Caballero B. (ed.) Encyclopaedia of Food Science, Food Technology and Nutrition. Ten-Volume Set

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Research Council (1989) attempted to set an optimal

intake level, and so recommended a higher RDA of

1000 RE per day for men and 800 RE per day for

women (the difference being due to a lower body

weight, on average). However, the most recent rec-

ommendations from the US Institute of Medicine are

calculated to maintain an adequate body pool size

and set an RDA of 900 mg of RAE for adult males,

700 mg of RAE for adult females.

Toxicity

003 3 Over600individualcasesofhumanvitaminAtoxicity

have been reported, owing to either acute (single or a

few large doses ingested over a brief period of time) or

chronic intake (moderately high doses taken fre-

quently for periods of months or years). Acute toxicity

in human adults is reported from doses of 300 000–

10 000 000 RE (1000–35 000 mmol); chronic doses of

15 000–300 000RE (50–1000 mmol) have produced

hypervitaminosis A. Symptoms include headache,

vomiting, diplopia, alopecia, dryness of mucous mem-

branes, desquamation, bone abnormalities, and liver

damage.However,singleoraldosesof60000 REinoil

have been successfully used in vitamin A intervention

programs for preschool children, with transient toxic

symptoms observed in no more than 3% of subjects.

Massive doses of b-carotene are not toxic, but may be

lessefficientlyabsorbedandusedthanvitaminAitself.

Rodent animal models have been extremely valuable

in elucidating vitamin A requirements and metabol-

ism, but the rat seems to be much less susceptible to

hypervitaminosis A than is the human.

0034 The toxic effects of high vitamin A intakes are

mediated by serum retinyl esters; retinol-RBP concen-

trations are maintained at normal levels in hypervita-

minosis A, but serum retinyl esters are markedly

elevated, bypassing the normal homeostatic controls

on vitamin A transport. Some carnivores, including

the dog, are unusual in having high fasting levels of

serum retinyl esters, presumably reflecting differences

in lipoprotein metabolism in these species; the impli-

cations of this for vitamin A metabolism and for

resistance to hypervitaminosis A are not clear.

0035 The most tragic consequences of excessive vitamin

A intake are teratogenicity (specifically, malforma-

tions of the cranium, face, heart, thymus, and central

nervous system) and embryotoxicity. Acidic retinoids

such as those that have been used in dermatology are

particularly potent, as they can attain high serum

levels and can readily pass the placental barrier. Al-

though large intakes of vitamin A itself (>7500 RE

per day, 26 mmol per day) early in human pregnancy

can cause birth defects (perhaps owing to metabolism

of retinol to retinoic acid?), serum concentrations of

retinol and retinyl esters are normally maintained at

moderate levels during pregnancy. It is assumed that

these teratogenic effects are related to the important

role of retinoids in differentiation of cells and that

these effects are mediated via the nuclear receptor

proteins. (Interestingly, the retinoid b-glucuronides

are much less teratogenic than retinoic acid.) In view

of these teratogenic effects occurring at less than

10 times the recommended daily intakes, a consensus

of several professional organizations is that women

should avoid vitamin A supplements during the first

trimester of pregnancy, and that subsequent supple-

ments, if taken at all, should be prudently limited to

8000 IU (2400 mg RE, 8.5 mmol) per day, although

10000 IU (3000 mg RE, 10 mmol) appears to be safe.

0036The previous two decades have been exciting in

retinoids research, with the disclosure of the roles of

retinoids in control of gene expression. Continuing

challenges in vitamin A research include: (1) the de-

velopment and confirmation of indirect indices of

vitamin A status; (2) elucidation of the mechanism

of control of serum retinol-RBP concentrations;

(3) more exact determination of vitamin A require-

ments for specific functions (not only growth and

prevention of blindness, but also immune function

and cell differentiation in individual tissues); and

(4) definition of the role of vitamin A in differenti-

ation in specific tissues, perhaps leading to chemical

design of distinctive retinoids to combat specific

cancers and dermatologic diseases.

Seealso: Carotenoids:Occurrence,Properties,and

Determination

Further Reading

Blomhoff R (1994) Vitamin A in Health and Disease. New

York: Marcel Dekker.

Chambon P (1996) A decade of molecular biology of reti-

noic acid receptors. FASEB Journal 10: 940–954.

Chambon P, Zelent A, Petkovich M et al. (1991) The family

of retinoic acid nuclear receptors. In: Saurat JH (ed.)

Retinoids: Ten Years On, pp. 10–27. Basel: Karger.

