**apparent yield stress**
For non-ideal
*viscoplastic* materials, where the
*yield stress* is indefinite, an apparent yield stress can be defined, for example, by extrapolation from the linear, high-
*shear-rate* portion of the
*flow curve* to the
*stress* axis. (see
*Bingham* relation)

**compliance** The quotient of *strain* and
*stress* (e.g.
*shear compliance*). The reciprocal of
*modulus*.

**deformation** Movement of parts or particles of a material body relative to one another such that the continuity of the body is not destroyed, resulting in a change of shape or volume or both.

**dilatant** A property often associated with suspensions of irregularly shaped particles, in which the liquid exhibits an increase in volume while being sheared. The term is also used in common practice to mean
*shear-thickening*, the increasing resistance to shear with
increasing
*shear rate*. It is possible for these two effects to exist in the
absence of the other.

**dynamic equilibrium** A state in which dynamic opposing forces just balance to obtain a quasi-equilibrium condition. Dynamic equilibrium is achieved during
*steady shear flow* when break down and rebuilding of
*structure* occur at similar rates, and the viscosity is constant at a given
*shear rate*.

**dynamic [oscillatory] shear flow** Condition under which
*stress* and *strain* vary harmonically with time during a
*rheometric* experiment.

**Einstein's law of viscosity** Describes the relationship between the viscosity of a dilute dispersion and the volume fraction of the dispersed particles. The relationship is derived with two major assumptions, that the particles are solid spheres and that their concentration is very low.

where _{S} is the viscosity of the suspending medium and
is the volume fraction. The factor 2.5 is known as the
**Einstein coefficient**. To describe
more concentrated dispersions, higher terms in the power series have been retained and analyzed with varying success.

**equilibrium [steady state] flow** Condition under which a constant
*stress* or
*shear rate* is maintained for a sufficient time to allow
*dynamic equilibrium* to be achieved in a fluid containing time-dependent structure. Equilibrium flow curves can be used to characterize the time-independent flow properties of a material.

**elastic modulus [modulus of elasticity]** A
*modulus* of a body that obeys
*Hooke's law*.

**flow** Continuously increasing
*deformation* of a material body under the action of finite forces. When the force is removed, if the *strain* does not eventually return to zero, then flow has occurred.

**flow curve** A graphical representation of the behavior of flowing materials in which
*shear stress* is related to
*shear rate*.

**Hooke's law** Provides that the quotient of
*stress* and *strain* (i.e., the
*modulus*) is a constant. A body obeying Hooke's law cannot be
*viscoelastic* nor does
*flow* occur.

**modulus** The quotient of
*stress* and *strain* where the type of stress and strain is defined by the type of
*deformation* employed (e.g.
*shear modulus* in shear deformation).

**Newtonian **
*Flow* model of fluids in which a linear relationship exists between
*shear stress* and
*shear rate*, where the
*coefficient of viscosity* is the constant of proportionality.

**no-slip** Condition in which fluid adjacent to a surface moves with the velocity of that surface. The assumption of no-slip is key to most
*rheometric* measurements. Slippage is a significant concern for
concentrated suspensions.

**non-equilibrium flow** Condition
under which
*shear* is varied at a rate that does not permit
*dynamic equilibrium* to be achieved. A
*thixotropic loop* is the result of non-equilibrium flow conditions during shear cycling.

**non-Newtonian** Any
*laminar flow* that is not characterized by a linear relationship
between
*shear stress* and
*shear rate*.

**normal stress**, _{n} The component of
*stress* that
acts in a direction normal to the plane of
*shear*.

**Peclet number**, *Pe* A dimensionless group used to compare the effect of applied
*shear* with the effect of thermal
(Brownian) motion; *Pe* = *r*^{ 2}
/*D _{T}* , where

**Poiseuille flow**
*Laminar flow* in a pipe of circular cross section under a constant pressure gradient.
(see also
*Capillary Methods*)

**Reynolds number**, *Re*
A dimensionless group that expresses the ratio of the inertial forces to the
*viscous* forces; *Re*=**D***v*/
, where **D** is a characteristic length (e.g. particle size or pipe diameter), *v* is a typical fluid speed, and
/ is the
*kinematic viscosity* of the fluid. The transition from
*laminar* to turbulent
*flow* is characterized by high *Re* values.

**rheology** The science of the
*deformation* and
*flow* of matter.

**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
*shear stress*. The reciprocal of
*shear modulus*.

**shear modulus [modulus of rigidity]**,
*G* The ratio of
*shear stress* to its corresponding
*shear strain*. The reciprocal of
*shear compliance*.

**shear rate (rate of shear strain),
** The rate of change of
*shear
strain* with time (*d*/*dt* ). For liquids, the
shear rate, rather than *strain*, is generally used in describing
*flow*.

**shear stress**, The component of
*stress* that causes successive parallel layers of a material body to move, in their own planes (i.e. the plane of
*shear*), relative to each other.

**shear strain**,
The relative in-plane displacement,
*x*, of two parallel layers in a
material body divided by their separation distance, *y*. Alternatively,
the shear strain can be defined as *tan* , where is the angle of
*deformation* as
shown in Figure 1.

**shear-thickening** An increase in viscosity with increasing
*shear rate* during
*steady shear flow*. The term
*dilatant* is used in common practice to mean shear-thickening, although this usage is strictly incorrect.

**shear-thinning [pseudoplastic]** A decrease
in viscosity with increasing
*shear rate* during
*steady shear flow*.

**simple shear** In simple shear there is no change in the dimension normal to the plane of
*shear*, and the relative displacement of successive parallel layers of a material body are proportional to their distance from a reference layer. The type of
*flow* used in most
*rheometric* measurements on fluids can be approximated by simple
shear.

**steady shear flow** Condition under which a fluid is sheared continuously in 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 formation of stable physical bonds between particles (or chemical bonds between macromolecules) in a fluid. These bonds result in aggregate, floc, or network structure, which impacts the rheological behavior of the fluid and provides
*elastic* and
*plastic* properties. The term may be extended to include structural effects caused by
*electroviscous* interactions, physical bonds between polymers (e.g. associative thickeners), shear-induced alignment of anisotropic particles, and close-packing (radial distribution) correlations in concentrated suspensions. The term "structure" is commonly invoked even when little is known about the cause of observed changes in rheological properties.

**Weissenberg effect** The tendency of
some
*viscoelastic* fluids to
*flow* in a direction normal to the direction of
*shear*. The effect is manifested by behavior such as the climbing of a fluid up a rotating rod.

**Weissenberg number**, *Wi*
A measure of the degree of nonlinearity or the degree to which
*normal stress* differences are exhibited in a
*flow*. For *steady simple shear*, the Weissenberg number is the product of the
*shear rate* and a characteristic time of the fluid. In oscillatory shear it is the product of the shear rate amplitude and the characteristic time of the fluid. In converging flows it is proportional to the
*Deborah number*.

**yield response** For non-ideal
*viscoplastic* materials, the
*yield stress* can be indefinite and yielding may occur continuously over a narrow range of
*stress* values. In this case, the behavior may be more properly termed a yield response.

**yield stress**, _{y} A critical
*shear stress* value below which an ideal
*plastic* or
*viscoplastic* material behaves like a solid (i.e. will not flow). Once the yield stress is exceeded, a plastic material yields (deforms plastically) while a viscoplastic material flows like a liquid.

**Figure 1. Shear strain schematic**