Vincent A. Hackley

Chiara F. Ferraris

960-

The Use of

Nomenclature in

Dispersion Science

and Technology

NIST recommended

Pu

The Use of

Nomenclature in

Dispersion Science

and Technology

Vincent A. Hackley

Materials Science and 

Engineering Laboratory

Chiara F. Ferraris

Building & Fire Research Laboratory

Previously issued as NIST

Special Publications 945 and 946

August 2001

U.S. Department of Commerce

Donald L.Evans, Secretary

Technology Administration

Karen H. Brown, Acting Under Secretary of 

Commerce for Technology

National Institute of Standards and Technology

Karen H. Brown, Acting Director

p
ii

Certain commercial entities, equipment, or materials may be identifie

document in order to describe an experimental procedure or concept ad

Such identification is not intended to imply recommendation or endor

by the National Institute of Standards and Technology, nor is it intend

imply that the entities, materials, or equipment are necessarily the bes

able for the purpose.

______________________________________

National Institute of Standards and Technology

Special Publication 960-3

Natl. Inst. Stand. Technol.

Spec. Publ. 960-3

72 pages (August 2001)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 2001

For sale by the Superintendent of Documents

U.S. Government Printing Office

Internet: bookstore.gpo.gov Phone: (202) 512-1800 Fax: (202) 512-

Mail: Stop SSOP, Washington, DC 20402-0001
Measurements and standards are universally recognized as playing 

role in the manufacturing process. They enhance reliability by prov

basis for quantifying and comparing material properties during each 

manufacturing, from raw materials to the finished product. Equally 

is the establishment of a uniform and widely accepted nomenclatur

describing experimental methods and instrumentation, for sharing t

ideas and concepts and to provide a sound basis on which to standa

urement methods and data reporting practices. This is especially tru

ceramics community, due to its cross-disciplinary nature and due to 

tion of ceramic powders throughout numerous industries.

Ceramic suspensions, gels and pastes (i.e., dispersions) are the start

als for a wide variety of applications, playing critical roles in the pr

products ranging from whitewares, pigments, paper, and cement for 

struction industry to multilayer ceramic packages and chemical mec

planarization slurries for the microelectronics industry. Unfortunate

researchers and engineers working in these diverse fields often spea

languages. Even within the same field, variations in terminology ar

The need for broadly accepted, uniform and precise nomenclature w

acknowledged recently by the Ceramic Processing Characterization

Consortium (CPCC), a voluntary cooperative organization with par

representing industry, instrument companies, academia and governm

principal goal of the consortium was to develop guidelines and reco

practices for the implementation of process measurements. CPCC m

identified nomenclature as a high priority issue in the areas of dispe

dispersion rheology. As a result, work was initiated on two nomenc

guides, which were ultimately distributed as NIST Special Publicat

and 946. 

The present document is essentially a compilation, with updates, of 

previous publications, and provides guidelines for the use of techni

entific nomenclature relevant to ceramic dispersions.

 

	

 

	
			 

	

	

				 

	

	


	 

		
			 


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The use of nomenclature for describing dispersed particulate system

with their associated properties and components, is often inconsiste

ject to misinterpretation in the technical and scientific literature. Fo

terms for describing the state of association of particles in suspensi

aggregate or agglomerate) often carry specific connotations that va

different authors. This guide has been prepared as a resource for res

engineers and students working in dispersion-based applications. In 

this guide, we drew on a number of resources, including books, rev

and published terminologies. To the extent possible, every effort wa

maintain a degree of uniformity with existing standards and conven

including published terminologies from the American Concrete Inst

(ACI), the British Standards Institute (BSI), the International Union 

and Applied Chemistry (IUPAC) and the Society of Rheology, as w

current and draft ASTM and ISO standards. 

We intend this guide to serve as a resource for practitioners workin

fields in which ceramic dispersions are used, where ceramic is broa

as a non-metallic inorganic material. Equations have been used spa

only where necessary for clarity or where they are integral to the su

hand. This is not, nor is it intended to be, an exhaustive compilation

this document focuses on commonly encountered terms, and endea

provide a consistent framework for improved technical communica

The technical nomenclature portion of this guide is divided into two 

The first section is derived from Special Publication 945, and deals 

general topics related to dispersion science and technology, such as 

agglomeration and colloidal stability. The second section is based o

Publication 946, and provides definitions of terms and expressions 

the measurement of rheological properties in liquid-based ceramic d

(i.e., suspensions, pastes and gels). 

In addition to the glossaries of basic terms, the guide is organized s

reader can more readily locate related terms associated with specifi

areas. Defined terms are indicated in boldface type. Where alternati

equivalent terms exist, they are shown in brackets adjacent to the p

term. Terms used in definitions, and which are defined separately in 

are indicated in italic at their first appearance in that paragraph or s

only exception to this rule is the term viscosity in Part II, which is n

italicized when it appears by itself, due to its ubiquity throughout th

Descriptions of instrumentation provided in this guide are generic i

and are presented solely for the purpose of identifying key measure

techniques and their associated nomenclature.
2

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aerosol

Droplets or particles dispersed in a gaseous phase.

continuous phase

Constituting the medium, a phase that exhibits continuity throughout 

dispersion; e.g., the liquid in a suspension.

dispersed phase [discontinuous phase]

In a dispersion, the phase that is distributed in the form of discrete di

ities (particles, droplets or bubbles), in a second immiscible phase tha

continuous.

dispersion

In general, a two-phase system in which discontinuities of any kind (

liquid, gas) are dispersed in a continuous phase of a different compos

state; more specifically in the field of ceramics, the term dispersion is 

describe a suspension of solid particles in a liquid medium.

emulsion

A dispersion consisting of two or more liquid phases.

hydrosol

A sol in which water forms the dispersion medium.

liquid phase

Consisting of a condensed fluid; e.g., the dispersion medium in a susp

organosol

A sol in which an organic liquid forms the dispersion medium.

particulate phase [solid phase]

The particles in a suspension, gel or aerosol.

slip

A term that refers to a suspension prepared for the expressed purpose 

solidating the solid phase (e.g., by slip-casting, tape-casting or spray 
A concentrated ceramic particulate suspension.

sol

A liquid dispersion containing particles of colloidal dimensions.

suspension

A liquid in which solid particles are dispersed.

	
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heterodisperse

Describes a polydisperse particulate system in which more than one 

size distribution mode occurs; e.g., bimodal, trimodal, etc.

monodisperse

Realistically, all dispersions exhibit a finite spread in their particle 

bution. In practice, the term monodisperse can be used to identify a 

system in which all particles are of nearly the same size, forming a 

(unimodal) distribution about an average value. Numerically, a disp

be considered monodisperse if 90 % of the distribution (1.645 , w

the standard deviation of the size distribution) lies within 5 % of t

size, d:

polydisperse

Describes a dispersed system in which many particle sizes occur. In 

system may be considered polydisperse if less than 90 % of the siz

tion (1.645 , where  is the standard deviation of the size distribu

within 5 % of the average size, d:

well-dispersed

A term used to describe a stable suspension in which the minimum 

size has been achieved.

0.05 1.645

 



d

0.05 1.645

 



d
4

relative concentration terms

It is recommended that relative descriptive terms relating to particle c

tion in suspension (e.g., dilute or concentrated) be defined in such a m

that the reader has a clear understanding of their relevance to the mea

or application at hand. For instance, in a light scattering measuremen

may infer the absence of multiple scattering, whereas in an ultrasonic 

urement this term may imply a linear response with concentration. Th

conditions may vary by several orders of magnitude with respect to p

concentration. Concentration can also by defined on a more fundame

taking into consideration the relative dominance of thermal, hydrodyn

surface forces in controlling suspension properties.

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nanosize [nanophase]

A special state of subdivision implying that the particles (or atomic c

have average dimensions smaller than roughly 100 nm, and exhibit p

not normally associated with the bulk phase (e.g., quantum optical eff

colloid

State of subdivision implying that the particles have at least in one di

dimension roughly between 1 nm and 1 	m. Colloids are significantly 

by Brownian motion when suspended in a liquid.

ultrafine 

State of subdivision implying that the particles have in any given dire

maximum dimension lying roughly between 1 	m and 10 	m.

fine [subsieve range]

State of subdivision implying that the particles have in any given dire

maximum dimension less than roughly 37 	m.

coarse [sieve range]

State of subdivision implying that the particles have in at least one di

dimension greater than roughly 37 	m. 
State of subdivision generally referring to dry particulates with dim

lying roughly in the 50 	m to 200 	m range; typically, granules are 

gates of finer particles produced by spray-drying. Granulation is pe

ease of handling during subsequent consolidation operations.

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particle

Any condensed-phase tridimensional discontinuity in a dispersed sy

generally be considered a particle; e.g., droplets in an emulsion or s

persed in a liquid. The term is normally used in reference to solid m

An aggregate may also be regarded as a particle. 

droplet

Liquid-phase particle in an emulsion or aerosol.

particulate

Composed of distinct particles.

primary particle

Smallest identifiable subdivision in a particulate system. Primary p

may also be subunits of aggregates. 

microsphere

Refers to a spherical particle in the micrometer size range.

aggregate

A cohesive mass consisting of particulate subunits.

hard-aggregate

An aggregate that cannot be easily redispersed by the application o

mechanical agitation (shaking, stirring, or ultrasonication) and/or m

cal treatment. Hard-aggregates consist of subunits that have been ch

bonded or fused.

agglomerate

In a suspension, an aggregate held together by physical or electrost

coagulate [coagulum]

In a suspension, an aggregate formed by the addition of electrolyte
6

In a suspension, an aggregate formed by the addition of a polymer. F

generally characterized by a loose structure (low density). 

powder

A relatively dry, undispersed accumulation of particulate matter with 

scopic consistency.

gel

Bicontinuous structure with a solid and a liquid component. The solid 

may consist of particles or polymers, held together by covalent, ionic 

persion (physical) forces. The network may be elastic, viscoelastic or 

The scale of the mesh of the network (distance between cross links) i

colloidal dimensions.

aerogel

A porous solid produced from a gel in such a way that very little shri

occurs. Typically, the term refers to materials made by supercritical e

of the solvent, although structurally equivalent materials can be made 

ambient conditions by increasing network stiffness and/or elastic reco

by reducing interfacial tension.

alcogel

A gel containing an alcoholic liquid phase.

hydrogel

A gel containing an aqueous liquid phase.

xerogel

Porous solid made by drying a gel under subcritical conditions. 

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average agglomeration number (AAN)

An estimate of the degree of agglomeration in a suspension. AAN is 

age number of primary particles contained within an agglomerate. A

calculated from the ratio of the median particle size, as determined by

example, light scattering, sedimentation or electrical zone sensing tec
adsorption method, such that:

where V50 is the equivalent spherical volume calculated from the m

diameter, D50 in 	m, SSA is the specific surface area in m2/g and 
 

particle density in g/cm3.

equivalent spherical diameter

The diameter of a sedimenting particle determined from Stokes' law 

assuming a spherical shape. The term is sometimes used in conjunc

other measurement techniques and theoretical constructs, where sph

geometry is assumed.

fractal

A structure that has an irregular geometry under all scales of observ

it is non-Euclidian). The fractal dimension of a species, Df, is the e

which a characteristic length scale must be raised to obtain proporti

with the overall size of the species. Destabilized suspensions tend t

aggregates with fractal structures. In this case, Df has a value lying 

and 3, where Df=3 is a fully dense object.

minimum particle size (MPS)

An experimental quantity operationally defined as the minimum pa

that can be achieved by a particular dispersion process as determine

appropriate measurement technique. The characteristic dimension u

determining the MPS should be clearly noted (e.g., mean size, med

modal size, etc.).

ultimate working unit

An individual particle or group of particles that retains its structure 

a dispersion process and subsequent application. See also minimum 

size.