Clarke SD, Thuillier P, Baillie RA and Sha X (1999) Peroxi-

some proliferator-activated receptors: a family of lipid-

activated transcription factors. American Journal of

Clinical Nutrition 70: 566–571.

Collingwood TN, Urnov FD and Wolffe AP (1999) Nuclear

receptors: coactivators, corepressors, and chromatin

remodeling in the control of transcription. Journal of

Molecular Endocrinology 23: 255–275.

Dietary Reference Intakes for Vitamin A, Vitamin K, Ar-

senic, Boron, Chromium, Copper, Iodine, Iron, Manga-

nese, Molybdenum, Nickel, Silicon, Vanadium, and Zinc

(2001), pp. 65–125. Washington, DC: National Acad-

emy Press. (available online at http://books.nap.edu/

books/0309072794/html/65.html).

4966 RETINOL/Physiology

McKenna NJ, Xu J, Nawaz Z et al. (1999) Nuclear receptor

coactivators: multiple enzymes, multiple complexes,

multiple functions. Journal of Steroid Biochemistry and

Molecular Biology 69: 3–12.

Mangelsdorf DJ, Umesono OK and Evans RM (1994) Reti-

noid receptors. In: Sporn MB, Roberts AB and Goodman

DS (eds) The Retinoids, 2nd edn, pp. 319–349. New

York: Raven Press.

Nalubola R and Nestel P (1999) The Effect of Vitamin A

Nutriture on Health: A Review, pp. 1–83. Washington,

DC: ILSI Press (available at www.ilsi.org/hnipubs.htm).

Napoli JL (1996) Retinoic acid biosynthesis and metabol-

ism. FASEB Journal 10: 993–1001.

Napoli JL (1999) Retinoic acid: its biosynthesis and metab-

olism. Progress in Nucleic Acid Research and Molecular

Biology 63: 139–188.

Ross AC (1999) Vitamin A and retinoids. In: Shils ME,

Olson JA, Shike M and Ross AC (eds) Modern Nutrition

in Health and Disease, pp. 305–327. Baltimore, MD:

Williams & Wilkins.

Sporn MB, Roberts AB and Goodman DS (eds) (1994) The

Retinoids, 2nd edn. New York: Raven Press.

Reverse Osmosis See Membrane Techniques: Principles of Reverse Osmosis; Applications of Reverse

Osmosis; Principles of Ultrafiltration; Applications of Ultrafiltration

RHEOLOGICAL PROPERTIES OF FOOD

MATERIALS

J Lefebvre, Institut National de la Recherche

Agronomique, Nantes, France

Introduction

0001 Rheological properties of ingredients and products

are involved in all stages of food, from formulation

to consumption. Their knowledge is therefore im-

portant to many aspects of food science and tech-

nology, such as modeling of processing operations

(pumping, mixing, heat exchange, etc.), design of

the processing and packaging machines, process

control, characterization of ingredients, intermediary

and end products, and instrumental evaluation of

texture. They even concern nutrition, since foodstuffs

have to be chewed and swallowed before being

digested. The interest of food scientists in rheology

is as old as rheology itself, and some of the pioneering

work in this comparatively young discipline has been

carried out on food materials.

0002 During the last decade, the most active research

areas in food rheology dealt with the characterization

of the viscoelastic behavior of liquid, semiliquid, or

gel food systems. Whereas flow properties are of

prime importance in all aspects of processing of liquid

materials, viscoelasticity measurements often consti-

tute in practice the only feasible approach (along with

microscopy) to obtain information on the structure of

complex concentrated systems (solids and liquids)

and on how it is affected by composition, or by

physical, chemical, or biochemical treatments. They

provide a unique tool to adapt formulations or to

develop new engineered foods to meet the demands

of changing technologies and evolving consumers’

requirements.

0003However, rheometry on food systems has long been

limited to the study of flow behavior (viscometry).

Because of theoretical and practical difficulties, and

especially because of the lack of affordable rheometers

with high enough sensitivity, the viscoelastic proper-

ties of food systems have only been evaluated empiric-

ally, using an impressive variety of instruments and

methods of testing, adapted to different specific types

of materials or problems, but which did not allow the

expression of measurements in terms of relevant phys-

ical variables because of the complexity of the deform-

ations and of the mechanical sollicitation patterns they

implemented. This situation has completely changed

since the mid-1980s with the development of com-

paratively low-priced performing commercial rhe-

ometers. Viscoelasticity studies in shear are now

within the reach of the average food science labora-

tory, opening up new, exciting perspectives. But this

does not mean they are easy to carry out and to inter-

pret, and a working knowledge of the essential con-

cepts has not spread as fast and wide as the equipment.

