908
A. G. WHITTAKER, T. h4. DONOVAN AND H. WILLIAMS
oxygen atoms diffusing through this new phase. .The lack of complete agreement of the experimental density results with those calculated according to the proposed mechanism may be due t o a change in the character of the voids resulting from oxidation and formation of the y-Ud07phase. summary Oxidation of uranium dioxide below 300" results in the immediate formation of a surface y-tetrc?r gonal Ua07phase. This reaction is controlled by diffusion of oxygen through the second phase. The evidence in support of the process is: (1) appearance of U307 X-ray spectra at a composition of UO2.06, (2) less than one a t o n per cent. oxygen solubility as indicated by the constancy of the UOz lattice parameters, (3) linear increase in density with oxygen concentration is near to that calcu-
Vol. 62
lated for formation of U307,(4) kinetic data which fit .Wagner's equation. Absence of U307X-ray spectra for low O/U ratios on powder samples is shown to be due to the small size of the U307crystals and not to the solution of oxygen in the UOs lattice. Although parameters of Ua07 change with the thickness of the tetragonal phase and the temperature of formation, the volume of the unit cell is nearly constant. The final composition at all temperatures (100 t o 300") is the same, U0z.b~* 0.01. This evidence demonstrates that there is a single phase, not two, three or more, as reported by other authors. Acknowledgments.-The authors are grateful t o C. C. Comenetz, R. R. Heikes and R. Ruka for their helpful suggestions and to J. Pantlik for his aid in constructing the apparatus.
BURNING-RATE STUDIES. PART 7. ONSET OF TURBULENT COMBUSTION OF LIQUIDS CONTAINED IN SMALL TUBES BYA. GREENVILLE WHIT TAKER,^ T. M. DONOVAN AND H. WILLIAMS Contribution from the Chenaistry Division, Research De artment, U.S. Naval Ordnance Test Station, China Lake, Jalifornia Received September 16, 1067
Studie8 on the combustion in small tubes of 95 different liquid systems show that the undergo transition frbm smooth to turbulent combustion at some consumption rat>echwacteristic of the system. The e d c t s of liquid viscosity, fuel vapor pressure, combustion tube diameter and shape on the onset of turbulent combustion were studied. The results indicate that the transition is due to physical phenomena and that the entrainment of liquid droplets and a critical Reynold's number in the vapor phase may be im ortant factors associated with the onset of turbulent combustion. Also, it is probable that the entrainment of liquid dropfets is the triggering mechanism. Some of the results are considered in the light of a theory by Landau on the transition from deflagration to detonation.
Introduction Perhaps the most striking phenomenon that occurs in the combustion of liquid systems in small tubes, is the onset of turbulent combustion. This effect has been reported p r e v i ~ u s l y , ~but - ~ the factors affecting the onset of turbulence have not received much attention. Generally the effect is ascribed t o physical aspects of the burning system. However, there was'some possibility that the onset of turbulence may be associated with some marked change in the chemical kinetics of the combustion process. It has been found that liquid systems show the transition from smooth t o turbulent combustion even though the chemical composition of the systems varied widely from single components like ethyl nitrate to fairly complex multi-component systems as exemplified by the system isobutyric acid-Nz04-HNOs. Because of this observation it seems unreasonable t o believe that the combustion kinetics of all these systems could have the necessary properties to cause the onset of turbulent (1) Sandia Corporation, Department 5150. Albuquerque, New
Mexico.
(2) K. K. Andreev and M. N. Purkaln, DokladV Akad. Nauk. USSR, 60, 281 (1945). (3) G. W. Stocks and L. A. Wiseman, Explosives, Research and Development Establishment, Waltham Abbey Eases, England, Report No. 31/R/49. (4) A. G. Whittaker, H. Williams and P. If. Rust, THIS JOURNAL, 69, 904 (1956).