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floccule

It is recommended that this term not be used in the ceramic literatu

floc)

3

50

BET

50

6

D SSA

V

V

AAN 




 



   
  
8

With the exception of the defined term hard-aggregate, it is recomme

such adjectives be avoided in the context of dispersed phase structure

use is deemed necessary to convey material-specific information, then 

author should make a clear statement that defines the meaning and ex

usage.

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aggregation

A general term defined as any process by which particles collect to fo

cohesive mass or cluster; the resulting structure is called an aggregat

agglomeration

Formation of aggregates in a suspension through physical (van der W

hydrophobic) or electrostatic forces. The resulting structure is called 

agglomerate.

coagulation

A specific type of agglomeration in which formation of aggregates is 

by the addition of electrolyte to a suspension. The resulting structure 

termed the coagulate or coagulum, while the electrolyte additive is te

coagulant.

flocculation

Formation of aggregates in a suspension mediated by polymeric spec

are either attached to the particles or exist freely in the suspending m

The resulting structure is called a floc, while the polymer additive is t

flocculant. Polymer bridging is a flocculation process.

gelation

Formation of a continuous (space-filling) solid network characterized 

finite static shear modulus (stress/strain ratio); results from percolatio

bonds between particles or polymers. The resulting structure is terme

fusion

Process by which particles form irreversibly bonded structures; often 

terized by the appearance of interparticle necks. (see also hard-aggreg
Generally refers to the aggregation of dissimilar particles; in ceram

tions, the formation of aggregates by the cohesion between particle

different materials (e.g., alumina and silica).

orthokinetic aggregation

The process of aggregation induced by hydrodynamic motions, suc

stirring, sedimentation or convection.

perikinetic aggregation

The process of aggregation induced by Brownian motion.

sol-gel

Process for making a gel from colloidal or molecular precursors.

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deagglomeration

Reversal of agglomeration, i.e., the dispersion of agglomerates to f

suspension.

deflocculation

Reversal of flocculation, i.e., the dispersion of flocs to form a suspe

comminution

Breaking down large pieces to the required size; term commonly us

association with milling of ceramic slurries.

peptization

Refers to the reversal of agglomeration by the addition of a strong 

strong base, such as HCl or NaOH.

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diffusion-limited rate

Refers to a rate of aggregation corresponding to the frequency of e

(collision rate) of the particles. Each collision results in particle adh

(i.e., a sticking probability equal to 1). The rate of encounter is con

the diffusion rate, which depends on the viscosity of the medium, th

sions of the particles, and the concentration of the particles.
10

Refers to a rate of aggregation that is controlled by the reactivity of t

particles (i.e., the frequency of collisions resulting in particle sticking

Usually characterized by a sticking probability much less than 1. A lo

sticking probability results from the presence of an energy barrier. 

syneresis

Spontaneous shrinking of a gel with exudation of liquid.

ultrasonication

Application of high-energy, high-frequency sound to a suspension in 

disperse aggregates. Dispersion is thought to arise from the energy re

during fluid cavitation.

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sonication, sonification

It is recommended that these terms not be used in the ceramic literatu

(see ultrasonication)

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colloidal stability

A physical state that characterizes the relative ability of colloids to re

dispersed in a liquid; suspensions that do not aggregate at a significa

said to be colloidally stable. The precise connotation depends on the t

frame under consideration. Colloidal stability is a form of kinetic stab

is therefore considered a metastable thermodynamic state. From this

perspective, aggregation may be described as a transition from a met

a stable state, occurring at rates that depend on the magnitude of the a

energy barrier that separates them.

kinetic stability

Most dispersed systems are thermodynamically unstable, relative to t

separate bulk phases; however, a dispersion may exist for an apprecia

length of time and therefore exhibit kinetic stability. The term may be 

reference to various destabilizing processes, e.g., aggregation, coales

sedimentation.
A suspension that has sufficient kinetic stability to prevent the occu

significant aggregation as measured over a relevant time frame. Sta

be ascertained by suitable experimental means, such as particle size

or sedimentation measurements.

unstable suspension

A suspension that lacks kinetic stability as measured over a relevan

frame; a highly unstable suspension is one that is subject to rapid (d

limited) aggregation.

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electrostatic stabilization

Mechanism in which aggregation is inhibited by the presence of a m

repulsive electrostatic potential that surrounds each particle.

steric stabilization

Mechanism in which aggregation is inhibited by the presence of an 

polymer layer that is firmly anchored to the particle surface so as n

desorb during collisions. In general, a steric stabilizing agent has on

of its structure that exhibits low solubility in the dispersion medium 

high affinity for the particle surface, and the other portion is solubl

medium.

electrosteric stabilization

Mechanism in which aggregation is inhibited by the combined effe

trostatic and steric stabilization. Usually associated with the adsorp

polyelectrolytes onto the particle surface.

depletion stabilization

Mechanism in which aggregation is inhibited by the presence of fre

(non-adsorbed) polymer due to the creation of high-energy depletio

(i.e., depleted of polymer compared to the bulk solution) between c

interacting particle surfaces.

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DLVO

An abbreviation for a theory of the stability of colloidal dispersions d

the pair-wise interaction between charged particles in a dielectric med
12

Overbeek, calculates the opposing effects of attractive van der Waals 

and repulsive electrostatic forces on the interaction potential.

interaction potential

The potential free energy between two surfaces, typically presented a

tion of separation distance. By convention, a positive potential is mut

repulsive and a negative potential is mutually attractive. 

primary maximum

The first appearance of a maximum in the interaction potential energ

with increasing separation distance. The primary maximum results fro

fact that repulsive and attractive forces decay at different rates as a fu

separation distance. In DLVO theory, a large primary maximum acts a

energy barrier, preventing aggregation of particles into the primary m

primary minimum

The first appearance of a minimum in the interaction potential curve 

increasing separation distance. The primary minimum results from th

that repulsive and attractive forces decay at different rates as a functio

separation distance. In DLVO theory, a deep (negative) primary minim

acts as an energy well, allowing particles to adhere and resulting in a 

colloidal stability.

secondary minimum

A shallow energy minimum (usually of the order of a few kT) in the i

tion potential curve occurring at relatively large separation distances 

that of the primary maximum. In the presence of such an energy well

ary minimum aggregation may occur. Because of the shallow nature 

secondary minimum, the aggregates formed are held together weakly 

such tend to be unstable toward rather small energy inputs such as sti

Born repulsion [hard core repulsion]

As two surfaces are brought into close contact, the attractive van der 

force between them increases continuously. At some point in their app

the electron clouds of the two surfaces begin to overlap, giving rise to 

sive force termed the Born or hard core repulsion. This results in a ste

increase in the interaction potential curve at very small interatomic se

distances, becoming effectively infinite when interpenetration occurs

solvation [structural] forces

Non-DLVO forces that occur at extremely small separation distances 
fluid medium. These forces arise whenever liquid molecules are ind

order into quasi-discrete layers between surfaces, and can result in 

ically increasing (repulsive), monotonically decreasing (attractive) or 

interaction potential. In aqueous solvents these forces may be refer

hydration forces.

Hamaker constant

In the case of particle interactions, a material constant that measure

tive strength of the attractive van der Waals forces between two sur

Particles interacting through an intervening fluid medium will expe

reduced attractive potential due to the presence of the third compon

hard sphere interaction

A largely theoretical construct in which the interaction potential be

approaching particles is assumed to equal zero, except upon contac

goes abruptly to infinity (i.e., no interpenetration occurs). 

noninteracting

If no barrier to particle approach, contact and adherence exists, the 

are said to be noninteracting. If the primary minimum is sufficiently 

every collision will result in particles sticking together. The rate of 

tion will then be kinetically controlled (diffusion-limited rate).

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critical coagulation concentration (CCC)

The molar concentration of electrolyte, Co, necessary to induce rap

(diffusion-limited) aggregation. Experimentally determined by extra

of ln W versus ln Co to ln W=0, where W is the stability ratio.

coagulant

An electrolyte additive that induces coagulation in a suspension.

Schulze-Hardy rule

An empirical rule summarizing the general tendency of the critical

coagulation concentration to vary inversely with the sixth power of 

counter ion charge number of added electrolyte.

lyotropic series

An ordered series of ions indicating, in decreasing order, their effec
14

ions relative propensity to coagulate a dispersion.

stability ratio

Ratio of the diffusion-limited to reaction-limited rate constants for

aggregation. A large ratio indicates a high degree of colloidal stabilit

as a ratio of unity indicates that diffusion-limited conditions prevail an

system is colloidally unstable. The rate constants are determined exper

from the initial rates of aggregation. Usually denoted by the symbol, 

defoaming agent [antifoaming agent]

A surfactant that, when present in small amounts, prevents the forma

foam or aides in the coalescence of bubbles.

dispersing agent [stabilizing agent, dispersant]

A substance that, when present in small amounts, facilitates the dispe

aggregates and improves the kinetic stability of particles. For exampl

polyelectrolytes are often used as dispersing agents in ceramic proces

surface active agent [surfactant]

A substance that lowers the interfacial tension between the solution in 

is dissolved, and other phases which are present (e.g., solid particles 

suspension), and, accordingly, is positively adsorbed at the interface.

polyelectrolyte

A macromolecular substance that, on dissolving in water or other ion

solvent, dissociates to give polyions (polycations or polyanions) - mu

charged ions - together with an equivalent amount of counter ions. A

polyelectrolyte can be a polyacid, a polybase, a polysalt or a polyamp

Frequently used as dispersing agents in ceramic slurries.

sedimentation

The settling of suspended particles or droplets due to the influence of 

or an applied centrifugal field.

sedimentation volume

The volume of particulate sediment formed in a suspension. If the se

formed in a centrifugal field, the strength of this field should be expli

indicated, otherwise normal gravity is understood.

Brownian motion [thermal motion]

Random fluctuations in the density of molecules in a liquid, due to th
random pathways. This random motion is termed Brownian motion

most noticeable for colloidal particles.

coacervation

When a colloidal suspension loses stability, a separation into two li

may occur. This process is termed coacervation. The phase that is m

concentrated in the colloid is the coacervate, and the other phase is 

equilibrium solution.

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deflocculant, dispersing aid

It is recommended that these terms not be used in the ceramic litera

(see dispersing agent)

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interface

A boundary between two immiscible phases, at least one of which i

condensed. Experimentally, the portion of the sample through whic

derivative of any concentration versus location plot has a measurab

from zero. In a suspension, the region of contact between the partic

and the suspending medium.

interfacial region [interphase]

The region that exists between two phases where the properties var

those in the bulk.

surface region

The tridimensional region, extending from the free surface of a con

phase towards the interior, where the properties differ from the bulk

electrical double layer (EDL)

The term describes the non-random array of ions at an interface in 

oppositely charged layers coexist. For particles dispersed in a fluid, 

consists of the surface charge and the solution charge. The solution 

may be further subdivided into Stern and diffuse layers, which is of

to as the triple layer model. 
16

Length characterizing the decrease of potential with distance from a c

interface. Typically defined as 1/, where  is the Debye-Hückel para

For low potentials it represents the distance over which the potential 

1/e or about one third, of the value of the surface potential.

diffuse layer

The region surrounding a suspended particle in which non-specificall

adsorbed ions are accumulated and distributed by the opposing action 

electric field and thermal motion.

