruption shear thinning)
Viscoelastic materials
Slow deformation: viscous reaction, quick: elastic (linear), contributions
separated by oscillatory shear experiments, for Hookean solid, the deformation
and stress are in phase, for a Newtonian fluid the deformation is out of phase
with the stress, and there is a phase shift δ ω: frequency
0≤δ≤0.5π, when δ is close to zero: elastic, close to 0.5π: viscous
G'= (σ0/γ0) cos(δ) G''= (σ0/γ0) sin(δ)
G': storage/elastic modulus, measure for the amount of energy that is
reversibly stored
G'': loss modulus, measure for the energy lost as result of viscous friction
G''/G' = sin δ / cos δ = tan δ loss tangent, measure for how viscous or elastic
the material is
tan δ < 1 : elastic, tan δ > 1 viscous
Linear viscoelastic materials: G' and G'' are constant, but generally they depend
on strain and time/ω
Time dependent behaviour
Apply a constant shear γ, then maximum (stress build-up) till steady state
value
Longer relaxation time (time when 1/e of stress) longer time to adapt structure
at a certain pressure, difficulty to reform network (high amount of covalent
crossbonds), sample history is important
Hysteresis occurs with non-Newtonian systems that slowly convert back to their
original form
it takes more time for the structures to reform than it did for them to break down
Chapter 2 Rheology
rheology: studies relation between forces (stress) applied on a material and its
(rate) of deformation
Applied force F or stress σ deformation γ, important in processing, sensory
perception, chewing
Viscous liquids and elastic solids, viscous: needs time, deforms slowly, elastic:
deforms instantaneous
Viscous liquids
shear rate γxy = δVx(y)/δy [s-1] Vx changing in y-direction
extensional γxx = δVx(x)/δy [s-1] uniaxial -> ---> ------>
x direction stress, y direction of velocity gradient
Shear = extensional + rotational
Relation between shear/extensional rate and stress [Pa]:
σxy = η · γxy η: shear viscosity [Pa s]
σxx = ηE · γxx ηE: extensional viscosity [Pa s]
Fluids are Newtonian if the viscosity stays constant, independent of shear rate
and time.
Newtonian fluid: ηE = η, no rotational shear, examples: water, glycerol
For most dispersions and macromolecular solutions: ηE ≠ η, the rotational
viscosity is nonzero, the large structures resist to rotation
Newtonian behaviour
linear model, η constant with deformation, stress linear to deformation
Some only show linear behaviour at very low shear rates (η 0: zero shear viscosity)
Types of Non-Newtonian behaviour
Shear thinning: shear will disentangle the chains, on its path through the chain
will form new entanglements, rate of disentanglement > rate of formation new
entanglements
Δtγ < Δte : only a few entanglements formed, number of entanglements decreases
for increasing shear rate, and as a result η decreases for increasing shear rate.
Mechanism for dispersions & emulsions : large clusters high friction, layered
structure less friction,
Shear thickening: At high shear rates, the layer structure becomes unstable
and the particles will start to form clusters again, increase in viscosity
Bingham and plastic flow: have a yield stress, below this stress this material
behaves solid like (deformation but no viscous flow), above it it starts to flow,
For Bingham viscosity is a constant, in plastic flow shear thinning
, Elastic solids
Solids do not flow and will deform, not γ shear rate in s-1, but γ displacement,
strain [no unit]
Ideal elastic solid, σxy = G · γxy γxy = δux(y)/δy ux = x - x 0
G: elastic or storage modulus [Pa], γxy: deformation [-]
Ideally the solid material stores all the energy applied to the system by a
deformation reversibly,
called a Hookean solid, then the modulus G is independent of deformation and
time
For small deformations: γxy = δux/δy = tanϑ
σxy = E · γxx γxx = δux(x)/δx = ΔL/L E: extensional modulus
Uni axial extension, does not conserve volume For most materials: E ≠ G
Bi axial extension: volume is conversed, E = 3G γ xx = δux(x)/δx and γxy = δux-
(y)/δx
Non-Hookean behaviour
strain thinning: entangled (not cross linked) macromolecules)
strain hardening: in chemically covalently crosslinked rubber like materials,
when there is a limit of stretching the network, disruption of strong bonds costing
energy (after disruption shear thinning)
Viscoelastic materials
Slow deformation: viscous reaction, quick: elastic (linear), contributions
separated by oscillatory shear experiments, for Hookean solid, the deformation
and stress are in phase, for a Newtonian fluid the deformation is out of phase
with the stress, and there is a phase shift δ ω: frequency
0≤δ≤0.5π, when δ is close to zero: elastic, close to 0.5π: viscous
G'= (σ0/γ0) cos(δ) G''= (σ0/γ0) sin(δ)
G': storage/elastic modulus, measure for the amount of energy that is
reversibly stored
G'': loss modulus, measure for the energy lost as result of viscous friction
G''/G' = sin δ / cos δ = tan δ loss tangent, measure for how viscous or elastic
the material is
tan δ < 1 : elastic, tan δ > 1 viscous
Linear viscoelastic materials: G' and G'' are constant, but generally they depend
on strain and time/ω
Time dependent behaviour
Apply a constant shear γ, then maximum (stress build-up) till steady state
value
Longer relaxation time (time when 1/e of stress) longer time to adapt structure
at a certain pressure, difficulty to reform network (high amount of covalent
crossbonds), sample history is important
Hysteresis occurs with non-Newtonian systems that slowly convert back to their
original form
it takes more time for the structures to reform than it did for them to break down