combustion by an associated change in the kinetics of the combustion process. This general observation in itself seems to establish that the onset of turbulent combustion is not associated with the chemical kinetics of the combustion reactions. Nevertheless, the effects of physical variables on the onset of turbulence were studied t o some extent in order to investigate this conclusion. Although a t least 95 chemically different systems were shown to undergo a transition from smooth t o turbulent combustion, only a few systems were chosen as characteristic and studied in some detail. Twocomponent systems containing nitric acid plus an organic fuel were selected. It is believed, however, that the results apply to liquid systems of any number of components. The variables studied were viscosity, fuel vapor pressure, combustion-tube diameter and shape, and metastable smooth combustion in the normally turbulent region. Reynold's number calculations were made on the gaseous combustion products to see whether the onset of turbulent combustion was associated with a characteristic value of this parameter. Also, entrainment of liquid droplets was considered in relation to turbulent combustion. Experimental The compounds used were purified as follows. Nitric acid, 2-nitropropane, sebaconitrile and nitrogen tetroxide
August, 1958
ONSETOF TURBULENT COMBUSTION OF LIQUIDS CONTAINED IN SMALL TUBES
were prepared as described previously.4-' Eastman White Label isobutyric acid was dried over Drierite and distilled. The center fraction was retained for use. Lucite and cellulose acetate were obtained as commercial sheet plastic and pulverized in a Wiley mill. This powdered material was used without further treatment. The apparatus and procedure used to make the consumption rate measurements was the same as that described p r e v i o ~ s l y . ~Viscosity ~~ was measured by using a standard Ostwald-Fenske viscometer.*
..
Results and Discussion The Effect of Lucite Addition on Consumption Rate and Onset of Turbulent Combustion.-The effect of liquid viscosity on burning rate and the onset of turbulence was studied. Both Lucite and cellulose acetate were used to increase the viscosity of the system 2-nitropropane-nitric acid. Although both polymers produced the same qualitative effects cellulose acetate was required in about 10 times the concentration of Lucite to produce the same increase in viscosity. Also, cellulose acetate showed a much more rapid aging effect. That is, the solutions containing polymer decreased in viscosity as a function of time. Only the results obtained with Lucite are given because the small concentration required probably perturbed the basic system least. In a11 cases no extra nitric acid was added to oxidize the Lucite; therefore, the systems were very slightly fuel-rich. It was always found that an appreciable fraction of the polymer remained in the bottom of the combustion tube after the combustion was completed. The data in Tables I and I1 show that the addition of Lucite had several effects on the consumption rate of the 2-nitropropane-nitric acid system. First, it decreased the consumption rate at any given pressure and as more Lucite was added a limiting consumption rate curve seemed to be approached. Part of the slowing down of the consumption rate may have been due to the fact that the Lucite tended to concentrate in the surface as evidenced by the existence of some of the Lucite in the combustion tube at the end of an experiment. This surface accumulation would hinder the evaporation of liquid and thereby decrease the consumption rate. Probably the more important effect of the Lucite was to decrease the convective heat transfer in the liquid phase. Temperature profile measurements showed that convective heat transfer in the liquid phase of this system was fairly i m p ~ r t a n talthough ,~ most of the heat transfer was by conduction. Convective heat transfer varies inversely as the viscosity of the liquid; consequently, as the viscosity of the system was increased the convective heat transfer decreased. This decreased the evaporation rate of the liquid; hence, the consumption rate decreased. Moreover, as the viscosity increased t o a rather large value, the heat transfer by convection in the liquid would essentially vanish. Then all the evaporation would (5) A. G. WhitLaker and H. Williams, THISJOURNAL, 61, 388 (1957). (6) M. H. Kaufman and A. G . Whittaker, J . Chem. Phvs., 24, 1104 (1956). (7) A. G. Whittaker, R. Sprague, S. Skolnik and G. B. L. Smith, J . Am. Chem. SOC..74, 4794 (1952). (8) A. Weissberger, "Physical Methods of Organic Chemistry," Interscience Publishers, New York, N. Y.,1945, p. 89. (9) D. L. Hildenbrand, A. G . Whittaker and C . 8 . Euaton, THIS JOURNAL.68, 1130 (1964).
W.
Inc.,
909
have to take place by conduction heating. This situation would lead to the observed result that a limiting consumption rate curve was approached as the viscosity increased to large values. Thus, it appears that the consumption rate curve for the system containing 0.75y0Lucite is close to the limiting curve associated with heat transfer by conduction alone (neglecting the small contribution due t o radiative heat transfer.) TABLE I CONSUMPTION RATE DATA FOR 2-NITROPROPANE-g7% NITRICACIDSYSTEM CONTAININU LUC~TE Prcssure
(atrn.)
(I
Consumption rate (cm./sec.)
