CAPILLARY VISCOMETRY 357 the capillary's axis to maxima at its wall, so does the rate of heat dissipa- tion vary. Therefore elements of fluid at different radial positions in the capillary are heated to different temperatures when viscous heat dissipa- tion is not negligible. No means is known for measuring the temperature at each radial position in the capillary. Even methods for measuring the temperature at a single radial position are crude at best. Furthermore under these conditions there is not a unique relation between shearing stress and rate of shear, since varying temperature must be included, so it is difficult, if not impossible, to analyze the experimental results of the • viscosity measurement. Attempts have been made to calculate theoretically (14-16) the tem- I perature rise as a function of radial position in a capillary with detectable • viscous heat dissipation. Calculations are made only for two ideal con- • ditions neither of which are closely realized in practice. One is the so- • called isothermal condition according to which the capillary wall remains • always at the ambient temperature and conducts away all excess heat I which reaches it. The other is the so-called adiabatic condition according I to which the capillary wall conducts no heat so that all heat dissipated in I the flowing fluid remains in the fluid. The most exact treatment of the I problem in either case becomes an eigenvalue problem, and the solutions. .' are difficult to use in analyzing experimental data though they have been ß ' applied in some special cases. A particularly troublesome confusion arising in connection with viscous heating effects is their confusion with non-Newtonian effects. If a meas- ured viscosity decreases with increasing rate of shear, the experimental material is non-Newtonian if there is no temperature rise. If there is a temperature rise, however, it alone can account for the decrease in viscosity in the complete absence of any non-Newtonian behavior whatever. Before concluding that a material is non-Newtonian, therefore, it is necessary to demonstrate that increasing rate of shear is not accompanied by an in- crease in temperature. Reputable investigators have erroneously con- cluded that a material was non-Newtonian when the observed decrease in viscosity with increasing shear rate was later discovered to originate in a heating effect. All investigators should stand warned in this matter. With regard to viscous heating effects in capillary viscometry, an investigator should examine his needs carefully to ascertain whether he cannot avoid conditions where they are detectable before he undertakes the difficult task of dealing with them. 5. SPECIFIC CAPILLARY VISCOMETERS This section attempts to indicate the scope of applications in which capillary viscometers are useful. This scope is illustrated by discussion of specific capillary viscometers designed to meet various experimental

358 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS requirements. No attempt is made to mention all capillary viscometers which have been used, or even all those which are in current use. Many interesting instruments are not mentioned. Those mentioned are selected to illustrate a variety of types of applications. It is believed that they provide at least an approach to complete coverage of the applications • range of this type of viscometer. A logical classification of capillary viscometers is according to the: treatment of the quantities, one kinematic (rate of flow) and one dynamical (driving force), which in general are measured in the instrument. Perhaps the most common class is (a) that special case in which the driving force is that of gravity and the resulting rate of flow is measured. Two other classifications used here are the logical ones in which (b) some sort of! controlled positive pressure is used as driving force and the resulting rate of" flow is measured and (c) a controlled rate of flow is maintained and the '. required driving force is measured. The viscometers considered here,. classified as above, are listed below: Gravity Drive Ostwald viscometer : Fenske viscometer Multiple-bulb viscometer Ubbelohde viscometer Positive Pressure Bingham viscometer Tsuda viscometer Rising column viscometer Willenberg and Fritz viscometer Controlled Flow Rate Swindells', Coe's and Godfrey's injection viscometer Maron and Kreiger viscometer McKee viscometer 5.1. Gravity Drive l•iscometers In this type of viscometer the experimental fluid is forced through the capillary by the force of gravity acting on a column of the fluid in one arm of the viscometer which is filled to a higher level than is another arm. If the difference in the levels of the two arms is h and the density of the fluid is o, the driving force is, of course, hog, where g is the acceleration of gravity. As the fluid flows through the capillary the difference between the fluid levels in the two viscometer arms decreases. Therefore the force driving the fluid through the capillary is continually decreasing during the course of a measurement. If one measures the time of flow for a given volume of liquid, it is therefore necessary to use some kind of integrated average pressure in the subsequent calculation of viscosity.