An approach to non-newtonian fluid mechanics☆

The theory of fluid mechanics based on Newton’s hypothesis-that (in present-day terms) the change of shape of a fluid element under applied stresses at any temperature may be described in terms of a single coefficient of viscosity, a physical constant of the material-suffices to explain many natural phenomena. Indeed, many features of the flow of the oceans, rivers and atmosphere can be accounted for, with negligible error, by the classical theory of hydrodynamics which neglects viscosity altogether. Many homogeneous liquids and gases in addition to the air and water that have provided the main stimulus for the development of Newtonian fluid mechanics, including most of those whose molecules consist of a small number of atoms, conform very well with the ideal of a liquid whose viscosity is a function of the temperature only. In recent years, liquids that do not occur in nature have assumed an ever-increasing importance in industry. Many of these are synthetic polymers -i.e. substances whose molecules are very large, usually in the form of long chains of similar monomeric units each comparable in size with the molecules of simple liquids-which often have to be handled in the molten state or dissolved in simple organic solvents. The flow of such a liquid is, in the main, found not to be characterized by a single viscosity coefficient. When a typical polymer solution is examined in a simple shearing experiment-or in flow down a pipe or between rotating coaxial cylinders, which is usually the nearest practically attainable equivalent-the ratio of shear stress to rate of shear is found to vary with the rate of shear at each temperature and also to be very sensitive to changes of temperature. Sometimes a drop of liquid will bounce on the floor like a rubber ball; a stream of liquid being poured from