0.0% Lucite
0.1%
0.5%
0.75%
0.076 .lo9 .165 .221 .267 .318 .356 .406 .480 .511 .572 .627 ,688 .724 .782 1.91"
0.074 .lo4 ,135 .203 .262 ,318 .358 ,422 .457 .523 ,533 ,566 .660 .648 .721 .798 .815 2.33"
Lucite
Luoite
0.114 0.079 14.6 21.4 .168 .168 28.2 .241 .251 .330 ,297 35.0 41.8 .432 ,348 .483 .406 48.6 55.4 .554 .460 62.2 .597 ,511 69.0 ,645 ,569 75.8 .737a .635 82.6 1.185 89.4 96.2 103.0 109.8 116.6 123.4 130.2 137.0 Turbulent combustion.
Lucite
TABLE I1 VISCOSlTY AND CONSUMPTION-RATE DATAFOR THE ONSET O F TURBULENT COMBUSTION I N THE SYSTEM %NITROPROPANE-97% NITRICACID (% by
Viscosity at 35' (centipoises)
Rate (cm./sec.)
Pressure (atrn.)
0.0 .1 .3 .5 * 75
0.70 1.80 4.60 12.61 35.0
0.645 .635 .i36 .782 .815
69.0 75.8 96.2 109.8 123.4
Lucite
wt.)
This decrease in consumption rate seems to be related to the second effect produced by the addition of Lucite. Empirically it was found that a certain consumption rate was required for turbulent combustion to occur. The value the rate must reach was almost independent of the composition of the system. Therefore, it was necessary to go t o higher pressure in order to get the consumption rate to the proper value for turbulent conbustion to start. The data in Table I1 show that as the viscosity of the system increased the rate necessary for turbulence to appear increased slightly as well as the pressure, but the pressure increase was about 3.5 times the rate increase. It was found that there was an empirical relation between the turbulence pressure and the viscosity of the system as Pt
E
74.8q0.'40
(1)
910
A. G. WHITTAKER,T. M. DONOVAN AND H. WILLIAMS
Vol. 62
LdC R, = p
where Pt is the pressure in atmospheres associated with the onset of turbulence, and q was the viscosity of the liquid a t room temperature in centipoises. A similar relationship between the rate at which turbulence occurred and viscosity appeared to hold. Unfortunately, the variation was not large enough t o demonstrate the relationship with a reasonable degree of confidence. In general, the results obtained by polymer addition show that it was possible t o change, by a large amount, the pressure a t which the onset of turbulent combustion occurs by varying the viscosity of the system a t essentially constant composition. Metastable Smooth Combustion.-Occasionally, it is possible to find a system that burns smoothly in the normally turbulent region. Table I11 gives data on two such systems. They had to be carefully ignited by means of an overlying layer of ethyl nitrate4 t o get the desired behavior. With such systems it was found that these points lie precisely on the extension of the curve through the points in the stable smooth burning region. This resdlt supports the notion that there is no change in the combustion kinetics a t the onset of turbulence, and that the increased consumption rate in the turbulent region is due entirely to increased burning surface.
(2)
Where Re is the Reynold’s number, L is the combustion tube inside diameter, C the linear consumption rate, d the liquid density and p the viscosity of the gas. The evaluation of all terms in equation 1 was straightforword except for the viscosity of the gas. Data on the viscosity of the gaseous combustion products as a function of temperature were obtained from the literature, l o and extrapolated to the maximum A ame temperature. The Reynold’s number was then calculated from these data plus the assumption that the viscosities of the components were additive on a mole fraction basis, and that the calculated composition of the combustion products corresponded to an equilibrium mixture at the flame temperature computed for complete combustion. Reynold’s number calculations were made for six different systems. Since they all gave similar results, only the data for the system 2-nitropropanenitric acid burned in 4-mm. i.d. tubes are given ‘in Table IV. Turbulence starts a t a Reynold’s number of approximately 600. This differs markedly from the Reynold’s number of 2000 found t o hold for the transition from laminar t o turbulent flow in pipes. However, the situation here is very different and there is no good reason TABLE I11 t o use the results obtained from pipe flow studies CONSUMPTION RATEDATAFOR STOICHIOMETRIC SYSTEMS as a criterion for the present situation. PREPARED WITH 99% NITRIC ACID
Pressure (atm.)