The first purpose of this article, focused on viscoelas-

ticity, is to give an outline of these concepts.

0004Food materials display an amazing variety of rheo-

logical behavior. They can nevertheless be reduced to a

relatively small number of basic types. The main one

along the views outlined above corresponds to transi-

ent networks. It will be illustrated here with a few

examples which will also be used to point out some

RHEOLOGICAL PROPERTIES OF FOOD MATERIALS 4967

fundamental or practical problems which are espe-

cially important or critical in the case of food systems.

0005 Only behaviors in shear (more precisely, in rota-

tional geometries) will be considered, as shear is the

most important type of deformation in rheological

studies with regard to the orientations of this short

article.

Solids and Liquids: Betwixt and Between

0006 Rheology emerged as a science to describe, analyse,

and rationalize the complex mechanical behavior dis-

played by most real materials, for which the classical

Hookean elastic solid and the Newtonian viscous

fluid represent only limiting behavior, which is seldom

encountered in practice. Two types of deviation from

the ideal behavior can occur, either separately or

together: time-dependence and nonlinearity.

0007 Let us revisit briefly these classical notions with

the help of a rheological experiment which is the

retardation test (creep and recovery): a stress s is

applied suddenly at time t ¼0 and maintained till

t ¼s. Then, the sample is suddenly unloaded; the

strain g is recorded during the loading period (creep)

and after the removal of stress (recovery); the results

are expressed in terms of the compliance function

JðtÞ¼gðtÞ=s in both parts of the test.

Viscoelasticity

0008In time-dependent behavior, the response depends on

the duration of excitation. The general case is that of

viscoelastic behavior, illustrated schematically in

Figure 1c and d. The responses of the ideal elastic

solid and of the ideal viscous liquid are shown for

comparison (Figure 1a and b); they are instantaneous

and defined by a constant value of the compliance

¼ g

=s (for the solid) or the compliance rate

dJðtÞ=dt ¼ 1= (for liquid of viscosity Z). To reach

steady state (i.e. the equilibrium compliance J

in the

case of a viscoelastic solid, or a constant rate of

Creep

Recovery

Time t (s)

(a)

Compliance J(t) (m

−1

)

Creep

Recovery

Slope 1/η

Time t (s)

(b)

Compliance J(t) (m

−1

)

J(S)

Creep

Recovery

Time t (s)

(c)

Compliance J(t) (m

−1

)

Creep Recovery

Time t (s)

(d)

Compliance J(t) (m

−1

)

t/η

S/η

fig0001 Figure 1 Schematic responses to a retardation test: (a) elastic solid; (b) viscous liquid; (c) viscoelastic solid; (d) viscoelastic liquid

within the linearity range. Solid curve: measured total compliance. Curve 1 (dashed line): contribution of flow. Curve 2 (dotted line):

recoverable compliance J

(t).

4968 RHEOLOGICAL PROPERTIES OF FOOD MATERIALS

compliance dJð tÞ=dt in that of a viscoelastic liquid)

requires a certain length of time after loading. And it

is the same after unloading for compliance to reach a

constant value. This value is zero in the case of a

viscoelastic solid: deformation is entirely reversible,

although not instantaneous. In contrast, for a visco-

elastic liquid, the strain gathered during creep is

progressively recovered after unloading, but only in-

completely; the residual compliance J

corresponds

to the irreversible part of the deformation, i.e., to the

contribution of flow to the total strain at the end of

the creep period: J

¼ S=. Flow contribution to

strain becomes dominant (J(t) becomes a linear func-

tion of time) only after a creep time t > t

; for t < t

elasticity dominates the response, although flow

begins as soon as stress is applied to the material. By

subtracting flow contribution t/Z from the compli-

ance in creep, the reversible contribution to the com-

pliance is obtained. This contribution similar to the

response of the viscoelastic solid is called the recover-

able compliance J

(t); it is identical, in the case of

linear behavior (see below), to the part of the final

compliance J(S) which is recovered during the re-

covery part of the test. The plateau value J



of J

(t)

can be taken as a gauge of the elastic character of the

liquid. The product t

¼  J



is the longest retard-

ation time of the material and corresponds to t

0009 Such behavior simultaneously displays elastic and

viscous characteristics. Elasticity dominates at short

times of observation; the behavior appears to be in-

creasingly viscous as the time scale of the experiment

broadens. Thus, a given material can display either

solid- or liquid-like behavior, depending on the time

scale of the deformation process. This scaling is rep-

resented by the Deborah number D ¼ t/, where t is

a characteristic time of material response (infinite for

an elastic solid, zero for a viscous liquid) and  is a

characteristic time of the experiment. A material will

display a solid-like behavior (high D values) if it

responds slowly (large t) or if its response is observed

at short time scales (small ). Although the distinc-

tion between solid and liquid subsists in theory for

viscoelastic materials, it can be difficult to draw it in

practice. Many materials which are felt as solids in

common experience are indeed viscoelastic liquids.