Stern layer [compact layer]

Counter and co-ions in immediate contact with a surface are said to r

the Stern layer, and form with the fixed surface charge a molecular ca

Often equated with the immobile portion of the electrical double-laye

exists inside the shear plane. 

inner Helmholtz plane (IHP)

At a charged interface, an imaginary plane representing the distance o

approach of desolvated ions to the surface, and containing the ions or

molecules that are specifically adsorbed.

outer Helmholtz plane (OHP)

At a charged interface, an imaginary plane representing the distance o

approach of solvated (hyrdrated) ions to the surface. Often equated w

position of the shear plane. 

shear plane [plane of shear, surface of shear]

In calculating the electrokinetic potential from electrokinetic phenom

often assumed that a sharp plane separates the liquid adhering to the 

surface from the mobile liquid. This imaginary plane is considered to 

to the solid surface.

1	#$%	

adsorption

The process by which a substance is accumulated at an interface or in 

interfacial region. Should not be confused with absorption, which den

accumulation inside a material or phase.

adsorbate

A substance that is adsorbed at the interface or into the interfacial reg

substrate material or adsorbent.
The substrate material onto which a substance is adsorbed.

adsorption isotherm

The relationship between the equilibrium quantity of a substance ad

the composition of the bulk phase, at constant temperature.

specific adsorption

Ions are specifically adsorbed when they are present in the Stern la

amounts that exceed those expected from simple electrostatic consi

Empirically, ions that are specifically adsorbed have a noticeable ef

isoelectric point.

non-specific adsorption

Ions are non-specifically adsorbed when they are kept in the interph

by long-range coulombic interactions. They are believed to retain th

solvation shell and in the position of closest approach to the interfa

separated from it by one or more solvent molecular layers. Empiric

that are non-specific (indifferent) have no measurable effect on the 

isoelectric point.

chemical adsorption [chemisorption]

Molecules are chemically adsorbed when they exist within the Stern 

form bonds with the surface groups, which have a significant valen

bution. Empirically, ions that are chemically adsorbed have a notice

on the isoelectric point of a suspension and exhibit a significant ent

(heat of adsorption).

physical adsorption [physisorption]

Adsorption in which the forces involved are intermolecular (i.e., va

Waals, hydrogen bonding) of the same kind as those responsible fo

non-ideality of real gases and the condensation of vapors, and whic

involve a significant change in the electronic orbital patterns of the 

involved.

monolayer adsorption

Adsorption in which only a single layer of molecules becomes adso

interface. In monolayer adsorption, all adsorbed molecules are in th

of closest approach to the substrate surface.

multilayer adsorption

Adsorption in which more than a single layer of molecules is adsor

interface. Molecules adsorbed in excess of monolayer adsorption a

the position of closest approach to the substrate surface.
18

The simultaneous adsorption of two or more species.

desorption

The process by which the amount of an adsorbed substance is reduce

1(	" $ !"	#$

isoelectric point (IEP)

For many ceramic systems, the pH at which dispersed particles show 

trophoretic mobility and the zeta potential has a value of zero. More g

the pI value at which zeta is zero, where I is the potential determining 

point of zero charge (PZC)

A particle carrying no fixed charge. The precise identification of pzc 

on the definition adopted for surface charge. Typically for ceramic sy

the pH at which hydroxyl and proton adsorption is just balanced to c

charge; here, the hydroxyl and proton are defined as the charge determ

species.

surface charge density

The quantity of electrical charge accumulated at a particle-solution in

expressed per unit area; usually represented by the symbol 0.

streaming potential

When a liquid under a pressure gradient is forced through a capillary 

plug, excess charges (ions) near the wall are swept along by the liqui

an accumulation of charge downstream. An electric field is also creat

opposes this accumulation. After a steady state has been established, 

measured potential difference across the capillary or plug is called the 

streaming potential and is related to the pressure gradient and to the s

plane potential.

zeta potential [electrokinetic potential, shear plane potential]

The potential drop, , across the mobile part of the electrical double l

is responsible for the electrokinetic phenomena.  is positive if the po

increases from the bulk of the liquid phase towards the shear plane. C

assumptions or estimations regarding the double layer properties mus

made in order to calculate  from experimental data. It is therefore es

indicate in all cases which equations have been used in the calculatio

It can be shown, however, that for the same assumptions about the do
electrokinetic potential.

potential determining ions

Those species of ions that by virtue of their equilibrium distribution 

two phases determine the difference in Galvani potential between th

phases. They are often, but not always, identical with the ions that 

colloidal suspension formed from these phases.

co-ions

In systems containing large ionic species (e.g., colloids), co-ions ar

that, compared to the large ions, have low molecular mass and the s

polarity. For instance, in a suspension of negatively charged particl

containing sodium chloride, the chloride ions are co-ions and the so

ions are counterions.

counterions

In systems containing large ionic species (e.g., colloids), counterion

that, compared to the large ions, have low molecular mass and the o

polarity. For instance, in a suspension of negatively charged particl

containing sodium chloride, the sodium ions are counterions and th

ions are co-ions.

charge reversal

The process wherein a charged particle is caused to assume a new 

the opposite polarity. Such a change can be brought about by oxida

reduction, dissociation, adsorption or ion exchange.

10	" $2%$ 	&& $

electrokinetics

Referring to the relative motions of charged species in an electric fi

field may be applied, or it may be created by the motion of a liquid 

solid phase.

electro-osmosis

When a liquid moves in response to an applied electric field, while 

solid phase remains stationary (e.g., in a capillary or porous plug), 

called electro-osmotic flow. Fluid motion is due to the reaction of c

species within the fluid, usually dissolved ions, to the applied field.
20

The motion of charged particles in an applied electric field.

electrophoretic mobility (static, dynamic)

The electrophoretic velocity per unit field strength, symbol 	e=v/E; 	

positive if the particle moves toward lower potential and negative in 

opposite direction. When measured in a d.c. electric field, 	e is referr

the static mobility. When measured in a high-frequency field it is refe

the dynamic mobility, and given the symbol 	d or 	(). Dynamic mo

may be a complex quantity at high frequencies.

electroacoustics

Referring to the electric-acoustic coupling in a fluid containing charg

colloids or ions; an effect that is responsible for the electrokinetic son

amplitude, colloid vibration potential and ion vibration potential.

acoustophoresis

The induced motion of particles subjected to an acoustic field. Charg

particles will generate an electric field as a result of this motion

(see ultrasonic vibration potential).

ultrasonic vibration potential (UVP)

When a sound wave propagates through a fluid containing charged pa

(ions or colloids), coherent acoustophoretic motion of the particles cr

alternating dipoles that generate a macroscopic potential difference te

ultrasonic vibration potential. 

ion vibration potential (IVP)

The ultrasonic vibration potential of an ionic solution; also known as 

Debye effect. 

colloid vibration current (CVI)

The alternating electrical current generated by the vibration potential 

colloidal suspension. The CVI is related to dynamic mobility of the p

related to colloid vibration potential.

colloid vibration potential (CVP)

The ultrasonic vibration potential of a colloidal suspension. The resu

potential difference is related to the dynamic mobility of the particles

cal effect to electrokinetic sonic amplitude.
When a high-frequency alternating electric field is applied to a disp

charged colloids, the oscillatory electrophoretic motion of the parti

to the surrounding medium results in a measurable acoustic field w

tude is related to the dynamic mobility; reciprocal effect of colloid v

potential. The phase difference between the applied field and the re

acoustic response can also be used to estimate the particle size distr

11	
"!$	'

amphoteric

Refers to a type of surface in which the same surface group (reactiv

able to function as both an acid and a base. That is, the site may dis

release a proton or accept a proton. 

zwitterionic

Refers to a type of surface in which two distinct surface groups (rea

are present. One is capable of dissociating to release a proton (acid 

the other is capable of accepting a proton (base group).

hydrophilic

May be used to describe the character of interaction of a particular 

group (or substance) with an aqueous medium. In this usage the ter

relative qualitative meaning of "water loving." The more general te

lyophilic ("solvent loving"), is used to distinguish a class of colloid

hydrophobic

The tendency of hydrocarbons (or of lipophilic hydrocarbon-like gr

solutes) to form intermolecular aggregates in an aqueous medium, 

analogous intramolecular interactions. In this usage the term has th

qualitative meaning of "water fearing." The more general term, lyop

("solvent fearing"), is used to distinguish a class of colloidal system

indifferent electrolyte [supporting electrolyte]

An ionic solution, whose constituents are not electroactive (i.e., the

significant effect on the surface potential of the material under stud

oxidative or reductive capacity) in the range of applied potentials bei

and whose ionic strength (and, therefore, contribution to the conduc

usually much larger than the concentration of an electroactive subst

dissolved in it. The ions constituting an indifferent electrolyte are s

exhibit no specificity for the particle surface.
22

A measure of electrolyte concentration given by I=1⁄2ci zi

2, where ci 

concentrations, in moles per liter, of the individual ions, i, and zi are t

charge numbers.

Debye-Hückel parameter

A parameter in the Debye-Hückel theory of electrolyte solutions, den

For aqueous solutions at 25 oC, =3.288I in reciprocal nanometers, 

is the ionic strength. See double layer thickness.

double layer compression [screening]

Increasing ionic strength causes the electrical potential near a charged 

to fall off more rapidly with distance. This is referred to as double lay

pression or screening, because the double layer thickness shrinks as t

Debye-Hückel parameter increases with increasing ionic strength.

electroviscous effects

For dispersions of charged particles, these are those components of th

viscosity connected with the charge on the particles.

suspension effect

The Donnan e.m.f. between a suspension and its equilibrium liquid. T

effect is most commonly encountered with pH measurements in collo

suspensions.

potentiometric analysis

Analysis based on the measurement of electrical potential using, for e

a pH or ion-selective electrode. Potentiometry is often combined with

titrimetric analysis in the determination of particle surface charge.

titrant

The solution containing the active agent with which a titration is mad

titration

The process of determining the amount of a substance A by adding in

of substance B with provision for some means of recognizing the poi

which all of A has reacted. This allows the amount of A to be found f

known amount of B added up to this point.

titrimetric analysis

Analysis of test sample properties based on titration.
3	'!	) 

Compendium of Chemical Terminology - IUPAC Recommendations

by V. Gold, K.L. Loening, A.D. McNaught, and P. Sehmi, Blackwe

Publications, Oxford, UK, 1987.

L.L. Schramm, The Language of Colloid and Interface Science - A 

of Terms, American Chemical Society, Washington, DC, 1993.

R.J. Hunter, Foundations of Colloid Science, Volume 1, Oxford Un

Press, Oxford, UK, 1989.

P.C. Hiemenz and R. Rajagopalan, Principles of Colloid and Surfac

Chemistry, 3rd Edition, Marcel Dekker, NY, 1997.

G.Y. Onoda and L.L. Hench, "Physical Characterization Terminolog

5, pp. 35-37 in Ceramic Processing Before Firing, Edited by G.Y. 

L.L. Hench, John Wiley & Sons, NY, 1978.

