THE JOURNAL OF I
P H Y S I C A L CHEMISTRY (Registered in U. 8. Patent Office)
VOLUME60
(0Copyright, 1966, by the American Chemical Society)
AUGUST 18, 1956
NUMBER8
LIQUID VISCOSITIES A T ,ELEVATED TEMPERATURES AND PRESSURES : VISCOSITY OF BENZENE FROM 90 O TO ITS CRITICAL TEMPERATURE BY JOHN R. H E I K SAND ~ ~EDWARD ORB AN'^ Mound Laboratory, Monsanto Chemical Company,Z Miamisburg, Ohio Received December 6 , 1964
A viscometer suitable for measurement of viscosities of fluids at elevated temperatures and pressures is described. The time of fall of a radioactive plummet is determined by means of two sets of coincident ionization chambers and an electronic timer. The viscosity of benzene was measured from 90" to its critical temperature. From 90" to about 180" the variation of the logarithm of the viscosity of benzene with the reciprocal of the temperature is a straight line, but above this temperature the rate of change increases with increasing temperature.
Introduction Viscosity measurements at elevated temperatures and pressures present a problem in construction of apparatus, particularly if a versatile apparatus is required which may be used for measurement of solutions of a conductive or corrosive nature and over a wide range of viscosities. A type of viscometer, originally developed by Lawaczeck,a appeared to be more adaptable to this work than others because: (1) it could be enclosed in a pressure vessel; (2) by a simple change of a plummet it could cover wide range of viscosities; (3) it and the containing pressure vessel could be constructed of non-corrosive materials; and (4)it could be constructed without a complicated internal device for timing the fall of the plummet. Bridgman4 employed a modification of such a viscometer for determining the viscosity of liquids at very high pressures but at low temperatures. Hawkins, Solberg and Potter5 used this type of instrument for their work on the viscosity of water and superheated steam. Versluys, Michels and Gervere used a falling-plummet viscometer for determining the viscosity of saturated mdthaneoil solutions a t elevated temperatures and pres(1) (a) E. I. du Pont de Nemours and Company, Wilmington, Del' (b) Monsanto Chemical Company, St. Louis, Missouri. (2) Mound Laboratory is operated by Monsanto Chemical Company for the United States Atomic Energy Commission under Contract Nurhber AT-33-1-GEN-53. (3) F. Lawaczeck, 2. Ver. Deut. Ing.. 63, 677 (1919). (4) P. W. Bridgman, Proc. Nal. Acad. Sci., 11, 603 (1925). (5) G. A. Hawkins, H. L. Solberg, and A. A. Potter, Trana. A m . SOC. Mech. E n g ~ e .61, , 395 (1935). (6) J. Versluys, A. Michels and J. Gerver, Physica, 3, 1093 (1936).
sures. Mason' also used a similar instrument for measuring the viscosity of liquids a t high pressures. The viscometer consists essentially of a tube which is closed a t 'its lower end and which has a diameter slightly greater than that of a plummet contained therein. As the plummet falls from the top to the bottom of the tube liquid moves by streamline flow through the annular space between the plummet and the wall of the tube. The rate of fall of the plummet can be controlled by proper selection of weight and diameter of the plummet. According to Lawaczeck,s there are three distinct resistances to the fall of the plummet through the liquid. These are the result of: (1) the resistance which results from the liquid flowing through the annular space between the plummet and the fall tube; (2) a viscous drag resulting from the relative moment of the two cylindrical walls; and (3) a head resistance caused by the formation of streamlines. The head resistance can be minimized by using a long plummet and a small clearance between the plummet and the fall tube. Neglecting the head resistance, the equation proposed by Lawaczeck for calculating the absolute viscosity is
where q is the absolute viscosity; t is the fall time; 1 is the distance the plummet falls in time t; u is the density of the plummet; p is the density of the liquid; d is the diameter of the plummet; and 6
1025
(7) C. C. Mason, Proc. €'bus. Soc., 47, 519 (1935).