Linearity and Nonlinearity

0010 The notion of linearity, which simply amounts to the

proportionality of the response to the solicitation for

the ideal solid or liquid (J



or Z independent of s,

respectively), has to be generalized to the time de-

pendence for viscoelastic materials. The viscoelastic

behavior is linear if the response to a sequence of

arbitrary solicitations is identical to the sum of the

responses to these stimuli if they were acting

independently. This is the Boltzmann superposition

principle which can be expressed as:

gðtÞ¼

1

Jðt t

dsðt

ð1Þ

in terms of the stress history. As to the retardation

test, linearity means that:

0011J(t) is independent of s;

0012The values of the steady-state limiting compliance



and viscosity Z are the same when obtained

from the creep or from the recovery parts of the

test;

0013The curve of the recoverable compliance against the

recovery time (tS), obtained from recovery, super-

imposes on that of the recoverable compliance

against creep time, obtained by subtracting the con-

tribution of flow from the creep compliance.

Most real materials behave linearly only up to some

limit of strain or strain rate limit, which is a material

property. Whilst handling and processing the material

generally involves solicitations which exceed this

limit (which may be fairly low), characterization of

its viscoelastic behavior within the linearity range is a

prerequisite for studies in the nonlinear regime. In the

linear regime, the results of any of the classical rheo-

logical tests are independent of the amplitude of the

solicitation and they can also be used to predict the

behavior of the material in the other tests. Beyond

the linearity range, this is no longer the case.

Classical Rheological Tests

0014The characterization of the rheological behavior of a

material requires the study of its viscoelasticity and,

in the case of a liquid, that of its steady flow behavior.

The rheologist uses very simple ‘system of loads’

patterns and deformations. Transient regime and

dynamic tests are used to study viscoelasticity. Flow

behavior is investigated using viscometry.

0015Very often, the study of viscoelasticity is restricted

to the linear range, for the reasons hinted at above.

Although within the linearity domain all viscoelasti-

city tests are equivalent in theory and their results can

be interconverted using theoretical relations or semi-

empirical approximation methods, their respective

applications differ in practice according to the

materials and the instruments and the experimentalist

should view them as complementary.

Transient Regime Tests

0016We have already given the principle of the retardation

test (creep and creep recovery). This test corresponds

to the ‘natural’ operating mode of stress-controlled

rheometers. The transient test with strain-controlled

RHEOLOGICAL PROPERTIES OF FOOD MATERIALS 4969

instruments is the (stress) relaxation test: at time zero,

the sample is suddenly deformed to a given value of

strain which is then kept constant while the decay

of stress with time is recorded. The experiment is

analyzed using the relaxation modulus function

GðtÞ¼sðtÞ=g, which does not depend on the strain

in the linear domain of behavior. The modulus and

the compliance functions are linked in the linear

regime by the integral equation:

t ¼

Jðt uÞGðuÞdu ¼

JðuÞGðt  uÞdu ð2Þ

so, GðtÞ6¼ 1=JðtÞ, except in the plateau regions of

these functions. Ideal elastic solids store integrally

and indefinitely the mechanical energy imput: stress

does not relax. For viscoelastic liquids, stress relaxes

gradually and vanishes after a long enough time; at

intermediate times, a region, called the viscoelastic

plateau G



, where the decrease of the modulus

slackens momentarily, is frequently observed on bilo-

garithmic scales (Figure 2a). Viscoelastic solids do not

relax completely: at long time values, the modulus

approaches a constant value G

, the equilibrium

modulus (Figure 2b).

0017 Stress relaxation tests are not easy to perform on

liquids with low elasticity or short characteristic

times. In such cases, it is preferable to submit the

material to a sudden constant shear rate

gg ¼ dg=dt

until an equilibrium value s

of stress is reached,

after which the shear rate is suddenly stopped while

stress continues to be recorded (Figure 3). Both parts of

this test can be analyzed in term of relaxation modulus:

GðtÞ¼ð1=

ggÞjdsðtÞ=dtjð3Þ

The retardation test is particularly interesting for vis-

coelastic liquids since the viscoelastic response can be

very simply separated from the steady flow contribu-

tion (Figure 1d), in contrast to the relaxation test; the

latter is better suited for solid materials.

