338 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Quite a number of other instruments for the determination of viscosities of fluids are available, among which may be cited the falling sphere, rolling ball, microviscometer, etc. The rolling ball instrument is useful when dealing with an opaque fluid or when observation on a volatile fluid over a period is needed, whilst the microviscometer needs but a millilitre or so of fluid. The falling sphere instrument allows measurement of a very wide range of viscosities merely by selecting steel spheres of suitable diameter. Viscosity is a constant for any given temperature and is independent of the rate of shear ruling during its determination. As a dynamic character- istic it only applies to true fluids in which there is no lower limit of applied stress below which no corresponding flow results (other than surface tension effects). Fluids do not, therefore, include any property of internal rigidity or elasticity. From a subjective standpoint the viscosity of a fluid determines the work necessary to stir it at a given rate and, in the case of very high viscosities, is probably closely related to stickiness and tack. In general, viscosity increases with molecular weight indeed, relative molecular weights are often determined by this means. True fluids are monophasic (true solutions included). When a system is made biphasic, as, for example, by dispersion of a powder or immiscible liquid in another liquid, or formation of froth by dispersion of air in liquid, it is no longer classifiable as a Newtonian fluid, but as a plastic body. Dis- persions of many high polymers in a solvent form non-Newtonian fluids, these being generally oi high viscosities and subjectively similar to Newtonian fluids. They differ, however, in rheological behaviour in that their apparent viscosities decrease with increasing rates of shear, but otherwise exhibit the properties of free-flow of true fluids unless highly concentrated, when they form gels. Plastic bodies, however, exhibit markedly different subjective and rheological characteristics. Thus, whilst sell-healing, they no longer freely flow, a limiting low value of applied stress being needed to effect internal flow. In other words, they exhibit an internal friction or rigidity. This rigidity may be sufficiently marked that the bodies exhibit jelly-like proper- ties, which indicates that sufficiently small applied stresses may result in recoverable elastic deformation without flow. Like non-Newtonian fluids, their apparent viscosities decrease with increasing rates oi shear. For the examination of such non-Newtonian materials rheologically, apparatus is needed wherewith different rates of shear may be measured. Whilst the falling sphere viscometer, operated with a range of steel spheres of different sizes, permits of recognition of such anomalous viscosity, for transparent, freely flowing non-Newtonian fluids, other apparatus is needed for opaque dispersions and pasty bodies. These fall roughly into the two classes of variable pressure capillary plastometers and rotary plastometers.

INTRODUCTION TO THE RHEOLOGY OF DISPERSE SYSTEMS 339 For the details of operation of the Goodeve, Stormer and other rotary instruments, the makers' descriptive pamphlets must be consulted, but in brief, data from the Goodeve viscometer is obtained by recording the relation- ship between angular deflection (stress X a constant) and R.P.M. (shear rate) X (a constant) at different rates of shear, and plotting the results as a rheological diagram. In the Stormer instrument the dependent and independent variables are operated inversely to the Goodeve instrument, a given load W (stress) X (a constant), effecting a speed of rotation in r.p.m. (shear rate) X (a constant), thus furnishing similar data. The capillary plastometer ot the writer (Fig. 4) is operated by admitting air at different pressures from a pump or cylinder into a stabilising bottle (B) leading to the jacket (H) containing the material under test. Pressure is regulated by the admittance valve (D) and relief valve (E) and recorded by the manometer (F). (For high pressures, a dial manometer is more con- venient.) Efflux velocities at different (decreasing) pressures are read on the flowmeter manometer (L) comprising the air-leak (K). In Fig. 5 is shown the disposition for calibrating the flowmeter in terms oi c.c./sec. The plots of applied stress against rates of volume effiux for a capillary plastometer, or torsion as angular deflection against angular rate oi rotation, are shown against those of Newtonian fluids in Fig. 6. It will be noticed that in spite of the known rigidity of the plastic body, no indication of this is shown on the rheological diagram. This is due to the uneven distribution of the shearing stresses across the radius of the capillary and in the annular space between the cylinders. The effect oi the application of increasing shearing stresses in a capillary plasto- meter or increasing rates of rotation given to the outer cylinder of a rotary instrument results in progressive de-solidification, as seen in Figs. 7 and 8 respectively. Fig. 4. Schematic lay-out of Plastometer. Shear rate Fig. 6.