Rheological Properties for Foods

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Rheological Properties for Foods

An-I Yeh, Professor EmeritusGraduate Institute of Food Science & Technology

National Taiwan University

[email protected]

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What You Will Learn from This Class

Principle of Rheology.

Operations of Rheometer.

Applications of Rheometry,

such as texture measurement.

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How do you recognize it ?

4

Which one you like?

5

What’s your preferences?

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General Concept in Rheology

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Rheology is defined as the study of deformation and flow of

matter.

Deformation pertains to solid; and flow to liquid.

In the simplest case, the rheological property of interest in

solids is their elasticity, and in liquids it is viscosity.

the International Organization for Standardization,

Texture encompasses all the rheological and structural

(geometrical and surface) attributes of a food product perceptible by

means of mechanical, tactile and, when appropriate, visual and

auditory receptors.

Rheology

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Relationship of the Senses with Sensory Properties

Viscosity, Yield

Stress,

Viscoelasticity

Q = ?

Fingers, Mouthfeel

（三叉神經）

（動覺）

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Interrelationships between Food Structure,

Rheology and Texture

Borwankar, 1992

Journal of Food Engineering 16:1- 16

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Utilization of Rheological Properties

Molecular Structure

•MW & MWD

•Chain Branching and Cross-linking

•Interaction of Fillers with Matrix Polymer

•Single or Multi-Phase Structure

Viscoelastic Properties

As a function of::

•Strain Rate(frequency)

•Strain Amplitude

•Temperature

Processability & Product Performance

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Definitions of Rheological Terms

(Jackman 1991)

Food Technology July p. 90

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Stress and Strain

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Consider a volume element in the shape of a unit cube. There

are two basic types of stresses that can be exerted on any

material in this volume element –

Normal stresses are those that act perpendicular to the

face of the cube and

Shear stresses are those that act tangential to the face of

the cube.

Two Types of Stresses

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Deformation of an Isolated Macromolecule

Shear deformation Extensional deformation

(Menjivar 1990)

Dough Rheology and Baked Product Texture p. 8

17

Perceived Sweetness and Thickness of 10% Sugar

Solution Thickened with Different Thickeners to Give

Different Rheological Properties

(Wood 1979)

Food Texture and Rheology p. 21

Sw

eetness d

ecrease

Th

ickn

ess increase

Flo

w b

ehav

ior in

dex

decrease

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Viscosity

A measure of a material’s

resistance to flow

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Elasticity

• Ability to store deformational energy

• Capacity to regain shape after being

deformed

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Viscoelasticity

• Stress response combines elastic and

viscous behavior

• Mechanical properties time - and

temperature - dependent

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Simple Classification of Rheological Behavior

(Steffe 1996)

Rheological Methods in Food Process Engineering

p. 50

22

童世煌科學發展 2012年8月，476:16-21

橡膠的彈性

23童世煌科學發展 2012年8月，476:16-21

軟性的果凍

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童世煌科學發展 2012年8月，476:16-21

麵糰的黏彈性

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How to Measure the Viscosity?

()

Shear Rate (g) =dv/dx = v/HAlso called shear strain rate

.

v = U/time

strain = U/H

Newton's law states that

the shear stress is

proportional to the shear

strain rate. The

proportionality constant is

known as the (dynamic)

viscosity (h or m).

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Fluids

Newtonian Fluids

t = h g

Shear Stress = constant x shear rate

Non-Newtonian Fluids (Herschel Bulkley Model)

t = k (g)n + to

k: consistency coefficient

n: flow behavior index,

to : yield stress (sometimes designated as o)

It is called power law equation when yield stress is zero.

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For a Power Law FluidsApparent Viscosity = Shear Stress/Shear Rate

1)()( −== n

n

kk

gg

gh

solvent

solution

relh

hh ==

1−== relsp hh

C

sp

red

hh ==

C

relinh

hh

ln==

0

int

→

==

c

sp

C

hh

Relative Viscosity

Specific Viscosity

Reduced Viscosity

Inherent Viscosity

Intrinsic Viscosity

where C is the concentration of the solution.

when yield stress is zero

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NON-IDEAL LIQUIDS

Shear-Rate Dependent Non-ideal Behavior

Pseudoplastic fluids. It manifests itself as a decrease in the

apparent viscosity of a fluid as the shear rate is increased,

and is therefore referred to as shear thinning.

Pseudoplasticity may occur for a number of different

reasons, e.g., polymers may align themselves with the flow

field, solvent molecules bound to a particle may be

removed, or aggregated particles may break down.

Dilatant fluids. Dilatant behavior is much less common

than pseudoplastic behavior. It manifests itself as an

increase in the apparent viscosity as the shear rate is

increased, and is therefore sometimes referred to as shear

thickening.http://www-unix.oit.umass.edu/~mcclemen/581Rheology.html

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Time Independent Fluids

Shear Stress Apparent Viscosity

(Steffe 1996)


p. 22, 25

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Time-Dependent Behavior of Fluids

(Steffe 1996)


p. 28

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Thixotropic Behavior of Paints

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Fundamental rheological measurements: steady shear and

dynamic viscometric measurements on fluids and

viscoelastic materials, or the small deformation testing of

solids.