0018Transient tests allow materials with very long

response times to be studied; the upper time limit

for the experiments only depends on the stability of

the material and the patience of the operator. But

since in practice the establishment or the release of a

constant value of the stress, strain, or strain rate takes

some time, transient tests do not measure correctly

the response at short times. Besides, the response

often shows at starts and stops transient damped

oscillations due to mechanical coupling between the

sample and the measuring device. These methods are

applicable to materials with characteristic times

longer than, say, 1 min.

0019Transient tests usually require relatively large

‘system of loads’ to give an accurately analyzable

response; this may be a problem for materials with a

low linearity limit.

Dynamic Measurements

0020Dynamic measurement consists of submitting the

sample to a sinusoidal ‘system of loads’ at an angular

frequency o rad s

1

. When stress is imposed, strain is

measured, and conversely: this type of test can be

performed either with stress- or with strain-controlled

log(t)

(s)

log(G(t))

(Pa)

(a)

log(t) (s)(b)

log(G(t))

(Pa)

fig0002 Figure 2 Schematic responses to a stress relaxation test:

(a) viscoelastic liquid; (b) viscoelastic solid.

0.002

0.001

010203040

Time (min)

Stress (Pa)

fig0003Figure 3 Response of a 3% bovine serum albumin solution

(isoionic conditions) to the sudden application of a shear rate of

0.05 s

1

over 12 min (step 1) followed by its sudden stop (stress

relaxation: step 2).

4970 RHEOLOGICAL PROPERTIES OF FOOD MATERIALS

instruments. Within the range of linear viscoelastic

behavior, the response of the material is also sinus-

oidal with the same frequency as the excitation, but

out of phase. If a strain g ¼ g

cosðotÞ is imposed, the

stress will be s ¼ s

cosðot þ dÞ; the phase angle d

is zero for an ideal solid and p/2 for an ideal liquid.

The results are often expressed in terms of the

storage and loss moduli G

¼ðs

Þ cosðdÞ and

¼ðs

Þ sinðdÞ, which are the real and ‘imagin-

ary’ parts of the complex modulus G



ðoÞ¼G

ðoÞþ

ðoÞ¼sðtÞ=gð tÞ, respectively. The viscoelastic be-

havior will be described by the variations of G

and

with o (the mechanical spectrum of the material);

however, the two moduli are not independent over the

frequency domain. Alternatively, the results can be

expressed in terms of the real and ‘imaginary’ com-

ponents of the complex compliance, or (for liquids

only) of the complex viscosity: J

¼ G

=ðG

þ G

002

Þ,

¼ G

=ðG

þ G

002

Þ, and 

¼ G

=o, 

¼ G

=o.

Although these representations contain strictly the

same information as G

, G

, they can prove more

interesting for viscoelastic liquids because they

weigh dissipative processes differently on the fre-

quency scale. Qualitatively, a measure at frequency

o in a dynamic test is equivalent to a measure at time t

¼ 1/o in a transient test.

002 1 Figure 4a and b show the schematic theoretical

mechanical spectra of a viscoelastic liquid and a

viscoelastic solid, respectively. Whereas G

(o) is

necessarily a monotonously increasing function,

(o) shows maxima which correspond to concen-

trations of dissipative processes in the material over

certain frequency regions. Two loss peaks are visible

on the liquid-type spectrum. They encompass an inter-

mediate frequency range where G

> G

and keeps a

nearly constant value G



– the viscoelastic plateau;

at this time scale, when energy dissipation is showing

a relative minimum, the material is transiently quasie-

lastic. On both sides of the plateau, G

> G

and both

moduli are strongly frequency-dependent. At high

frequencies, G

and G

first both increase approxi-

mately as o

with a*0.5 (the transition zone); then G

tends towards its very high ‘glassy’ limit G

, whereas

drops: the ‘glassy behavior’ corresponds to solici-

tations which are too fast for the structural elements

in the material to respond. Below the viscoelastic

plateau, G

a o

and G

a o; this is the terminal region

of the mechanical spectrum, corresponding to flow.