3	$	) 

Adsorption of Inorganics at Solid-Liquid Interfaces, Edited by M.A

and A.J. Rubin, Ann Arbor Science Publishers, Ann Arbor, MI, 198

Chemical Processing of Ceramics, Edited by B.I. Lee and E.J.A. Po

Dekker, NY, 1994.

Sample Preparation for the Determination of Particle Size Distribu

Ceramic Powders, ISO/DIS 14703, 1998.

Particle Size Analysis: Dispersing Agents for Powders in Liquids, I

Working Document 14887, 1997.

Surface and Colloid Chemistry in Advanced Ceramics Processing, 

R.J. Pugh and L. Bergström, Marcel Dekker, NY, 1994.

Ultrasonic and Dielectric Characterization Techniques for Suspend

Particulates, Edited by V.A. Hackley and J. Texter, American Ceram

Westerville, OH, 1998.
24

D.F. Evans and H. Wennerström, The Colloidal Domain, VCH Publis

1994.

E.K. Fischer, Colloidal Dispersions, John Wiley & Sons, NY, 1950.

R.J. Hunter, Zeta Potential in Colloid Science - Principles and Applic

Academic Press, NY, 1981.

D. Myers, Surfaces, Interfaces, and Colloids - Principles and Applica

Chapter 10, "Colloids and Colloidal Stability," VCH Publishers, NY, 

D.H. Napper, Polymeric Stabilization of Colloidal Dispersions, Acade

Press, NY, 1983.

R.H. Ottewill, "Stability and Instability in Dispersed Systems," Journ

Colloid and Interface Science, 58, 357-373 (1977).

Th.F. Tadros, "Control of the Properties of Suspensions," Colloids an

Surfaces, 18, 137-173 (1986).

 2%"4'%$

A number of terms were included courtesy of the American Chemical 

from the book by L.L. Schramm. Some definitions contained in the

Compendium of Chemical Terminology were used, in part or in whol

tesy of the International Union on Pure and Applied Chemistry.

$	&	
+

James H. Adair, Merrilea J. Mayo

The Pennsylvania State University, Particulate Materials Center

Jon A. Casey

IBM, Materials Technology

Robert A. Condrate

Alfred University, New York State College of Ceramics

Matthew Frey, William Hunt, Thomas Wood

3M Company, Ceramic Technology Center
National Institute of Standards and Technology, Ceramics Division

Robert J. Hunter

University of Sydney, School of Chemistry, Australia

George W. Scherer

Princeton University, Department of Chemical Engineering

Ponisseril Somasundaran

Columbia University, Langmuir Center for Colloids and Interfaces
26

(	)%!'%$!"	
"4 !"	#$

elastic A conservative property in which part of the mechanical ener

to produce deformation is stored in the material and recovered on rele

stress.

electroviscous The collective effects by which the presence of an el

double-layer influences the flow behavior of a liquid. The double-laye

usually associated with charged particles suspended in the liquid or

polyelectrolytes dissolved in solution. There are three electroviscous 

primary The increase of fluid viscosity due to distortion of the 

layer during shear. Distortion exerts a drag, increasing energy dis

secondary The increase of fluid viscosity due to the interaction 

overlap of adjacent double-layers. Responsible for the formation 

gelatin.

tertiary The variation in fluid viscosity that arises from geomet

changes within the fluid due to double-layer interactions. The vis

of a polyelectrolyte solution depends on the conformation of the 

molecules, which in turn is affected by intramolecular electrostati

interactions between charged segments located along the polymer

backbone or on side chains.

plastic The property of a solid body that is in the elastic state when 

is below a critical value, termed the yield stress, and in the plastic sta

this value is exceeded. During ideal plastic flow, energy dissipation a

are independent of the rate of deformation.

viscoelastic A time-dependent property in which a material under st

produces both a viscous and an elastic response. A viscoelastic mater

exhibit viscous flow under constant stress, but a portion of mechanica

is conserved and recovered after stress is released. Often associated w

polymer solutions, melts and structured suspensions, viscoelastic prop

are usually measured as responses to an instantaneously applied or re

constant stress or strain or a dynamic stress or strain.

viscoelectric An effect by which the electric field near a charged int

influences the structure of the surrounding fluid and thereby modifies 

viscosity of the fluid.
some critical stress value, the yield stress, but flows like a viscous l

this stress is exceeded. Often associated with highly aggregated sus

and polymeric gels.

viscous The tendency of a liquid to resist flow as a result of intern

During viscous flow, mechanical energy is dissipated as heat and th

that develops depends on the rate of deformation.

(	)% $%!"	'	&	5 $

Viscosity nomenclature related to oscillatory measurements is defin

general terms, but are described more explicitly in section 8.

apparent viscosity, app The value of viscosity evaluated at some 

average value of the shear rate. The apparent viscosity applies, for 

the capillary method, where a range of shear rates are employed.

coefficient of fluidity [fluidity],  Reciprocal of the coefficient of 

= 1 / 

coefficient of viscosity [viscosity],  The ratio of shear stress to s

under simple steady shear. The abbreviated form "viscosity" is used 

often in practice, and is frequently employed without discriminating 

Newtonian and non-Newtonian behavior. When the quotient is inde

of shear rate (i.e., follows the Newtonian model), it is considered a 

constant. When the quotient is dependent on shear rate (i.e., non-Ne

it should be referred to as the non-Newtonian viscosity. 

complex viscosity, * The frequency-dependent viscosity functio

mined during forced harmonic oscillation of shear stress; contains 

and imaginary parts.

differential viscosity, diff The derivative of shear stress with re

shear rate.

   /  diff

   / 
28

determined during forced harmonic oscillation (dynamic) measureme

real part of the complex viscosity.

= G / 

infinite shear viscosity,  The high shear rate limiting value of vi

Often associated with the second Newtonian region in pseudoplastic f

inherent viscosity [logarithmic viscosity], inh A natural logarithm

function of the relative viscosity reduced by the solute concentration.

intrinsic viscosity [limiting viscosity number], [] The zero conce

limiting value of the reduced specific viscosity. A characteristic functi

the single molecule in solution. [] is equivalent to the effective hydr

specific volume for the solute.

kinematic viscosity, The ratio of the viscosity of a fluid to its den

 = s / 


out-of-phase viscosity,   The ratio of the storage modulus to the 

frequency, determined during forced harmonic oscillation (dynamic) 

ments. The imaginary part of the complex viscosity.

= G / 

plastic viscosity, pl For a Bingham model, the excess of the shear 

over the yield stress divided by the shear rate, and equal to the differ

viscosity. For non-ideal Bingham materials, the differential viscosity de

in the high-shear limiting, linear portion of the flow curve; associated 

viscoplastic fluids.

c

r

inh

 ln 

red c

 

0

[ ] lim





  



     

lim / pl
tion to the concentration, c, of the solute or particulate phase. By no

viscosity in this way, concentration effects become more apparent. 

instance, the reduced specific viscosity is:

relative viscosity [viscosity ratio], r Ratio of the viscosity in a s

or solution to the viscosity of the suspending medium or solvent.

specific viscosity, sp The relative viscosity minus unity.

zero shear viscosity, 0 The low shear rate limiting value of visc

Associated with the first Newtonian region in many pseudoplastic f

((	"!	&	.! 	'%"4

apparent yield stress For non-ideal viscoplastic materials, where 

stress is indefinite, an apparent yield stress can be defined, for exam

extrapolation from the linear, high-shear-rate portion of the flow cu

stress axis. (see Bingham relation)

compliance The quotient of strain and stress (e.g., shear complian

reciprocal of modulus.

deformation Movement of parts or particles of a material body re

one another such that the continuity of the body is not destroyed, re

change of shape or volume or both.

dilatant A property often associated with suspensions of irregular

particles, in which the liquid exhibits an increase in volume while b

sheared. The term is also used in common practice to mean shear-t

the increasing resistance to shear with increasing shear rate. It is po

either of these two effects to exist in the absence of the other.

c red sp   /

r  S  /

 !1 sp r

 

 0 0 lim

 
30

ance to obtain a quasi-equilibrium condition. Dynamic equilibrium is 

during steady shear flow when break down and rebuilding of structur

at similar rates, and the viscosity is constant at a given shear rate.

dynamic [oscillatory] shear flow Condition under which stress and 

vary harmonically with time during a rheometric experiment.

Einstein's Law of Viscosity Describes the relationship between the 

of a dilute dispersion and the volume fraction of the dispersed particl

relationship is derived with two major assumptions, that the particles 

spheres and that their concentration is very low. 

where S is the viscosity of the suspending medium and  is the volu

fraction. The factor 2.5 is known as the Einstein coefficient. To desc

concentrated dispersions, higher terms in the power series have been 

and analyzed with varying success.

equilibrium [steady state] flow Condition under which a constant s

shear rate is maintained for a sufficient time to allow dynamic equilib

be achieved in a fluid containing time-dependent structure. An equilib

flow curve can be used to characterize the time-independent flow prop

a material.

elastic modulus [modulus of elasticity] A modulus of a body that o

Hooke's law.

flow Continuously increasing deformation of a material body under 

action of finite forces. When the force is removed, if the strain does n

tually return to zero, then flow has occurred.

flow curve A graphical representation of the behavior of flowing ma

which shear stress is related to shear rate.

Hooke's law Provides that the quotient of stress and strain (i.e., the 

is a constant. A body obeying Hooke's law cannot be viscoelastic nor 

flow occur.

laminar flow Flow without turbulence.

1 2.5 ....

S

 "  "




is defined by the type of deformation employed (e.g., shear modulu

deformation).

Navier-Stokes equations The equations of motion for a Newtonia

model describing the balance between external forces (like gravity)

pressure force and the viscous force.

Newtonian Flow model of fluids in which a linear relationship ex

between shear stress and shear rate, where the coefficient of viscos

constant of proportionality.

no-slip Condition in which fluid adjacent to a surface moves with 

velocity of that surface. The assumption of no-slip is key to most rh

measurements. Slippage is a significant concern in concentrated sus

non-equilibrium flow Condition under which shear is varied at a 

does not permit dynamic equilibrium to be achieved. A thixotropic 

result of non-equilibrium flow conditions during shear cycling.

non-Newtonian Any laminar flow that is not characterized by a li

relationship between shear stress and shear rate.

normal stress, n The component of stress that acts in a direction 

to the plane of shear.

Peclet number, Pe A dimensionless group used to compare the ef

applied shear with the effect of thermal (Brownian) motion; Pe=r2 

where r is the particle radius and D is the translational diffusion co

For Pe << 1, particle behavior is dominated by diffusional relaxati

for Pe >>1, hydrodynamic effects dominate.

Poiseuille flow Laminar flow in a pipe of circular cross section un

constant pressure gradient. (see also Capillary Methods)

Reynolds number, Re A dimensionless group that expresses the r

inertial forces to the viscous forces; Re=D 
/, where D is a chara

length (e.g., particle size or pipe diameter), is a typical fluid spee

is the kinematic viscosity of the fluid. The transition from laminar t

flow is characterized by high Re values.


