constant pressure line could have been too short to be observed. If a three-phase system exists a t ambient temperatures, the over-all compobition can be determined from the pressure at elevated temperatures (prior to reaction) where only two-phase systems exist. However, in such cases, the over-all composition can be predetermined only by actually measuring the amount of gas charged to the autoclave. Alternatively, the autoclave may be charged above the critical solution temperature, if the reaction temperature is well above the latter. It is also possible to charge the autoclave a t ambient temperature at some pressure other than the three-phase pressure. However, in this region the system may be sensitive to small temperature changes, and phase separations may occur which are not immediately apparent. In the study of the telomerization reaction between ethyl bromoacetate and ethylene it was found convenient to use a 500-ml. rocking autoclave as a reservoir from which a microreactor (6) was charged. This method permitted charging the reactor with a single phase of known composition and thus avoided complications arising from phase separations.
Literature Cited
(1) Baniel, A., Shorr, L. M. (to Maktsavei Israel), Israeli Patent 10,830 (Jan. 22, 1959); C.A. 53, 12185 (1959). (2) Gilliland. E. R., Kallal, R. J., Chem. Eng. Progr. 49, 647 (1953). (3)' Kirkland, E. V., Znd. Eng. Chem. 52, 397 (1960). (4) Nesmeyanov, A. N. et ai.. Chem. Technof. 9, 139 (1957). (5) Nesmeyanov, A. N., Freidlina, R.Kh., Zakhorkin, L. I., Quart. Rea. 10, 330 (1956). (6) Shorr, L. M., Rogozinski. M., Varsanyi, A , , Rev. Sci. Znstr. 33, 1468 (1962). (7) Skinner, LV, A , , Johnston, G. B., Fisher, M., J . Am. Chem. Soc. 79, 5790 (1957). (8) Todd, D. B., Elgin, J. C., A . I. Ch. E. J . 1, 20 (1955).
L. M . S H O R R MANFRED R O G O Z I N S K I ANDRE VARSAYYI AVRAHAM BANIEL
Israel Mining Industries Laboratories Haija, Israel
Acknowledgment
We are grateful to the Israel Mining Industries for permission to publish this work.
RECEIVED for review August 30, 1962 ACCEPTED September 10, 1963
C O M MUN I CAT1ON
N O N - N E W T O N I A N FLOW IN A ROLLING-BALL VISCOMETER A straightforward extension of the Lewis theory for Newtonian fluids which might be applied to other nonNewtonian models.
(2) has developed a theory for rolling-ball viscometers which seems to work rather well for Newtonian fluids. This theory can be paralleled for the power-law model ( 7 ) for non-Newtonian flow: LEWIS
TTy
= -m
dv 1 2
idyl
- ' dux
-
4
(1)
'The result is given as a relation among the following quantities: the linear speed of the rolling ball Ti, the diameter of the tube D , the diameter of the sphere d. the angle of inclination of the tube from the horizontal p. the acceleration of gravity g, and the densities of the fluid and the sphere p and p s :
Some values of J , are: J I = 0.531, J 1 , s = 1.082, J 1 / 3 = 1.440, J 1 / 4 = 1.697, J1;. = 1.892. The quantity J I is just 4/3 of the integral called I by Lewis. The algebraic and numerical details are given elsewhere ( 3 ) . literature Cited (1) Bird, R. B., Stewart, LV. E., Lightfoot, E. N., "Transport Phenomena," Second Corrected Printing, p. 11, bViley, New York. 1962 ( 2 ) - Lewis, H. \V., Anal. Chem. 2 5 , 507 (1953). (3) Turian, R. M., Ph.D. thesis, University of byisconsin, Madison, \Vis., 1964
R . BYRON BIRD RAFFI M . TURIAN Department of Chemical Engineering Uniaersitj of Ll'isconsin
Here the J , are integrals:
Madison, Wis. (3) where
RECEIVED for review November 13, 1963 ACCEPTED Xovember 13, 1963 Supported by National Science Foundation grant G-11996. VOL. 3
NO. 1
FEBRUARY 1964
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