On the anomalous flow of colloidal systems

Abstract

Part I—The Nature of Anomalous Flow The flow of many solutions, most of them colloidal, is now known to be anomalous since they do not obey the linear Poiseuille relation connecting volume efflux with pressure applied. Under small pressure heads, the rate is disproportinately small compared with that under higher pressures so that the "viscosity coefficient" calculated from these rates is not a constant but becomes larger as the rate of flow decreases. This was first established by Hess in 1906; although in 1903 it had been found that the oscillating disc method gave "viscosities" for colloidal systems which varied with the amplitude of the oscillation. In 1913 Hatschek found similar effects in many colloidal systems using the Couette co-axial cylinder viscometer. Most lyophilic colloids show anomaly to a greater or less extent; and for these systems particularly viscosity has always been regarded as a characteristic property and used as an indicator of lyotropic changes. It is because viscosity is a property so suitable for investigation of lyophilic colloids that it is of importance that more should be known of the relation between viscosities and particle dimensions; of the nature of anomalous flow and its origin. Anomaly is obvious as deviations from a linear relation between pressure head and volume efflux, but its detection in this manner throws no light upon its nature or its origin. Hagenbach's derivation of the so-called Poiseuille equation first showed that this depends upon a parabolic velocity distribution across the flowing liquid, as postulated by Newton. If the equation fails, the velocity distribution is not parabolic. Porter proposed a formula for anomalous flow upon the assumption that the "viscosity coefficient" varied with rate of shear and that the velocity distribution has an exponent less than 2. From the observed volume efflux under known pressures, its value was then to be calculated. The anomaly is, however, too complex to be dealt with in this manner.