32

rheometric Refers to the measurement of rheological properties.

shear The relative movement of parallel adjacent layers.

shear compliance, J The ratio of shear strain to its corresponding s

stress. The reciprocal of shear modulus.

shear modulus [modulus of rigidity], G The ratio of shear stress t

corresponding shear strain. The reciprocal of shear compliance.

shear rate (rate of shear strain), The rate of change of shear str

time (d/ dt). For liquids, the shear rate, rather than strain, is genera

in describing flow.

shear stress,  The component of stress that causes successive para

layers of a material body to move, in their own planes (i.e., the plane 

shear), relative to each other.

shear strain,  The relative in-plane displacement, #x, of two parall

in a material body divided by their separation distance, y. Alternative

shear strain can be defined as tan $, where $ is the angle of deformat

shown in Figure 1.

shear-thickening An increase in viscosity with increasing shear rat

steady shear flow. The term dilatant is commonly used in practice to 

shear-thickening, although this usage is strictly incorrect.

shear-thinning [pseudoplastic] A decrease in viscosity with increas

shear rate during steady shear flow.

4		!	$!%	 '!$ 


the plane of shear, and the relative displacement of successive para

of a material body are proportional to their distance from a referenc

The type of flow used in most rheometric measurements on fluids c

approximated by simple shear.

steady shear flow Condition under which a fluid is sheared contin

one direction during the duration of a rheometric experiment.

stress Force per unit area.

structure In rheology, structure is a term that refers to the formatio

physical bonds between particles (or chemical bonds between macr

cules) in a fluid. These bonds result in aggregate, floc, or network s

which impacts the rheological behavior of the fluid and provides el

plastic properties. The term may be extended to include structural e

caused by electroviscous interactions, physical bonds between poly

(e.g., associative thickeners), shear-induced alignment of anisotropi

and close-packing (radial distribution) correlations in concentrated s

The term "structure" is commonly invoked even when little is know

cause of observed changes in rheological properties.

Weissenberg effect The tendency of some viscoelastic fluids to fl

direction normal to the direction of shear. The effect is manifested 

such as the climbing of a fluid up a rotating rod.

Weissenberg number, Wi A measure of the degree of nonlinearity 

degree to which normal stress differences are exhibited in a flow. F

simple shear, the Weissenberg number is the product of the shear r

characteristic time of the fluid. In oscillatory shear it is the product 

shear rate amplitude and the characteristic time of the fluid. In conv

flows it is proportional to the Deborah number.

yield response For non-ideal viscoplastic materials, the yield stres

indefinite and yielding may occur continuously over a narrow range 

values. In this case, the behavior may be more properly termed a yi

response.

yield stress, y A critical shear stress value below which an ideal 

viscoplastic material behaves like a solid (i.e., will not flow). Once 

stress is exceeded, a plastic material yields (deforms plastically) wh

viscoplastic material flows like a liquid.
34

Steady-shear flow curves for suspensions and solutions measured und

librium conditions may exhibit a variety of behaviors over a limited r

shear rates. Additionally, some materials may exhibit more than one 

behavior over different shear rate regions of the same flow curve. Sev

types of behavior can be classified according to their characteristic sh

following classification system covers the six most frequently encoun

flow types as illustrated in the accompanying graph.

1. Newtonian Differential viscosity and coefficient of viscosity are c

with shear rate.

2. shear-thickening Differential viscosity and coefficient of viscosity 

continuously with shear rate.

3. shear-thinning [pseudoplastic] Differential viscosity and coeffic

viscosity decrease continuously with shear rate. No yield value.

4. shear thinning [pseudoplastic]

with yield response Differential

viscosity and coefficient of viscosity

decrease continuously with shear

rate once the apparent yield stress,

app, has been exceeded.

5. Bingham plastic (ideal)

Obeys the Bingham relation

ideally. Above the Bingham

yield stress (B in Figure 2) the

differential viscosity is constant

and is called the plastic viscosity,

while the coefficient of viscosity

decreases continuously to some

limiting value at infinite shear

rate.

6. Bingham plastic (non-ideal) Above the apparent yield stress the

coefficient of viscosity decreases continuously, while the differential v

approaches a constant value with increasing shear rate. Extrapolation 

flow curve from the linear, high shear rate region (plastic region) to th

4			
%$& !$%	&	&"

*!	%	$	 !! $$ 
differential viscosity in the linear region is termed the plastic viscos

(1	7#%	&	 *%4	$!	!	%8

"

The expressions shown in this section are used to characterize the n

Newtonian behavior of fluids under equilibrium, steady shear flow 

Many phenomenological and empirical models have been reported 

ature. Only those having a direct and significant implication for sus

gels and pastes have been included here. A brief description of each 

ship is given with examples of the types of materials to which it is 

applied. In defining the number of parameters associated with a par

model, the term "parameter" in this case refers to adjustable (arbitra

constants, and therefore excludes measured quantities. Some of the

equations have alternative representations other than the one shown

detailed descriptions and alternative expressions can be found in th

listed in the bibliography.

Bingham

The Bingham relation is a two parameter model used for describing 

fluids exhibiting a yield response. The ideal Bingham material is an 

solid at low shear stress values and a Newtonian fluid above a criti

called the Bingham yield stress, B. The plastic viscosity region ex

linear relationship between shear stress and shear rate, with a const

differential viscosity equal to the plastic viscosity, pl.

Carreau-Yasuda

A model that describes pseudoplastic flow with asymptotic viscosit

(0) and infinite () shear rates, and with no yield stress. The par

is a constant with units of time, where 1/% is the critical shear rate a

viscosity begins to decrease. The power-law slope is (n-1) and the p

B

B pl

  0 for  & 

   "  





) * ' ( ' ( n a a 1 /

0

1 !



  " !

! %

 

  
36

region. If 0 and  are not known independently from experiment, 

quantities may be treated as additional adjustable parameters.

Casson

A two parameter model for describing flow behavior in viscoplastic fl

exhibiting a yield response. The parameter y is the yield stress and 

differential high shear (plastic) viscosity. This equation is of the same 

the Bingham relation, such that the exponent is 1/2 for a Casson plast

for a Bingham plastic.

Cross

A model, similar in form to the Carreau-Yasuda relation, that describ

pseudoplastic flow with asymptotic viscosities at zero (0) and infini

shear rates, and no yield stress. The parameter % is a constant with un

time, and m is a dimensionless constant with a typical range from 2/3 

0 and  are not known independently from experiment, these quan

may be treated as additional adjustable parameters.

Ellis

A two parameter model, written in terms of shear stress, used to repr

pseudoplastic material exhibiting a power-law relationship between s

stress and shear rate, with a low shear rate asymptotic viscosity. The p

2 can be roughly identified as the shear stress value at which  has f

half its final asymptotic value.

Herschel-Bulkley

y

1/ 2 1/ 2

pl

1/ 2

y

1/ 2

  0 for  & 

   "  





' ( m

0 1

1

" %   ! 

 ! 







1

2

0

1

+!






 







" 



 

n   y " k
yield response with a power-law relationship between shear stress a

rate above the yield stress, y. A plot of log ( - y) versus log g

n that differs from unity. The Herschel-Bulkley relation reduces to 

tion for a Bingham plastic when n=1.

Krieger-Dougherty

A model for describing the effect of particle self-crowding on suspe

cosity, where , is the particle volume fraction, ,m is a parameter r

the maximum packing fraction and [] is the intrinsic viscosity. For 

spherical particles []=2.5 (i.e., the Einstein coefficient). Non-sphe

highly charged particles will exhibit values for [] exceeding 2.5. T

[] is also affected by the particle size distribution. The parameter ,

function of particle shape, particle size distribution and shear rate. 

and ,m may be treated as adjustable model parameters.

The aggregate volume fraction (representing the effective volume o

particle aggregates, including entrapped fluid) can be determined u

equation if ,m is fixed at a reasonable value (e.g., 0.64 for random 

ing or 0.74 for hexagonal close packing) and [] is set to 2.5. In thi

the adjustable parameter and is equivalent to the aggregate volume 

Meter

A model, expressed in terms of shear stress, used to represent a pse

material exhibiting a power-law relationship between shear stress a

rate, with both high () and low (0) shear rate asymptotic viscos

The parameter 2 can be roughly identified as the shear stress value 

 has fallen to half its final asymptotic value. The Meter and Carre

models give equivalent representations in terms of shear stress and 

respectively. If 0 and  are not known independently from exper

these quantities may be treated as additional adjustable parameters.

[ ] m

m r 1

!  ,






 





,   ! ,

' ( 1

2

0

1 +!





"  

 !     "


38

Derived from the theory of rate processes, this relation is relevant pri

to molecular fluids, but can be used in some cases to describe the visc

behavior of polymer solutions and viscoelastic suspensions over a wi

of shear rates. Here,  is the infinite shear viscosity, 0 is the zero s

viscosity and the fitting parameter - represents a characteristic time o

measured system. If 0 and  are not known independently from ex

ment, these quantities may be treated as additional adjustable parame

power-law [Ostwald-de Waele]

A two parameter model for describing pseudoplastic or shear-thicken

behavior in materials that show a negligible yield response and a vary

differential viscosity. A log-log plot of  versus gives a slope n (the 

law exponent), where n<1 indicates pseudoplastic behavior and n>1 i

shear-thickening behavior.

(3	'8#%%$	&& $

Time-dependence includes those effects associated with transient flow 

tions as well as those effects associated with irreversible changes that 

from shear history.

creep The response of a material to the instantaneous application of 

constant stress. 

creep function In an applied stress test, where an instantaneous and 

stress is applied to a material while the shear rate (or shear strain) is m

over time, the shear rate (or strain) vs. time function is termed the cre

function. The function J(t)=(t)/F is referred to as the creep complian

Deborah number, De The ratio of a characteristic relaxation time o

material to the duration of the observation. In equilibrium flow, the ef

duration of the experiment is infinity, and De=0. In oscillatory shear, 

product of the frequency and the relaxation time of the fluid. In conv

flows, the Deborah number is proportional to the Weissenberg numbe

' ( ' (

-

-    "  ! 

!

  

 1

0

sinh

n   K


dissipation due to shear history. In a typical rheometric test, shear s

shear rate is ramped at a fixed speed up to a maximum value, then 

back down at the same speed to the beginning. In hysteresis, one flo

lies above the other, forming a continuous loop whose internal area 

on the shear and thermal history of the material, and on how rapidly 

or shear rate was ramped. If the down-curve lies below the up-curv

referred to as a thixotropic loop, whereas if the down-curve lies abo

curve, then it is called a negative thixotropic loop.

negative thixotropy [anti-thixotropy] A reversible time-depende

in viscosity at a particular shear rate. Shearing causes a gradual gro

structure over time.

relaxation time, - A time characterizing the response of a viscoel

material to the instantaneous application of a constant strain.

retardation time, - A time characterizing the response of a viscoe

material to the instantaneous application of a constant stress.

rheomalaxis An irreversible decrease of viscosity during shearing

to permanent changes in the material structure.

rheopexy An effect by which a material recovers some of its pre-

cosity at a faster rate when it is gently sheared compared to when it 

to stand. Not to be confused with negative thixotropy.

stress growth When an instantaneous and constant strain (or shea

applied to a material while stress is measured over time, an increasi

vs. time or modulus vs. time function is termed stress growth.

stress relaxation When an instantaneous and constant strain (or s

is applied to a material while stress is measured over time, a decrea

vs. time or modulus vs. time function is termed stress relaxation.

thixotropy A reversible time-dependent decrease in viscosity at a 

shear rate. Shearing causes a gradual breakdown in structure over 

(9	 ""!$	!)'%$

forced harmonic oscillation is a dynamic rheometric test in which 

and strain vary harmonically with time, and both viscous and elasti
40

ried out in the linear viscoelastic regime, which is characterized by a 

response of dynamic viscosity and elasticity with increasing strain am

(9	!$!"	)% $%	+	&'	 ""!$	$	

In a typical sinusoidal oscillation experiment, the applied stress and r

strain wave forms can be described as follows:

where 0 is the stress amplitude

0 is the strain amplitude

=2.f is the angular frequency

t is time

/ is the phase lag (loss angle)

The phase lag and amplitude ratio (0/0) will generally vary with fre

but are considered material properties under linear viscoelastic condit

an ideal solid, /=0o, and the response is purely elastic, whereas for a

Newtonian fluid yielding a purely viscous response, /=90o.