Consumption rate (cm./sec.) Isobutyric n-Butyric acid acid-NzOP
14.6 0.234 0.197 21.4 .314 .257 28.2 ,392 .314 35.0 ,440 ,367 41.8 ,508 .418 48.6 ,563 .452 55.4 ,634 .511 62.2 ,701 ,550 69.0 0.775 1.4gb .595 75.8 ,854 1.4gb .686 82.6 ,893 1.9Sb 0.749 1.34b 89.4 ... ... 0.784 1.37b a Composition of system in mole per cent.: CaHsOz, 20.23: HN03, 74.50; N204,3.97; H20, 1.30. Turbulent combustion
Reynold’s Number and Turbulent Combustion. -On comparing the results obtained from all the liquid systems, it was found that the consumption rate corresponding t o the onset of turbulent combustion falls in the region between 0.3 t o 1.2 cm./ sec. when 4 mm. i.d. tubes were used. About 90% of the systems go into turbulent combustion a t a consumption rate lying between 0.6 and 0.7 cm./ sec. This tendency may indicate that the Reynold’s number of the combustion products is related to the onset of turbulent combustion. I n fact, many investigators in this field have suggested that the turbulence starts in the gas phase and that the gas phase turbulence disturbs the liquid surface. This has been shown to be the case for combustion of gases in tubes and the idea has been extended to liquid systems by analogy. The Reynold’s number was calculated according t o the expression
TABLEIV REYNOLD’S NUMBERS OF THE COMBUSTION PRODUCTS FOR THE SYSTEM 2-NITROPROPANE-95% NITRIC ACID Pressure (atm.)
(1
14.6 28.2 41.8 55.4 69.0 75.8 82.6 96.2 Theoretical.
Flame ty.pa
b
Viscosity, poise X IO7
2872 7.130 2916 7.160 2954 7.190 2977 7.203 2992 7.212 3000 7.218 3006 7.225 3016 7.230 Turbulent combustion.
Reynold‘s number
73 154 275 351 409 467 571b 1125 , ,
00 the other hand, it has been pointed out by Rice1’ that larger Reynold’s numbers can be obtained by considering the conditions closer to the burning surface. In this region the molecules are larger; the gas viscosity is lower. Using this notion it is possible t o show that a Reynold’s number of 2000 may be reached a t a temperature of 200 to 300’ above the known surface temperature. Because of the steep temperature gradient in this region, this Reynold’s number occurs only 5 or 10 U , above the burning surface. While this allows practically zero distance for turbulence to develop, it does agree with direct observations of turbulent combustion. Namely, the turbulence is most noticeable close to the liquid surface, and gas flow becomes nearly laminar again approximately (10) J. 0. Hirschfelder, R . B. Bird and E. L. Spotz, Am. Soc. Mech. Engr. Fra?ia., 71, 921 (1949),sde also NBS-NACA “Tables of Thermal Properties of Gases,” compiled ‘by R. L. Nuttall. (11) T. K. Rice, Naval Ordnance Laboratory, White Oak Maryland, private communication.
..
,
August, 1958
ONSETOF TURBULENT COMBUSTION OF LIQUIDE CONTAINED IN SMALL TUBES
1.25 cm. above the surface where maximum flame temperature exists. Therefore, it may be that a critical Reynold’s number of 2000 does hold for the combustion of liquids, and that the number must be evaluated for the conditions that exist near the burning surface rather than out in the gas phase where combustion is essentially complete. If it is assumed that turbulent combustion starts at a particular Reynold’s number regardless of what the absolute value may be, then it can be seen in eq. 1 that the consumption rate a t the onset of turbulence should be inversely related t o the combustion tube diameter. In addition, if it is assumed that the consumption rate just before turbulence is reached is related to the pressure according to the equation c = kP” (3) where C is the consumption rate, P is the bomb pressure and IC and n are constants; then the pressure a t the onset of turbulence should decrease as tube diameter increases. The data given in Table V show that the pressure does indeed decrease with increasing tube diameter but not nearly as rapidly as expected. Moreover, the rate a t the onset of turbulence does not show the expected relationship. This lack of correlation may mean that Reynold’s number is the wrong parameter t o use or that the tube diameter is not the correct characteristic length to be used in evaluating the Reynold’s number. Another factor that may affect this result is that the relative heat loss to the surroundings is quite different in going from 2 to 6 mm. tubes. Hence, it is possible that the expected correlation was not observed because the relative heat loss was not held constant.