1026
JOHN R. HEIKSAND EDWARD ORBAN
Vol. 60
met is returned to the top of the tube, and prevents gas bubbles from entering the fall tube. The plummet, constructed of stainless steel (type 304)) is a 2-5/8 inches long hollow cylinder with rounded ends. The cylinder is threaded a t one end so that it can be opened to insert, a radioactive cobalt-60 source and be filled with the liquid under investigation. The vapor pressure of the liquid inside prevents collapse of the plummet under most circumstances, but where the over-pressure is considerably greater than the vapor pressure, only a small air space is left inside for expansion. The amount of clearance between the plummet and the fall'tube and the weight of the plummet are determined by the range of viscosities being investigated. For viscosities between 0.06 and 1 .O centipoise, a plummet-fall tube combination having a clearance of 0.008 inch is used. The weight of this plummet is 19.834 g. For more viscous 9 ( . P ) t media, slightly larger clearances and slightly heavier plum-_ (2) mets were used. The weight used in equat,ion 2 as the den90 (no - Polto sity of the plummet, however, must include the weight of where 7 and 70 are the absolute viscosities of the liquid in the hollow portion of the plummet. The Reynolds solution and the reference liquid; u and uo are the number of the liquid flowing between the plummet and fall densities of the plummet filled with the solution tube for the above set of conditions never exceeded 500, and in most measurements it waR near 100. Three centering and the reference liquid; p and po are the densi- projections were positioned on the plummet at. each end to ties of the solution and reference liquid; and 1 and prevent the plummet from wobbling during its fall. The t o are the fall times of the plummet in the solution diameter around the centering projections is 0.001 inch less than the inside diameter of the fall tube. Inside of the and in the reference liquid, respectively. a t its lower end is a screw containing a radioactive An important innovation in the measurement plummet cobalt-60 source which is used for timing the fall of the of the fall times was the development of a timer plummet. The fall tube is positioned concentrically within a stainless whereby the time of fall of a plummet containing a (type 347) pressure vessel which is capable of safely radioactive source could be measured by means of steel holding a pressure of 3,000 pounds per square inch at temtwo sets of coincident ionization chambers. The peratures to 300". complete timing device, except the cobalt-60 source, The vessel itself is a 36" long pressure cylinder with a blank was external to the viscometer system. Problems head a t the bottom threaded in a manner to hold the fall tube involved in using a window in a pressure vessel to rigidly vertical, and an extended head a t the top drilled a pressure inlet and a thermocouple well which extends observe the time of flow of a liquid or fall of a ball or for into the body of the liquid. Screw caps tighten the heads plummet were avoided. Also, problems caused by to the vessel with seals being accomplished with stainless introduction of an electrical circuit into a pressure steel gaskets. The entire pressure vessel is surrounded with an electric vessel, which might contain an ionic or corrosive mantle. liquid a t 300°, were eliminated. Only one other heating Temperature measurements are made to trhe nearest 0.2' reference t o the use of a radioactive source for meas- with a single-junction copper constantan thermocouple uring viscosities appears in the literature.8 enclosed in a copper slug which is positioned next to the The viscometer has been used to measure the fall tube in the middle of the fall path. whole unit is supported by a trunnion about which viscosity of heavy water to 250°9 and is presently theThe apparatus can be rotated through an angle of 180' so measuring the viscosity of uranyl sulfate in water that the plummet can be returned to the top of the fall tube a t elevated temperatures to 3,000 pounds per for succeeding determinations. Temperatures are controlled square inch pressure. Plans are being made to manually by means of a Variae transformer. Three 250-ml. pressure vessels are connected to the vismeasure the viscosities of some aqueous suspensions cometer with high-pressure tubing to provide for expansion and some fused salts and metals. of the liquid at elevated temperatures. This design perThe viscosity of benzene to 185.7" has been re- mits the viscometer to be filled completely with liquid at all ported in the literature,l" but no data in the vicinity temperatures, minimizing tQe formation of gas bubbles of the critical temperature are available. It is of on the plummet. Nitrogen is introduced into the syst,em through an expansion chamber to obtain the desired presinterest to observe the behavior of benzene as the sure. An over-pressure of approximately one atmosphere critical temperature is approached. greater than the vapor pressure of benzene was used for the viscosity determination' of benzene. Pressures are read to Viscometer the nearest 5 pounds per square inch by means of an AshThe measuring apparatus consists of the viscometer, pres- crolt Duragauge of the proper range. sure vessel, heating mantle and timing device. The timing assembly chosen for this work," consists of a The viscometer consists of a type 304 stainless sleel fall 12-millicurie cobalt-60 source placed within the plummet, tube through which the plummet of slightly fimaller diame- three separate electronic units; and shielding for two pairs ter is allowed to fall under the influence of gravity. The of coincidence Geiger-Mueller tubes placed outside of the fall tube, 35 inches long and 0.020 inch wall thickness, has an heating mantle opposite the starting and finishing points inside diameter of 0.4992 f: 0.002 inch, throughout the of the fall path. The three electronic units are a low-voltlength of the fall path, as measured by a Shoffield Precision- age regulated power supply; a four-channel high-voltage aire Gage. A funnel shaped plug, having a hole 0.03 inch regulated power supply; and 3 coincidence timer. The in diameter through it, is inserted in the to of the tube. Rhielding assembly, constructed of lead and steel, completely This plug provides a stop for the plummet wten the plum- encases the two pairs of Geiger-NIueller tubes except for narrow collimating slits opening . - in the direction of the (8) J. Cueron, "Proceedings of the Isotope Techniques Conferviscometer. ence, Oxford, July, 1951," Her Majesty's Stationery Office, Vol. 11, The top pair of Geiger-Mueller tubes detect the position 1952, p. 11. of the plummet (cobalt-60) at the start of the fall path and (9) J. R. Heiks, M. K. Barnett, L. V. Jones and E . Orban, THIS activate a timing clock. Pulses from the Geiger-Mueller
is the annular space between the fall body and the fall tube. Although this type of viscometer has been used by some previous investigatorsa for the absolute measurement of viscosity, it is not recommended for use as an absolute instrument since the effect of the head resistance on the above equation has not been evaluated. However, when a reference liquid with a kinematic viscosity similar to the liquid under investigation is used, the instrument can be used satisfactorily for relative measurements. The relative viscosity is calculated by use of the equation '
I
JOURNAL, 68, 488 (1954). (10) "Landolt-Bornstein Physical-Chemical Tables," 5th Edition, Vol. I, Julius Springer, Berlin, 1923, p. 128.
