4. Glossary of Basic Terms

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 r is the particle radius and D_T is the translational diffusion coefficient. For Pe << 1, particle behavior is dominated by diffusional relaxation, whereas for Pe >>1, hydrodynamic effects dominate.

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=Dv/ , 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