911
rectangular tube a t a rate given by 1.2(3.7/10) = 0.44 cm./sec. This corresponds t o about 25 atm. assuming that the consumption rate curve is independent of combustion tube shape. Actually the system went into turbulent combustion at 15 atm. This result was qualitatively in agreement with the expected result. However, the quantitative agreement was rather poor. Again the heat losses in the two cases were not the same because the surface through which heat may escape is larger for the square section tube. Liquid Entrainment and Vapor Pressure.-If a model is assumed for the combustion of liquids in which the important reactions are in the vapor phase and the liquid simply evaporates to produce gaseous reactants for these vapor phase reactions, then the evaporation rate must be the same as the consumption rate. It has been shown that entrainment of liquids becomes noticeable when evaporation rates reach a value of about 5 X g./cm.2 sec. as an upper limit.12 The mass consumption rate a t the onset of turbulence is about 1 g./cm.2 sec. This is over two orders of magnitude greater than the upper limit where entrainment is known t o occur. Indeed, the lowest rate for sustained combustion is usually about an order of magnitude greater than this limit. It follows that entrainment of liquid droplets is a very likely phenomenon to occur in the combustion of liquids. It has been demonstrated that nitric acid-fuel systems have no smooth burning region when solid organic compounds were used as fuels.6 I n order t o establish that this was not due to the relatively high melting point of these compounds the system 99% nitric acid-sebaconitrile was studied. This system did not burn until a pressure of 154 atm. was reached and then it burned only turbulently. TABLE V Sebaconitrile was chosen because it was a liquid of RELATIONSHIP BETWEEN COMBUSTION TUBE DIAMETER AND approximately the same vapor pressure as mCONSUMPTION RATE DATA AT ONSET OF TURBULENT dinitrobenzene (approximately 1 p of Hg a t 45’) COMBUSTION IN THE 2-NITROPROPANE-NITRIC ACIDSYSTEM” which was one of the solids previously studied.6 Tube Many systems have been studied in which low inside 99% HNOa Q5% ”On diarnRt Rt vapor fuels were used, and in every case the systems (om./ Pt (cm./ eter Pt (mm.) (atm.) sec.) n (atm.) seo.) n have no smooth burning region. These results 1 . 8 5 5 . 4 2 ~ 30 . 9 5 0 . 7 6 8 7 . 7 1 1 . 5 1.07 0.95 show that the vapor pressure of the fuel is impor4 . 0 52.02C3 1.20 0 . 5 2 8 2 . 6 i c 1 . 5 1.54 .75 tant. Presumably, the vapor pressure of the fuel 6 . 0 41 8 & 3 0.95 1 66 7 5 . 8 z k 2 . 0 1 . 1 4 .62 a t the surface temperature was too low to produce a P t , pressure at onset of turbulence; Rt, rate a t onset of an adequate supply of fuel t o maintain the vapor turbulence; n, pressure exponent in equation 3 just before phase reactions. Sustained combustion could occur turbulent combustion is reached. only in the turbulent region where particles of fuel Another experiment on the applicability of Rey- were entrained in the vapor phase. Then the nold’s number to the onset of turbulence was tried droplets of fuel can burn by a diffusion flame by changing the shape of the combustion tube. mechanism in an oxidizing atmosphere. Direct Tubes with rectangular cross section 1 mm. by 10 observation of the combustion of liquids by high mm. were used. ‘These have approximately the speed photography indicates the possibility that same cross sectional area as a 3.7 mm. i.d. circular entrainment is the process that triggers the onset cross section tube. Since the largest dimension of of turbulent combustion. This may be why poor the rectangular tube will yield the highest Reyn- correlation with Reynold’s number was obtained old’s number for a given consumption rate it was since combustion product gas velocity while imassumed that this is the one to be used in predicting portant may not be a controlling factor. Landau’s Theory.-A theory on the transition the rate for onset of turbulence. I n the circular tube for the system 2-nitropropane-999;b nitric acid from deflagration to detonation developed by the rate for the onset of turbulence is approximately Landau yields an equation which gives the critical 1.2 cm./sec. Consequently, if the critical Reynold’s burning velocity for the transition from smooth t o number is constant for tubes of different shape the (12) “Chern. Engr. Handbook,” J. H. Perry, Editor, Third Edition, system should go into turbulent combustion in the McGraw-Hill Book Co., New York, N. Y., 1950, p. 514. ~
R. H. OTTEWILL AND H. C. PARREIRA
912
pulsating combustion of liquid@ (presumably “pulsating combustion” has the same meaning as the term “turbulent combustion” used in this discussion). This critical velocity V is given by V‘ = 4gffape