Empirical measurements: amylograph, commonly used in

studies on starch gelatinization; Brookfield viscometers.

Imitative measurements: instrumental texture profile

method developed at General Foods (Friedman et al., 1963).

In this test, the first two bites of the mastication process are

imitated with an instrument.

Instrumental Measurements of Rheology of Foods

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Common Rheological Instruments

(Steffe 1996)


p. 3

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Schematic of a Typical Rotational Rheometer

apply torque to the sample

measure sample deformation and

deformation rate

stabilize the spindle

constrain the sample

regulate temperature

All rheometers calculate stress and shear rate from the measured

torques and speeds, respectively.

Some rheometers use a separate transducer to measure the torque,

whereas most integrate this measurement into the motor controller.

36Plate & Plate

Cone & Plate

Concentric Cylinders

Motor Applies Torque

Strain read from

Optical Encoder.

Fixed Gap

Variable Gap

Geometry of Shear for Rotational Rheometers [Controlled Stress]

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Parallel Plate Geometry

Dm

Torque MNm

Rad/sRm

=2M

3

RRim=

Dg

RRim

.

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2cm

4cm

6cm

Shear Stress

Gap

Shear Rate

Decreases

Increases0

Infinity

Plate Gaps and Diameters

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Cone & Plate Truncation Height = Gap

Truncation Heights:

1 degree ~ 20 - 30 microns

2 degrees ~ 60 microns

4 degrees ~ 120 microns

Gap must be > or = 10 [particle size]!!

Limitations of Cone & Plate for Dispersions - Fixed Gap!

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100% Elastic Behavior

Phase angle =0o

( = 0)

100% Viscous Behavior

Phase angle = 90o

( = 90)

Strain(應變)

Stress(應力)

Hooke’s law E = /e Newton’s law e = h .d /dt

Ideal Elastic and Viscous Response to Stress

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黏彈行為(Viscoelastic Behavior)

相角介於0與90度間

(0 < 90) G*(complex

modulus)

G‘(elastic modulus)

複數模量=應力波幅/應變波幅(G* = stress amp/strain amp )

彈性(儲存)模量(G')= G*cos

黏彈(損失)模數(G")= G*sin

阻尼(damping or tan ) = G"/G‘

應力(Stress)

應變(Strain)

G”(v

iscous m

odulu

s)

動態理論:黏彈性材料黏與彈的解析

G : Shear Modulus

quantifies the balance between energy loss and storage.

> 1 ➔ more "liquid" properties,

< 1 ➔ more "solid" properties, regardless of the viscosity.

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Calculation of Shear Modulus

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SUPER BALL

TENNIS

BALL X

STORAGE

LOSS

Schematics for Storage and Loss Moduli

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Strain Sweep Mode in Dynamic Testing

(Steffe 1996)


p. 319

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Non-Linear Region

G = f(g)Linear Region

G is constant

t

G

% strain

str

es

s (

Pa

)

Linear and Non-Linear Stress-Strain Behavior of Solids

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(Steffe 1996)


p. 329

Dynamic Mechanical Spectra for a Dilution Solution

Terminal Region : G”>G’

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Terminal to Rubbery Region : G” Crossover G’

Dynamic Mechanical Spectra for a Concentrated Solution

(Steffe 1996)


p. 330

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Dynamic Mechanical Spectra for a Gel

Rubbery Plateau Region : G’ > G”

(Steffe 1996)


p. 330

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Texture Profile Analysis

Texture Profile Analysis

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Some Food Texture Terminology

TIC Gum Co. White paper

Gelatin free gummy vitamins

Accessed Oct. 8, 2016

Pound cake: 重奶油蛋糕

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Definition of Texture Attributes

Chuang & Yeh, 2006

J. Food Eng. 74:314

Typical Tensile Stress-Strain Curves for Polymers

Strain(%)

Str

ess(

psi

)

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a capillary viscometer

The sample is dropped down the larger hole of

the capillary viscometer (tube G) and then

sucked through the other end with an auto-

pipette. Next, clamp it to the water bath of 30

degrees Celsius and record the time it takes the

meniscus of the solution to fall from point C on

the tube to point E.

hrel＝t / ts

From Hagen-Poiseuille equation

h = Dp R4/8 Q L

R:radius of tube

L: length of tube

Q: volumetric flow rate

Measuring Intrinsic Viscosity

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A polymer chain in solution has a coil conformation that behaves

hydrodynamically like an ‘equivalent hard sphere’ as described

by the Einstein equation

Vh

Einstein Equation

[h]M = 2.5 Vh = 2.5(4/3 Rh3) = 10.47 Rh

3

Thus, the intrinsic viscosity is inversely proportional to the molecular

density, one could call it the hydrodynamic density.

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1−=−

== rel

s

s

sp hh

hhhSpecific viscosity

C (concentration)

hsp

Slope ≅ 3.4

Slope ≅ 1

Dilute solution

xx

x

xx

x

x

x

x

x

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0

int

→

==

c

sp

C

hhIntrinsic Viscosity

C (concentration)

C

sph

good

Due to the ionic strength

Change the conformational structure

Thus, viscosity is raised

No good

x x

x

x

x

xx

x

x

x

Documents

Rheological Properties for Foods