For viscoelastic solids, the terminal region is not ob-

served; at low enough frequencies, G

reaches

a constant value – the equilibrium modulus G

Frequently, the loss peaks overlap strongly; then the

viscoelastic plateau reduces to an inflection in G

0022Dynamic measurements are very popular. They are

easy to perform, accurate even with fairly fluid ma-

terials, and cause minimal perturbation to the sample

since the amplitude of strain is controlled and can be

kept to quite low values (minimum value *0.1% on

strain-controlled instruments, but *1% on stress-

controlled ones). They permit the study of materials

with a low linearity limit.

0023However, some limitations of dynamic tests should

not be overlooked:

0024Beyond the linearity limit, the response signal is no

longer sinusoidal. The calculation of the real and

‘imaginary’ components of the rheological func-

tions, as outlined above, performed automatically

by the rheometer softwares, is then invalid.

0025The frequency range is restricted for practical

reasons. Because of mechanical problems, rota-

tional rheometers cannot operate above 200–

500 rad s

1

, but the upper limit may be as low as

* 10 rad s

1

when rather fluid materials are tested.

Instrument softwares generally permit operation

down to 10

4

rad s

1

, but below 10

3

rad s

1

measurements take an exceedingly long time. The

practical range of operation is thus 10

3

–100 rad

1

, corresponding to the 10

2

–10

3

1

time scale,

extending well below the lower limit of transient

log(ω) (rad s

−1

)

log(G'), log(G") (Pa)

(b)

Slope 1

Slope 2

⬚

log(ω) (rad s

−1

)

log(G'), log(G") (Pa)

(a)

fig0004 Figure 4 Dynamic measurements. Schematic mechanical spectrum of: (a) a viscoelastic liquid: 1, terminal zone; 2, viscoelastic

plateau; 3, transition zone; 4, glassy zone; (b) a viscoelastic solid.

RHEOLOGICAL PROPERTIES OF FOOD MATERIALS 4971

tests but stopping short for many materials, as will

be shown later.

Viscometry

0026 Flow behavior is usually investigated through visco-

metric experiments: a shear rate (or stress) is imposed

on the liquid and the resulting response (shear stress

or rate) is measured; viscosity is defined as  ¼ s=

gg.

Viscometry is primarily concerned with the steady-

state response.

0027 Simple liquids and solutions of low-molecular-

weight molecules are Newtonian (constant viscosity)

over the wide shear rate range of practical interest,

which extends roughly from * 10

4

1

(sedimenta-

tion) to 10

1

(spraying); chewing and swallowing

or pumping and mixing involve intermediate typical

shear rate values (10

–10

1

). But for most mater-

ials, viscosity depends on the shear rate (or stress),

although generally it tends to be Newtonian at low

enough shear rates, and in many applications non-

Newtonian flow properties are important.

0028 The usual behavior is shear-thinning: as

gg increases,

Z decreases from an initial Newtonian plateau Z

to a final one Z

; but one or both of them may often

be out of the experimental window (Figure 5). Shear-

thickening behavior is exceptional in food systems.

0029 Non-Newtonian flow curves are usually recorded

by applying shear rate (or stress) ramps. However,

artifacts can result from the inertia of the measuring

device or from the viscoelasticity of the sample. It is

better to apply a series of shear rate (or stress) steps,

waiting at each step for the steady-state response.

Performing retardation tests under different stress

values is almost the only method applicable to highly

viscoelastic liquids (Figure 6) or to very viscous

inelastic ones; it allows viscosity measurements at

very low shear rates.

0030Many relatively inelastic shear-thinning liquids dis-

play viscosities which also depend on the duration

of shear. When viscosity decreases during shear,

the behaviour is said to be thixotropic; the reverse

case is called antithixotropy; the changes may be

completely or partially reversible. Thixotropy is a

time-dependent behavior which in principle is to be

distinguished from viscoelasticity. But in practice,

these two properties may be difficult to differentiate;

besides, thixotropic materials often show appreciable

−

2.2 g l

−

3.2 g l

−

7.4 g l

−

13.9 g l

−

22.2 g l

−

Shear rate (1/s)

Viscosity (Pa s

−

)

−

fig0005 Figure 5 Shear-thinning behavior. Flow curves of solutions of a high-viscosity hydroxyethylcellulose sample at different concen-

trations. Above a concentration of *2gl

1

, the solutions exhibit typical shear-thinning behavior. The master curve (dots) is built by

collapsing the different curves on the 22.2 g l

1

one by shifting them along the two axes. The continuous line shows the fit of Cross

equation: ð  

Þ¼ð

 

Þ=½1 þð

gg=

 to the master curve data, where Z

¼initial Newtonian plateau viscosity; Z

¼high shear

rate Newtonian viscosity (taken as zero here since it is negligible compared to Z);

¼ critical shear rate; and m ¼ dimensionless

exponent. The fit gives Z

¼ 118 Pa s

1

¼ 0.15 s

1

and m ¼ 0.60.

