unit N?m^2 ¼Pa). The stress can be normal, i.e., in a direction
perpendicular to the plane on which it acts, or tangential, i.e., acting in
the direction of the plane. Of course, intermediate situations also occur;
the stress vector can then be resolved into a tangential and a normal
component.
Deformation implies change(s) in the distance between two points in
the material.Strainis used rather than deformation; it is defined as the
relative deformation, i.e., the change in distance (e.g., length of a specimen)
divided by the original distance; it is thus a dimensionless quantity. It may
be noted in passing that the words stress and strain have almost identical
meanings in everyday language, but that they apply to fundamentally
different variables in rheology.
The notion oftime scaleneeds some elaboration. It is generally defined
as the characteristic time needed for an event to occur, e.g., a reaction
between two colliding molecules, the rotation of a particle in a flow field, or
the transformation of some dough into a loaf of bread. In rheology, the
characteristic parameter is thestrain rate, i.e., the time derivative of the
strain. This will be further discussed below. The strain rate is expressed in
reciprocal seconds, and the characteristic time scale during deformation is
the reciprocal of the strain rate, rather than the duration of the experiment.
In many systems, the relation between stress and strain is dependent on the
strain rate.
A main problem in doing rheological work is that in most situations
stress and strain vary from place to place. Moreover, the strain rate often
varies during the deformation. One generally tries to do experiments in such
a way that well-defined conditions apply throughout the test piece, thereby
establishing true material properties, i.e., results that do not depend on the
size or shape of the test piece.
Section 5.1 discusses, besides some basic notions, the rheology of
liquids and liquidlike systems, i.e., those systems that exhibit flow. Solidlike
systems are discussed in Section 17.1. This all concerns bulk rheology.
Surface rheology is discussed in Section 10.8.
5.1.1 Flow
If a stress, however slight, is applied to a fluid, it will flow. A fluid may be a
gas or a liquid, and we will primarily consider liquids. The flow may be
laminar or turbulent. The latter is chaotic, implying that a volume element
may at any moment move in any direction, though the average flow is in one
direction. In laminar flow, the streamlines, i.e., the trajectories of small
volume elements, exhibit a smooth and regular pattern.