The material functions can be described in terms of complex variable

both real and imaginary parts. Thus, using the relationship:

   ' (  ! /

   

cos t

cos t

0

0

4	(		%)!"	!+	&'	&	$	!%	$!%	&)% 
Then the stress and strain can be expressed as follows:

where (0e-j/) is termed the complex strain amplitude. The shear 

modulus [or storage modulus, for short], which represents the in-ph

(elastic) component of oscillatory flow, is defined as: 

The out-of-phase (viscous) component is termed the shear loss mo

[or loss modulus, for short]:

The complex shear modulus, G*, is then defined as follows:

so that:

The function G"/G' measures the

relative importance of viscous to

elastic contributions for a material

at a given frequency.

Additionally, a complex viscosity, *,

can be defined using the complex strain

rate, = j, such that:

where j 1 !

' (

' ( ' (' ( j t j j t

j t

e e e

e

 / / 



  

 

! !  0  0

 0

0 0

0

/



 G  storage  cos

0

0 modulus

/



 G  loss  sin

0

0 modulus

/



 / "



   cos jsin

complex strain amplitude

complex stress amplitude G*

0

0

0

0

Tan G G

G* G jG

/   

  " 

4	0		5 $!"	

$!$%	&	'

   



   /

j

G *

e

complex strain rate amplitude j

complex stress amplitude * j

0

0


42

where ' is termed the dynamic viscosity, and is equivalent to the rati

stress in phase with the rate of strain (0 sin /) to the amplitude of th

strain (0). The term '' is referred to as the out-of-phase viscosity, a

equivalent to the ratio of the stress 90° out of phase with the rate of s

cos /) to the amplitude of the rate of strain (0) in the forced oscilla

Finally, an absolute shear modulus is defined as the ratio of the amp

the stress to the amplitude of the strain in forced oscillation (simple s

Alternatively, forced oscillation experiments can be equivalently desc

terms of compliance, as opposed to the derivation above based on the 

lus. Similar arguments lead to the following analogous terms:

complex shear compliance, J* The ratio of the complex strain (*) 

complex stress (*) in forced oscillation (simple shear).

shear storage compliance, J' The ratio of the amplitude of the strai

phase with the stress (0 cos /) to the amplitude of the stress (0) in f

oscillation (simple shear).

shear loss compliance, J'' The ratio of the amplitude of the strain 9

phase with the stress (0 sin /) to the amplitude of the stress (0) in f

oscillation (simple shear).

absolute shear compliance, |J*| The ratio of the amplitude of the st

to the amplitude of the stress (0) in forced oscillation (simple shear)

 

 

  

G

G

j

  

  

*   ! 

2 2 1 2

0

0 G *  (G " G )



 
There are two common methods used for rheometric measurements 

systems: capillary (or tube) and rotational. In this section, a brief su

given for each general method along with descriptions of common 

ment devices and geometries. Measurement devices can be grouped 

of two general classifications. A viscometer is a device used princi

the measurement of viscosity, while a rheometer is a device used f

measurement of rheological properties over a varied and extended r

conditions. More detailed descriptions of these instruments and me

be found in the primary sources listed in the bibliography. Only a b

coverage is provided here.

(:	!#""!	$

In capillary methods the test fluid is made to flow through a narrow 

a result of hydrostatic or applied pressure. Capillary measurements 

considered the most precise way of determining the viscosity of Ne

and some non-Newtonian viscous fluids, and are generally simpler 

and less expensive relative to rotational instruments. Poiseuille's L

relates the rate of flow through a capillary to the viscosity of the liq

basis for the capillary method.

Glass Capillary Viscometer

Widely used for measuring the viscosity of Newtonian fluids, inclu

solutions and suspensions, the glass capillary viscometer is the simp

least expensive viscometric system available commercially. Typical

technique, the time required for a given volume of fluid to flow thr

defined length, L, of glass capillary under its own

hydrostatic head is measured. The flow time, t, is

related to the viscosity using a simple relationship

derived from Poiseuille's Law, of the form:

t

B  At "






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44

side is related to the kinetic energy correction, and can be ignored for 

flow times. In this case, a simple linear equation results. The viscome

be easily calibrated using a standard fluid with known viscosity at the

measurement temperature. Capillaries with different diameters can be 

different viscosity ranges, while maintaining reasonable flow times.

Extrusion Capillary Viscometer

These instruments are widely used for measuring viscous fluids, such 

asphalt cements, polymer melts, and stable concentrated suspensions.

Extrusion viscometers have the advantage of high precision and simp

and are less subject to temperature effects that can occur during shear

highly viscous fluids in rotational devices. 

Extrusion viscometers use a cylindrical piston to force the test fluid f

reservoir through the capillary tube at a constant velocity. By measur

pressure drop across the capillary as a function of flow rate for multip

capillaries of the same diameter, d, but differing length, L, it is possib

determine the viscosity as a function of shear rate. 

(:	
$!$%!"	$

In rotational methods the test fluid is continuously sheared between tw

surfaces, one or both of which are rotating. These devices have the ad

of being able to shear the sample for an unlimited period of time, per

transient behavior to be monitored or an equilibrium state to be achie

under controlled rheometric conditions. Rotational methods can also 

rate oscillatory and normal stress tests for characterizing the viscoela

properties of samples. In general, rotational methods are better suited 

measurement of concentrated suspensions, gels and pastes, but are ge

less precise as compared to capillary methods. 

4	3		!4!'	&	!	'#"	7$)%	+ '$
rate-controlled. In stress-controlled measurements, a constant torq

applied to the measuring tool in order to generate rotation, and the 

rotation speed is then determined. If a well-defined tool geometry i

rotation speed can be converted into a corresponding shear rate. In 

controlled measurements, a constant rotation speed is maintained an

resulting torque generated by the sample is determined using a suita

sensing device, such as a torsion spring or strain gauge. Some comm

instruments have the capability of operating in either stress-controll

rate-controlled modes.

Simple Rotational Viscometer ("Brookfield type")

The least expensive commercial variant of the controlled-rate rotati

viscometer is commonly referred to as a "Brookfield type" viscome

device measures fluid viscosity at fixed rotation speeds by driving a

measurement tool ("spindle"), immersed in the test fluid, through a

calibrated torsion spring. Viscous drag of the fluid against the spind

the spring to deflect, and this deflection is correlated with torque. T

calculated shear rate depends on the rotation speed, the tool geome

he size and shape of the sample container. Conversion factors are n

to calculate viscosity from the measured

torque, and are typically pre-calibrated for

specific tool and container geometries. For

Newtonian fluids the torque is proportional

to the product of viscosity and rotational

speed, but this proportionality is lost in the

case of a non-Newtonian fluid. Because

these instruments are robust and fairly

simple to use, they have found wide

application in industry, but they offer

limited capabilities and precision for

research-oriented applications. 

Rotational Rheometer

High-precision, continuously-variableshear instruments in which the test fluid

is sheared between rotating cylinders,

cones or plates, under controlled-stress

or controlled-rate conditions, are termed

rotational rheometers. Instruments

producing oscillatory strains are

available, and a few commercial

4	9		 '!$ 

&	!	.2&"

+ '$
46

consists of four parts: (i) a measurement tool with a well-defined geo

(ii) a device to apply a constant torque or rotation speed to the tool ov

wide range of shear stress or shear rate values, (iii) a device to deter

stress or shear rate response, and (iv) some means of temperature con

the test fluid and tool. Depending on the design specifications, rheom

also include built-in corrections or compensations for inertia, drift, an

perature fluctuations during measurement.

Most rheometers are based on the relative rotation about a common a

one of three tool geometries: concentric cylinder, cone and plate or pa

plates (See Figure 8).

In the concentric cylinder (also called Couette or Coaxial) geometr

the inner, outer or both cylinders may rotate, depending on instrumen

The test fluid is maintained in the annulus between the cylinder surfa

tool geometry comes in several configurations, of which the three mo

monly encountered are illustrated in Figure 9. The double-gap config

is useful for low viscosity fluids, as it increases the total area, and the

the viscous drag, on the rotating inner cylinder, and generally increas

accuracy of the measurement. The cone and hollow cavity configurat

specifically designed to reduce or account for end effects. In addition

prevent slippage, the inner cylinder surface is sometimes serrated or o

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of fluid suspensions.

The cone and plate geometry consists of an inverted cone in near 

with a lower plate. The cone is usually designed with an angle of le

Either the upper or lower surface may rotate depending on instrume

The parallel plate geometry can be considered a simplified versio

cone and plate, having an angle of 0°. The test fluid is constrained 

arrow gap between the two surfaces. Cone and plate and parallel pl

measurement tools are most often used for highly viscous pastes, g

concentrated suspensions.

(=	% $	!%	$	!8!%	!$!"

Ceramic materials are typically fabricated from particles in the sub

fine size range (i.e., less than roughly 37 	m), though coarse agglom

may play a role during some phase of processing. On the other han

is classified as a ceramic material, but containing a considerably br

of particle sizes, from less than one micrometer up to about 20 mm 

into the sieve range). This wide range results from the heterogeneou

composition, which includes cement (5 	m to 60 	m), mineral fille

to 100 	m), fine aggregates (0.1 mm to 5 mm) and coarse aggregat

to 30 mm or higher in some special concretes) or stones.

4	=		 '!$ 	!4!'	%4	$	!"$%!$+	 

$"	4%	%	 )$8!!	+<	,!-	)*"	4!#;	,*-	 %	

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48

As a result of the broad range of particle sizes and the presence of sie

particles, methods to measure the flow properties of concrete differ si

ly from those methods specified for applications involving suspension

particles. Test methods applied to concrete tend to be largely empirica

nature or they are scaled up versions of the techniques described in se

for fine particle suspensions. In the former case are the most common

tests in the industry; they generally represent an attempt to "imitate" a 

placement or flow of the concrete during production. In the latter cas

common methods that attempt to measure fundamental rheological pr

of concrete. In addition, rheological test methods for concrete tend to 

one of four general categories:

confined flow The material flows under its own weight or under an 

pressure through a narrow orifice. The orifice is defined as an openin

three to five times larger than the maximum particle size. Because co

aggregates are often of the order of 30 mm, the orifice must typically 

90 mm to 150 mm in diameter. Confined flow methods include flow c

filling ability devices, flow test through an opening and the Orimet ap

free flow The material either flows under its own weight, without an

confinement or an object penetrates the material by gravitational settl

flow methods include slump, modified slump, penetrating rod and tur

viscometer. 

vibration The material flows under the influence of applied vibratio

vibration is applied by using a vibrating table (e.g., Ve-Be time and re

test), dropping the base supporting the material (DIN slump cone test

external vibrator (e.g., LCL apparatus) or an internal vibrator (e.g., se

method). 

rotational rheometers The material is sheared between two paralle

surfaces, one or both of which are rotating. These tests are analogous 

rheometers described in section 9, except in this case the gap between 

must be scaled up to reflect the much larger dimensions of the concre

particles. Rotational rheometers include BTRHEOM, CEMAGREF, tw

or Tattersall, IBB, and BML.