−5

−4

−3

Shear rate (1/s)

η (Pa s

−1

)

−2

fig0006Figure 6 Flow curve of a toothpaste determined from the

analysis of creep tests carried out at different values of the

applied stress.

4972 RHEOLOGICAL PROPERTIES OF FOOD MATERIALS

viscoelasticity at the same time. When the material is

submitted to a shear rate cycle from zero to a max-

imum and back to zero, a thixotropic loop is observed

(Figure 7). This is a popular way to spot the existence

or the apparition of thixotropy, but it only allows

comparative work; moreover, there are risks of

confusion with inertia effects or with the manifest-

ation of viscoelasticity, which also shows as loops.

The responses to sequences of step changes of shear

rate are used for thorough studies, but thixotropy is a

difficult topic.

0031Yield stress behavior or plasticity, another type of

complex flow properties, has been the subject of much

discussion. Plastic material would not flow until the

stress has exceeded a yield value s

, below which vis-

cosity is infinite (solid behavior). Many materials show

apparent yield stress behavior over limited ranges of

stress or shear rate (Figure 8). However, whenever it

has been possible to go down to low enough stresses

or shear rates (using creep test, for instance), such

materials were found to flow, but with the peculiarity

that viscosity drops from very high values to relatively

low ones over quite a narrow range of stress in the

region of low shear rates (Figure 9).

Problems in Rheological Characterization

of Food Systems

Structural Basis of Viscoelasticity in Food Systems

0032Viscoelasticity is the manifestation of the internal

structure of the material, i.e., the distribution in

space of the structural elements and their inter-

actions. Thixotropy and plasticity derive from flow-

induced large-scale structural changes.

0033Structural elements can be molecules, macromol-

ecules, or particles (solid particles, liquid droplets, gas

bubbles), or associations of such elements (aggre-

gates, micelles, etc.) and their combinations. The

two simplest cases to consider are the solutions of

polymer-like chain macromolecules (polysaccharides,

gelatin) and the dispersions of (quasi-)spherical par-

ticles (including globular protein solutions). When

dilute, such systems show no appreciable viscoelasti-

city in practical conditions – the longest relaxation

time of a macromolecular chain or of an emulsion

droplet is shorter than *10

2

s. Beyond a certain

polymer concentration or disperse phase volume frac-

tion in the system, an elasticity of entropic nature

develops due to topological constraints between

macromolecular chains (entanglements), or from

crowding effects between the particles which result

in a local order. Semidilute polysaccharide solutions

should normally display this type of viscoelasticity.

This is indeed the case for guar gum galactomannan

solutions; their mechanical spectrum (Figure 10)

shows in the upper region of the experimental fre-

quency range the beginning of the viscoelastic plateau

due to entanglements. But locust bean gum galacto-

mannan (LBG) solutions progressively depart from

this behavior upon aging, with the development of a

viscoelastic plateau at low frequencies (Figure 11):

the system slowly changes into a gel. This reflects

the establishment of relatively long-lived linkages

between the chains, probably due to hydrophobic

interactions between the ‘smooth’ regions (devoid of

100

2nd shear cycle

1st shear cycle

Shear rate (1/s)

Shear stress (Pa)

100

fig0007 Figure 7 Thixotropic loops. Application of two successive

shear cycles (0–100–0 s

1

) to a guar gum galactomannan/

xanthan mixture (ratio 90/10 w/w) in water at a total polysacchar-

ide concentration of 0.5% w/w (curve 1). The first cycle causes

drastic irreversible damage to the structure of the mixed system.

A residual slight thixotropic behavior is observed during the

second cycle and remains unchanged upon subsequent cycles.

No thixotropy is displayed by guar gum solutions or xanthan

solutions; the results for a 0.5% guar gum galactomannan solu-

tion are given for comparison (curve 2).

−1

Shear rate (1/s)

Shear stress (Pa)

−1

fig0008 Figure 8 Apparent yield stress behavior. Flow curve recorded

at 60



C of a wheat starch paste prepared in the presence of

sodium caseinate (concentrations 6% starch, 7.5% caseinate).

The continuous line is the fit of the Herschel–Bulkley equation:

s ¼ s

þ k

; it gives an apparent yield stress value

¼ 0:34 Pa:

RHEOLOGICAL PROPERTIES OF FOOD MATERIALS 4973

galactose groups) of the mannose backbone, which

do not exist in the case of guar. Similarly, a 3% bovine

serum albumin (BSA) isoionic solution departs from

the purely viscous and Newtonian behavior expected

for dilute hard sphere dispersion (Figure 3), indicating

that protein molecules are strongly interacting.

