Every elementary school pupil is taught that there are three states of matter: solid, liquid,
and gas. To these might be added "plasma," which exists at extremely high temperatures,
or the "Bose-Einstein condensate," at extremely low ones. However, one needn't resort to
superfrigid or superhot extremes to find states of matter that challenge the ordinary division
into solids, liquids, and gases. Such everyday substances as mayonnaise or window glass
will do the trick.
While it is true that the classical definition of "liquid" as opposed to "solid" provides
a basis for deciding whether a substance is a solid or a liquid, the classical definition
is inadequate not only for many everyday purposes, but for engineering ones as well.
According to the classical definition, a "fluid" is any substance that deforms continuously
under the application of an arbitrarily small shearing stress. By this definition, mayonnaise
is a solid, since it holds its shape against gravity, while window glass is a liquid (!), since
it creeps, albeit ever so slowly, against forces even much weaker than gravity. Clearly,
for many workaday uses, in the home and on the factory floor, the classical definition is
inadequate.
This book deals with the thick, rubbery, gooey, and pasty substances that defy the
classical definitions of solids and liquids. These substances are often called "complex
fluids," which I define as "substances that flow at modest stresses." By "flow," I mean
a smooth deformation on a humanly accessible time scale. A piece of slate or ceramic does
not "flow"; it deflects under modest loads, and it fractures under great ones. Peanut butter, on
the other hand, "flows" rather smoothly when a child pushes a butter knife across it. Hence
peanut butter is a "complex fluid," while a brick is not. Although the packed ices of glaciers
"flow" on geological time scales, and metals creep under large loads by defect motion, and
"even the mountains flow before the Lord," we mortals usually prefer to call these solids.
Clearly, there are ambiguous cases: A piece of window glass seems solid enough at room
temperature and ordinary periods of time, but heat it up a bit, or wait a few decades, and
its solidity becomes dubious. Reiner A949) expressed well the dilemma: "Strictly defined
rheological divisions belong to ideal abstract bodies and not to real materials. If we say that
concrete is a liquid, every builder will laugh at us.... If we say that glass is a solid, the
theoretical physicists will consider us to be simple and crude." The definition of a "complex
fluid" might therefore seem as plastic as the materials it is meant to define! Nevertheless,
so many materials fall well within the rough definition given above that "complex fluids"
are worthy of a title—and indeed, a book—of their own.