High‐Pressure Capillary Flow: Theory of Non‐Uniform Viscosity; Illustrated by Experimental Data

A further development is given in this paper of the theory of the flow of liquids in capillaries under inlet pressures that are high enough to cause an appreciable change in viscosity, such that the viscosity can no longer be treated as uniform. The results are put in the form of Poiseuille's law, with a correction factor. Starting from any given empirical relation between viscosity and pressure, an expression for the corresponding correction factor can be obtained by integration. Conversely, if the form of the function connecting viscosity with pressure is unknown, it can be determined by differentiation of the observed flow‐pressure graph connecting rate of flow with inlet pressure. For the usual case it can be shown that the rate of flow approaches an asymptotic limiting value. If for any reason the logarithmic viscosity‐pressure diagram takes an upward bend, the viscosity increasing more rapidly than before, the rate of flow must actually decrease with further increase of inlet pressure, and the flow‐pressure graph will pass through a maximum. The foregoing analysis makes possible several different methods for computing the viscosity‐pressure characteristics of a lubricating oil, or other liquid, from the simple experimental procedure of observing the efflux out of a long metal capillary into the free atmosphere. The paper includes a review of the calculations by S. Kiesskalt for flat capillaries; and indicates under what conditions the extrusion type of high‐pressure gage proposed by C. Barus might be realized. The theory is illustrated by the experiments of C. Barus on marine glue to 30,000 pounds per square inch, and by more recent experiments of the authors on pressure‐gun and cup grease, and on castor oil, to approximately 45,000 pounds per square inch. The long capillary method is less sensitive and less precise but much more rapid than the two methods previously used in the work of the A. S. M. E. Special Research Committee on Lubrication. From the data presented on castor oil it appears that all three methods are in reasonable agreement.