0034 Because of their chemical structure and of the

specific properties of water, food macromolecules

generally interact through hydrogen and hydro-

phobic interactions. As a result, viscoelasticity of

the transient network type (noncovalent gels) can be

observed at relatively low concentrations. Transient

networks also result from partial destabilization

(flocculation) of suspensions or emulsions due to

colloidal interactions.

Monitoring Structural Transitions

0035The example of LBG solution (Figure 11) showed that

viscoelastic measurements can be used to follow

structural changes in a system. In this case, the change

Shear stress (Pa)

Viscosity (Pa s

−1

)

fig0009 Figure 9 Apparent yield stress behavior. Flow curve of a commercial mayonnaise. The filled circles correspond to the results

recorded during the imposition of a shear rate ramp, the empty circles to data obtained by application of retardation tests. The latter

data demonstrate unequivocally that the behavior is in fact shear-thinning.

−1

−2

−3

−2

−1

G',G" (Pa)

ω (rad s

−1

)

fig0010 Figure 10 Typical mechanical spectra of biopolymer solutions: guar gum galactomannan solutions in water (20



C) at two concen-

trations: 1.87% w/w (circles) and 1% w/w (triangles). Filled symbols, storage modulus G

; open symbols, loss modulus G

4974 RHEOLOGICAL PROPERTIES OF FOOD MATERIALS

was slow enough to allow viscoelasticity to be char-

acterized over a certain frequency range at different

steps of its evolution. However, structural changes are

generally rather fast, and once started, can rarely be

stopped at will. Single-frequency dynamic measure-

ments, since the time required for each individual

measure is short provided that o > 0.01 rad s

1

, are

very precious indeed to monitor the kinetics of struc-

ture changes, as exemplified in Figure 12 for milk

clotting, an instance of colloidal gel formation. But

they do not characterize rheologically the evolution

of the system. Mechanical spectra can be obtained

in the classical way only when the system remains

practically unchanged during the time necessary to

record them. However, advanced techniques which

are outside our scope require much shorter times than

with the classical frequency sweep, and allow study of

systems undergoing relatively fast structural changes.

0036In classical follow-up experiments at fixed fre-

quency, the choice of frequency may be critical.

No change would be detected in LBG solutions if

o ¼10 rad s

1

were selected to monitor aging

(Figure 11)!

The Need to Enlarge the Experimental Window

0037Figure 13 shows the mechanical spectra of food

systems we know to differ largely in nature and in

texture or consistency. Nevertheless, these spectra

are qualitatively similar; those of the commercial

mayonnaise and the 61 mg ml

1

BSA heat-set gel

even superimpose. They show the viscoelastic plateau

region of transient networks of the colloidal gel type,

with gently ascending moduli curves and with G

higher than G

over the frequency window but rela-

tively large G

ratios (0.1–0.5); in the case of the

gluten sample, however, the upper end of the plateau

is visibly approached. Beyond this assignation to a

general type of structure, such flat spectra allow

only a rough estimation of the plateau modulus. But

quantitative comparison can be misleading, since the

viscoelastic plateau often extends beyond both limits

200

100

300

400

500

5 101520

pH 5.3

G', G" (Pa)

Time (h)

fig0012 Figure 12 Monitoring lactic acid bacteria milk clotting using

dynamic measurements at fixed frequency (40



C, o ¼ 6 rad s

1

strain amplitude g

¼ 0.02). The gelation starts after about

150 min fermentation, when the pH has decreased to 5.3. The

decline in the G

curve after *11 h is an artifact due to syneresis.

The experiment was performed using coaxial cylinders to minim-

ize the incidence of syneresis; with cone–plate or plate–plate

geometries, syneresis causes slippage and its effect is seen

much earlier, even when measuring devices with striated or

sanded surfaces are used.

−3

−2

−1

−2

−1

G',G" (Pa)

ω (rad s

−1

)

fig0011 Figure 11 Progressive departure from the solution state during aging of a locust bean gum galactomannan solution (concentration

10 g l

1

;20



C). Mechanical spectra of the freshly prepared solution (circles), of the system after 6 days’ aging (lines), and of the system

after 15 days’ aging (triangles). Filled symbols and solid line, G

; open symbols and interrupted line, G

RHEOLOGICAL PROPERTIES OF FOOD MATERIALS 4975