Separate glossaries of rheological terms and test methods are provide

For more detailed summaries of the numerous rheological tests used t

out the concrete industry, including empirical tests that are widely im

ed, see Ferraris (1999) in the list of primary sources.
Much of the rheological work on concrete and other cementitious m

has, historically, been directed toward the practical exploitation of t

and, as a result, numerous terms are in common use that are unique 

concrete, mortar and cement industries. The most frequently encoun

rheological terms are defined here.

consistency The relative mobility or ability of freshly mixed conc

mortar to flow; the usual measurements are slump for concrete, flow 

mortar or grout, and penetration resistance for neat cement paste. (s

consistency, plastic consistency, wettest stable consistency)

consistency factor A measure of grout fluidity, roughly analogous 

viscosity, that describes the ease with which grout may be pumped 

or fissures; usually a laboratory measurement in which consistency 

in degrees of rotation of a torque viscometer in a specimen of grout

consolidation The process of inducing a closer arrangement of th

particles in freshly mixed concrete or mortar, during and after place

setting, by the reduction of voids. Consolidation is accomplished by 

centrifugation, rodding, tamping or some combination of these actio

term is also applicable to similar manipulation of other cementitiou

soils, aggregates or the like.

finishing Leveling, smoothing, consolidating and otherwise treatin

surfaces of fresh or recently placed concrete or mortar to produce th

appearance and service.

impending slough Consistency of a shotcrete mixture containing 

maximum amount of water such that the product will not flow or sa

placement.

mobility The ability of fresh mixed concrete or mortar to flow.

normal consistency (1) The degree of wetness exhibited by a fres

concrete, mortar, or neat cement grout when the workability of the 

considered acceptable for the purpose at hand. (2) The physical con

neat cement paste as determined with the Vicat apparatus in accord

standard test method (e.g., ASTM C 187).
50

concrete such that deformation will be sustained continuously in any 

without rupture.

slump A measure of consistency of freshly mixed concrete, mortar o

equal to the subsidence measured to the nearest 5 mm (1/4 in) of the 

specimen after removal of the slump cone.

wettest stable consistency The condition of maximum water conten

which cement grout and mortar will adhere to a vertical surface witho

sloughing.

workability [placeability] That property of freshly mixed concrete 

that determines the ease and homogeneity with which it can be mixed

consolidated and finished.

(=	"!	&	$	$

BML Commercial rotational rheometer derived from the two-point 

principle of operation is identical to the two-point test, but the shape 

vane has been modified. The vane is as shown in Figure 10(c).

4	>		5!)	+!%	4'$	)	%	 % $	'

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can be performed with and without applied vibration.

CEMAGREF Coaxial rotational rheometer originally developed 

fluid lava. It has been occasionally employed to test concrete. Only 

type currently exists.

DIN slump cone test A vibration method. A variation of the slump 

in which the cone is placed on a metal sheet. After filling the cone 

crete, it is lifted and the metal support sheet is raised on one side an

from a pre-established height (usually about 100 mm) a specified n

times. The spread of the concrete is measured. This standard test is 

in DIN 1045.

filling ability Confined flow method measuring the ability of conc

flow into a predefined form. Several different molds are used: U-sh

L-shaped are the most common. In both cases the concrete is forced 

to flow into and fill the mold. The volume occupied by the concrete 

end of the test is a measure of the ability of the concrete to flow or 

ability.

flow cone [V-funnel cone] Confined flow method consisting in fil

funnel with concrete or cement paste and determining the time for t

to flow out through the orifice. This time is a measure of the materi

to flow. There are several types of funnel, some with round and oth

parallel piped orifice and upper opening.

flow test Used in accordance with ASTM C1362. This test measu

of concrete or mortar into a perforated tube. This method is applica

concrete with coarse aggregates less than 37.5 mm in diameter. The 

consists of a hollow perforated tube that is inserted in the concrete 

after which the material is allowed to flow into the hollow tube. Th

the concrete in the hollow tube is considered a measure of the cons

the concrete.

IBB Commercially available rotational rheometer. It is derived fr

point test. The principle of operation is identical, but the vane shap

modified, and the vane moves in a planetary motion and on its axis

is shaped like the letter H and is shown in Figure 10(b).

LCL apparatus A vibration method. The concrete is poured behin

a large parallel piped container. The gate is opened and the vibrator 
52

measured. A longer time suggests a lower ability of the concrete to fl

modified slump test Modification of the slump test described in A

C143. It permits the measurement of the rate at which the concrete is

slumping, which gives an estimate of the concrete plastic viscosity. T

was developed at NIST, but is not currently a standard method (see F

(1999) in primary sources).

Orimet apparatus Confined flow method instrument consisting of a 

600 mm in length that is closed at the bottom by a removable trap do

time for the concrete to flow through the tube once the trap is released 

determined. This time is a measure of the ability of concrete to flow.

penetrating rod Free flow method measuring the distance a rod of f

mass can penetrate a concrete sample. It is a crude determination of w

the yield stress of the concrete is higher or lower than a predefined va

used to monitor concrete at the job site. A specific application of this 

Vicat apparatus. 

settling method [Fritsch test] A vibration method, this test measure

capability of concrete to consolidate under vibration. Concrete is plac

container with an internal vibrator. The time to obtain full consolidati

measured. The full consolidation is determined when the surface of th

concrete no longer moves.

slump cone test Free flow method in which a truncated metal cone, 

both ends and sitting on a horizontal surface, is filled with concrete a

gradually. The slump of the concrete is measured. This standard test i

described in ASTM C143.

turning tube viscometer Free flow method consisting of a tube 60 

diameter and 800 mm long that can be filled with cement paste or mo

ball is dropped into the fluid and its velocity is measured between tw

370 mm apart. Using the Stokes equation, the viscosity can be calcula

two-point test [Tattersall rheometer] First commercially available 

al rheometer for concrete. It is the first attempt to shear concrete at d

rates and to measure the induced stress. It consists of a bucket filled w

concrete and a vane, shown in Figure 10(a), that rotates at controlled 

The torque generated during rotation is measured.
shape under vibration. Concrete is placed in a slump cone. After the 

lifted away, the time it takes for the concrete to remold itself into a 

while under vibration is measured.

Vicat apparatus A free flow method, the Vicat apparatus is a pene

device used in the testing of hydraulic cements and similar material

full description of this instrument and the correct procedure to dete

normal consistency of cement is described in ASTM C187.

(>	%$	!%	'*"

(>	
'$ 	%$

All units should conform to the International System of Units (SI) a

by the National Institute of Standards and Technology.1 The use of 

other non-SI units is discouraged. For convenience, SI units are sho

Table 1 in association with their common non-SI equivalents (inclu

mal submultiples and conversion factors where appropriate). Table 

SI-derived units with their underlying base units.

!*"		
	!%	6)+!"%$	'$ 	)%$

Quantity SI Units Equivalent CGS U

viscosity Pa · s 10 P (poise) or 1000 cP (ce

kinematic viscosity m2 · s-1 104 St (stoke) or 106 cSt (c

shear stress Pa 0.1 dyn · cm-2

strain unitless

shear rate s-1 s-1

modulus Pa 0.1 dyn · cm-2

compliance Pa-1 10 cm2 · dyn-1

frequency Hz

angular frequency 2.f

phase angle rad

1 B.N. Taylor, Guide for the Use of the International System of Units (SI), NIST S

Publication 811, 2nd Edition, National Institute of Standards and Technology, U.S

Printing Office, Washington, DC, 1995.
54

Symbol Special Name Other SI Units SI Base U

Pa Pascal N · m-2 kg · m-1 · 

Hz Hertz s-1

rad radian m · m-1 =

(>	$	&	'*"

 shear stress

n normal stress

y yield stress

 strain

shear rate [rate of shear strain]

De Deborah number

Pe Peclet number

Re Reynolds number

 coefficient of viscosity [viscosity] 

app apparent viscosity

diff differential viscosity

 infinite shear viscosity

inh inherent viscosity

[] intrinsic viscosity

red reduced viscosity

r relative viscosity

s viscosity of suspending medium or solvent 

sp specific viscosity

0 zero shear viscosity

 kinematic viscosity

 fluidity

G shear modulus

G* complex shear modulus

G' shear storage modulus

G" shear loss modulus 

|G*| absolute shear modulus

1 complex viscosity

' dynamic viscosity (real component of the complex viscosit

" imaginary component of the complex viscosity


J* complex shear compliance

J' shear storage compliance

J'' shear loss compliance 

|J*| absolute shear compliance 

- relaxation time, retardation time

0 stress amplitude

0 strain amplitude

/ phase angle

 angular frequency

f frequency
56

This bibliography cites sources used in the compilation of this guide. 

nor is it intended to be, an exhaustive list of references available on th

subject of rheology or rheological instrumentation. Nevertheless, it m

as a good starting point for those who are relatively new to this field 

ing for relatively fundamental information.

(	'!	) 

American Concrete Institute, Cement and Concrete Terminology, ACI 

ACI Manual of Concrete Practice 2000, Part 1, Farmington Hills, M

British Standards Institution, Glossary of Rheological Terms, BS 516

A.A. Collyer and D.W. Clegg, Editors, Rheological Measurement, Ch

and Hall, London, 1998.

J.M. Dealy, "Official Nomenclature for Material Functions Describin

Response of a Viscoelastic Fluid to Various Shearing and Extensional

Deformations," Journal of Rheology, 39[1], 253-265 (1995).

C.F. Ferraris, "Measurement of the Rheological Properties of High

Performance Concrete: State of the Art Report," Journal of Research 

National Institute of Standards and Technology, 104[5], 461-478 (199

A. Kaye, R.F.T. Stepto, W.J. Work, J.V. Alemán and A.Ya. Malkin, "D

of Terms Relating to the Non-Ultimate Mechanical Properties of Poly

IUPAC Recommendations 1997, Pure and Applied Chemistry, 70, 70

(1998).

(	$	) 

H.A. Barnes, "Shear-Thickening ("Dilatancy") in Suspensions of

Nonaggregating Solid Particles Dispersed in Newtonian Liquids," Jou

Rheology, 33[2], 329-366 (1989).

M. Bohdanecky and J. Kovár, Viscosity of Polymer Solutions, Elsevie

Amsterdam, 1982.
Standards Bulletin, 13, 309-353 (1916).

F.R. Eirich, Editor, Rheology - Theory and Applications, Vol. 1, Ac

Press, NY, 1956; Vol. 3, 1960; Vol. 4, 1967.

J.W. Goodwin, "Rheology of Ceramic Materials," Ceramic Bulletin

1694-1698 (1990).

P.C. Hiemenz and R. Rajagopalan, Principles of Colloid and Surfac

Chemistry, 3rd Edition, Chapter 4, pp. 145-192, Marcel-Dekker, 19

R.J. Hunter, "Rheology of Colloidal Dispersions," Chapter 18 in Fo

of Colloid Science, Vol. 2, Oxford University Press, NY, 1989.

J. Mewis and A.J.B. Spaull, "Rheology of Concentrated Dispersion

Advances in Colloid and Interface Science, 6, 173-200 (1976).