(11) A. J. Rogers, J. W, Heyd, W. L. Hood and J. A. Williamson, Nucleonics, 1.2, No. 6, 62 (1954); MLM-805, Fehruary 27, 1952.
Aug., 1956
VISCOSITYOF BENZENE FROM 90"
tubes are injected into one channel of the coincidence time where they are amplified, equalized, and then applied to a coincidence mixer. This coincidence mixer generates an output pulse when pulses in the two Geiger-Mueller tubes occur within approximately 90 microseconds of each other. A conventional scaler totals the mixer output pulses. When the number of scaled mixer pulses exceeds a preset value, a clock-timer is activated. To prevent activation of the timer before the plummet is opposite the collimating dit, a resetting pulse is fed into all of the resetting grids of both scalers a t a rate which prevents the totaling of sufficient counts to activate the timer until the plummet, (cobalt-60 source) is directly opposite the Geiger-Mueller tubes. The resetting pulse is obtained from a line-voltage-synchronized multivibrator. When tQe plummet reaches the bottom of the fall pnth, the timing clock is stopped by an analogous electronic assembly. The timing clock may be read to 0.1 second.
TO
CRITICAL TEMPERATURE
1027
A@/T (3') where 7 is .the absolute viscosity and A and R are constants. Above 180' the rate of change of the logarithm of visc0sit.y with the reciprocal of thn temperature is no longer constant, but. increases with increasing temperature.
Procedure The two sets of coincident counting tubes are placed 20 inches apart so that the central part of the fall tube may be used as the fall path of the plummet. A sufficient length of fall tube a t both ends of the fall path allows time for acceleration of the plummet and reduces resistance effects caused by the closed ends of the tube. The times required for the plummet to fall 20 inches a t various temperatures and pressures are measured, first, with the viscometer filled with an appropriate reference liquid, and then with the viscometer filled with the solution under investigation. The average of five unidirectional fall times is taken a t each predetermined temperature and pressure over the range being investigated. The viscosity can then be calculated by means of equation 2, since the fall times of the plummet in the reference liquid and in the solution are known, as are the densities of the plummet, solution and reference liquid over the entire temperature and pressure range. The standard deviation of a single determination, based on duplicate runs of an aqueous uranyl sulfate solution a t ten different temperatures between 30 and 200" was calculated to be 0.00218 centipoise over a viscosit,y range of about 0.15 to 1.0 centipoise.
1 / T X 10-3. Fig. 1.-Viscosity of benzene in centipoises us. reciprocal of absolute temperature, 90-288.5".
TABLE I VISCOSITY OF BENZENE (IN CENTIPOISES) Temp., OC.
Pressure, P.S.I.
7 7 Ha0
. 'laHzO
0 Benzene
90 35 0.901 0.317 0.286 100 40 .922 ,283 .261 125 60 ,941 ,223 .210 150 100 ,921 .186 .171 175 150 ,910 ,158 .144 Viscosity of Benzene .88G ,136 ,121 200 225 The viscosit,y of benzene (Mallincl~odtAnalytical Re225 315 ,810 .123 ,100 agent grade) was determined a t twelve temperatures be250 445 ,723 ,113 ,082 tween 90 and 288.5'. The literature values of the density 275 635 ,629 .lo4 ,065 of benzene12 and the absolute viscosity of wnter'a were used for calculations. The data are given in Table I and are 280 650 ,610 ,102 ,062 plotted in Fig. 1. Inspection of the curve shows that the 285 700 .590 .loo .059 exponential equat,ion for the general relationship between 288.5 720 ,568 099 .056 temperature and viscosity for undissociated liquids developed by Andrade,I4 but. first suggested by Reyn~lds,~s a A. Jaumotte, Rev. Universelle Mine, 17, 213 (1951). holds only to a temprrature of 180'. This relationship is b Critical temperature.
.
(12) Ref. 10,0.273. (13) A. Jaumotte, Rev. Uniuerselle Mine, 17, 213 (1951). (14) E. N. Andrade, Phil. M a g . , IT, 497,698 (192G); "Viscosity and Plasticity," Chemical Publishing Co., New York, N. Y.,1951,p. 22. (15) 0.Reynolds, Phil. Trans., 171, 157 (1886).
Acknowledgment.-The authors express their gratitude to Mr. T. G. Moore for the design of the pressure vessel and heating mantle used in this work.