D. Quemada, "Models for Rheological Behavior of Concentrated D

Media under Shear", pp. 571-582 in Advances in Rheology, Vol. 2: 

Universidad Nacional Autonoma de Mexico, Mexico, 1984.

H.N. Stein, "Rheological Behavior of Suspensions," pp. 3-48 in En

of Fluid Mechanics, Vol. 5: Slurry Flow Technology, Gulf Publishin

Company, Houston, 1986.

J.R. Van Wazer, J.W. Lyons, K.Y. Kim, and R.E. Colwell, Viscosity 

Measurement - A Laboratory Handbook of Rheology, Interscience P

New York, 1963.

R.W. Whorlow, Rheological Techniques, Ellis Horwood Ltd., Chich

A.A. Zaman, Techniques in Rheological Measurements: Fundamen

Applications, Instructional Module, NSF Engineering Research Cen

Particle Science and Technology, University of Florida, Gainesville

 2%"4'%$

American Concrete Institute, International Union of Pure and Appli

Chemistry (IUPAC), and The Society of Rheology (Journal of Rheo

have kindly granted permission to use or adapt their published defin
58

of primary sources shown above. Extracts from BS 5168:1975 are rep

with the permission of British Standards Institution under license num

PD\1999 0296. Complete copies of the standard can be obtained by p

BSI Customer Services, 389 Chiswick High Road, London W4 4AL. 

		
+	''$$

Lennart Bergström

YKI (Institute for Surface Chemistry), Stockholm, Sweden

John M. Dealy

Faculty of Engineering, McGill University, Montreal, Canada

Edward J. Garboczi

Leader, Inorganic Materials Group, National Institute of Standards an

Technology, Gaithersburg, MD

Robert J. Hunter

School of Chemistry, University of Sydney, Sydney, Australia

Kamal Khayat

Department of Civil Engineering, University of Sherbrooke, Sherbroo

Canada

François de Larrard

Méthodes et Matériels de Construction et d'Entretien des Routes, Lab

Central des Ponts et Chaussees, Bouguenais, France

Makio Naito

Japan Fine Ceramics Center, Nagoya, Japan

Celik Ozyildirim

Virginia Transportation Research Council, Charlottesville, VA

Ponserril Somasundaran

Langmuir Center for Colloids & Interfaces, Department of Chemical

Engineering, Columbia University, New York, NY

Abbas A. Zaman

NSF Engineering Research Center for Particle Science & Technology

University of Florida, Gainesville, FL


AAN. See average agglomeration

number

acoustophoresis, 20

adsorbate, 16

adsorbent, 17

adsorption, 16

chemical, 17

monolayer, 17

multilayer, 17

non-specific, 17

physical, 17

specific, 17

adsorption isotherm, 17

aerogel, 6

aerosol, 2

agent

antifoaming, 14

defoaming, 14

dispersing, 14

stabilizing, 14

surface active, 14

agglomerate, 5

agglomeration, 8

aggregate, 5

aggregation, 8

orthokinetic, 9

perikinetic, 9

alcogel, 6

amphoteric, 21

anti-thixotropy. See thixotropy,

negative

average agglomeration number, 6

.

Bingham equation, 35

BML, 50

Born repulsion, 12

Brownian motion, 14

BTRHEOM, 51



capillary methods, 43

Carreau-Yasuda equatio

Casson equation, 36

CCC. See critical coagu

concentration

CEMAGREF, 51

charge reversal, 19

chemisorption, 17

coacervation, 15

coadsorption, 18

coagulant, 13

coagulate, 5

coagulation, 8

coagulum. See coagulate

coaxial. See concentric c

coefficient of fluidity, 27

co-ions, 19

colloid, 4

comminution, 9

compact layer, See Stern 

compliance, 29

absolute shear modulus, 

complex shear, 42

shear, 32

shear loss, 42

shear storage, 42

concentration. See relat

concentration terms

concentric cylinder, 46

cone configuration, 46

double-gap configuratio

hollow cavity configura

confined flow methods, 

consistency, 49

normal, 49
60

wettest stable, 50

consistency factor, 49

consolidation, 49

Couette. See concentric cylinder.

counterions, 19

creep, 38

creep function, 38

critical coagulation

concentration, 13

Cross equation, 36

CVP. See potential, colloid vibration



deagglomeration, 9

deborah number, 38

Debye effect. See potential, ion

vibration

Debye-Hückel parameter, 22

deflocculant. See agent, dispersing

deflocculation, 9

deformation, 29

desorption, 18

diffuse layer, 16

dilatant, 29

dispersant, 14

dispersing aid. See agent, dispersing

dispersion, 2

DLVO, 11

double layer. See electrical double

layer

double layer compression, 22

droplet, 5

dynamic equilibrium, 30



EDL. See electrical double layer

Einstein coefficient, 30

Einstein's law of viscosity, 30

elastic, 26

electroacoustics, 20

electroactive. See indiffere

electrolyte

electrokinetics, 19

electrokinetic sonic ampli

electro-osmosis, 19

electrophoresis, 20

electroviscous, 26

electroviscous effects

primary, 26

secondary, 26

tertiary, 26

Ellis equation, 36

emulsion, 2

equivalent spherical diam

ESA. See electrokinetic so

amplitude



filling ability, 51

finishing, 49

floc, 6

flocculation, 8

floccule, 7

flow, 30

dynamic shear, 30

equilibrium, 30

laminar, 30

non-equilibrium, 31

oscillatory. See flow, dyna

shear

steady shear, 33

steady state. See flow, equ

flow cone, 51

flow curve, 30

Bingham plastic, ideal, 34

Bingham plastic, non-idea

Newtonian, 34

pseudoplastic with yield, 

shear-thickening, 34
shear-thinning, 34

flow hysteresis, 39

flow test, 51

fluidity. See coefficient of fluidity

forced harmonic oscillation, 39

fractal, 7

free flow methods, 48

Fritsch test. See settling method

fusion, 8



gel, 6

gelation, 8

granule, 5



Hamaker constant, 13

hard core repulsion. See Born

repulsion

hard sphere interaction, 13

hard-aggregate, 5

Herschel-Bulkley equation, 36

heteroagglomeration, 9

heterocoagulation, 9

heterodisperse, 3

heteroflocculation, 9

Hooke's law, 30

hydration forces. See solvation

forces

hydrogel, 6

hydrophilic, 21

hydrophobic, 21

hydrosol, 2




IBB, 51

IEP. See isoelectric point

IHP. See plane, inner Helmholtz 

indifferent electrolyte, 2

interface, 15

interfacial region, 15

interphase, 15

ionic strength, 22

isoelectric point, 18

IVP. See potential, ion v

?

Krieger-Dougherty equa



LCL apparatus, 51

limiting viscosity numbe

viscosity, intrinsic

loss angle. See phase lag

lyophilic. See hydrophil

lyophobic. See hydropho

lyotropic series, 13



Meter equation, 37

microsphere, 5

minimum particle size, 

mobility (concrete), 49

mobility

dynamic, 20

electrophoretic, 20

static, 20

modified slump test, 52

modulus, 31

absolute shear, 42

complex shear, 41

elastic, 30

shear, 32

shear loss, 41

shear storage, 41
62

elastic

modulus of rigidity. See modulus,

shear

monodisperse, 3

MPS. See minimum particle size



nanosize, 4

Navier-Stokes equations, 31

Newtonian, 31

noninteracting, 13

non-Newtonian, 31

no-slip, 31



OHP. See plane, outer Helmoltz, 2

Orimet apparatus, 52

Ostwald-de Waele equation. See

power-law

outer Helmholtz plane, 16



particle, 5

coarse, 4

fine, 4

primary, 5

ultrafine, 4

particulate, 5

Peclet number, 31

penetrating rod, 52

peptization, 9

phase

continuous, 2

discontinuous, 2

dispersed, 2

liquid, 2

particulate, 2

solid, 2

physisorption, 17

placeability. See workabil

plane

inner Helmholtz, 16

outer Helmholtz, 16

shear, 16

plane of shear. See plane, 

plastic, 26

point of zero charge, 18

Poiseuille flow, 31

Poiseuille's Law, 43

polydisperse, 3

polyelectrolyte, 14

potential

colloid vibration, 20

electrokinetic, 19

interaction, 12

ion-vibration, 20

shear plane, 18

streaming, 18

ultrasonic vibration, 20

zeta, 18

potential determining ion

potentiometric analysis, 2

powder, 6

Powell-Eyring equation, 3

power-law equation, 38

primary maximum, 12

primary minimum, 12

pseudoplastic. See shear-t

PZC. See point of zero ch




rate

diffusion-limited, 9

reaction-limited, 10

rate of shear strain. See sh

rate-controlled (rheometr

relative concentration term

relaxation time, 39
retardation time, 39

Reynolds number, 31

rheology, 32

rheomalaxis, 39

rheometer, 43

Tattersall, 52

rheometric, 32

rheopexy, 39

rotational methods, 44

rotational rheometers, 48



Schulze-Hardy rule, 13

screening, 22

secondary minimum, 12

sedimentation, 14

sedimentation volume, 14

settling method, 52

shear, 32

simple, 33

shear rate, 32

shear-thickening, 32

shear-thinning, 32

sieve range. See particle, coarse

slip, 2

slump, 50

slump cone test, 52

slurry, 3

sol, 3

sol-gel, 9

solvation forces, 12

sonication, 10

sonification, 10

stability

colloidal, 10

kinetic, 10

stability ratio, 14

stabilization

depletion, 11

electrostatic, 11

steric, 11

Stern layer, 16

strain

shear, 32

strain amplitude, 40

stress, 33

normal, 33

shear, 32

yield, 33

stress amplitude, 40

stress growth, 39

stress relaxation, 39

stress-controlled (rheom

structural forces, 12

structure, 33

subsieve range. See part

supporting electrolyte, 2

surface charge density, 

surface of shear, 16

surface potential, See po

surface

surface region, 15

surfactant, 14

suspension, 3

stable, 11

unstable, 11

suspension effect, 22

syneresis, 10



Tattersall. See rheomete

Tattersall

thermal motion, 14

thixotropy, 39

negative, 39

titrant, 22

titration, 22

titrimetric analysis, 22

triple layer model. See e

double layer

two-point test, 52
64

ultimate working unit, 7

ultrasonication, 10

UVP. See potential, ultrasonic

vibration

5

Ve-Be time, 53

V-funnel cone. See flow cone

vibration methods, 48

Vicat apparatus, 53

viscoelastic, 26

viscoelectric, 26

viscometer, 43

Brookfield type. See simple

rotational

extrusion capillary, 44

glass capillary, 43

simple rotational, 45

turning tube, 52

viscoplastic, 27

viscosity

apparent, 27

coefficient of, 27

complex, 27

differential, 27

dynamic, 28

infinite shear, 28

intrinsic, 28

kinematic, 28

non-Newtonian, 27

out-of-phase, 28

plastic, 28

relative, 29

specific, 29

zero shear, 29

viscosity number. See visc

reduced

viscosity ratio. See viscosi

relative

viscous, 27

@

Weissenberg effect, 33

Weissenberg number, 33

well-dispersed, 3

workability, 50

A

xerogel, 6



yield response, 33

yield stress, 33

apparent, 29

B

zero point of charge. See p

zero charge

zeta potential. See potenti

zwitterionic, 21



August 2001