(4)
where g is the acceleration due to gravity, CY is the surface tension of the liquid at its boiling point, 6 is the density of the liquid and p is the density of the gaseous combustion products. It is interesting that V depends only on quantities that do not involve the detailed chemical kinetics of the combustion process. Fortunately data were available to evaluate eq. 4 for the system Z-nitropropane97% nitric acid. The calculated critical value of V turned out to be 1.22 cm./sec. which is in fairly good agreement with the observed value of 0.76 cm./sec. The gas density was calculated assuming complete combustion and perfect gas behavior. The surface tension (10 dyne em.) was an extrapolated value at the surface temperature of the burning liquid. Although eq. 4 gives a good prediction of the critical velocity, it does not seem to be compatible with other experimental results. According to eq. 4 the critical velocity should vary approximately as the square root of the bomb pressure. Data in Table V shorn that the critical velocity stays nearly constant, but the pressure did not stay constant. Also, eq. 4 does not contain a term dependent on liquid viscosity; hence, the critical velocity and pressure should be independent of liquid viscosity. This is not borne out by the results in Table 11. In these systems the surface tension at room temperature was increased only about 2 dyne centimeters in going from the pure system to the 0.75y0 (13) L. L. Landau, Ezp. and Theor. Phys., 14, 240 (1944).
Vol. 62
Lucite system and this difference tended to decrease as temperature increased. Hence, it is unlikely that the observed increase in the critical velocity was due to an increase in the surface tension of the Lucite systems. Finally, eq. 4 does not seem to be able to describe the behavior of the systems containing low vapor pressure fuels, unless it is assumed that in these cases the surface temperature reaches the critical temperature of the system so that the surface tension goes to zero. Then any burning velocity would exceed the critical velocity and the system would not have a smooth burning region. However, it has been shown by temperature profile studies that it is unlikely that burning liquids reach their critical temperature at the onset of turbulent combustion. l4 Also good qualitative evidence that turbulent burning liquids have a surface tension is given by the fact that their burning surface clings to the fine thermocouple wires used to make temperature profile measurements. Although Landau’s theory does not appear to correlate adequately some of the data obtained in this study, it is possible that the theory may be extended to do it. In fact, this is implied in ref. 1, but quantitative relations are not given. Acknowledgments.-The authors wish to express their thanks to Mr. P. M. Rust for obtaining the consumption rate data on the Lucite containing systems and to Mrs. M. M. Williams for making calculations of the adiabatic flame temperature and equilibrium gas composition at the flame temperature for the 2-nitropropane-nitric acid system. (14) D. L. Hildenbrand and A. G. Whittaker, “Fifth Symposium (International) on Combustion.” Reinhold Publ. Corp., New York, N. Y.,1955, p. 212.
A PHOTOMETER FOR LIGHT SCATTERING AND KINETIC MEASUREMENTS AT CONSTANT TEMPERATURES BYR. H. OTTEWILL AND H. C. PARREIRA Department of Colloid Science, Cambridge University, England Received November 96,I067
A versatile light scattering apparatus has been constructed which enables a wide variety of problems to be studied at controlled temperatures’ such problems range from the measurement of low molecular weights (ca. 5,000) to the study of the formation of inorgank sols. Particular attention has been paid to electrical design in order to obtain a high sensitivity and maintain high stability, To eliminate stray internal reflections, which were found to become very important when measuring turbidities of the order of 10-6 cm.-l, a rectangular channel enclosure for the incident beam, placed just before the cell, was found to be successful. The performance of the apparatus was tested by measuring the Rayleigh ratios of carbon tetrachloride, benzene and toluene and the micellar weights of dodecylpyridinium chloride and dodecylpyridinium bromide in water. I n order to follow kinetic rocesses the apparatus was adapted to take a microcell with a rapid mixing device; this was tested by following the rate ohormation of silver iodide from dilute solutions M ) of silver nitrate and potassium iodide.
Introduction Light scattering has now become a well established technique for the investigation of colloids in solution, and many pieces of apparatus for such measurements have been described.‘ However, .
(1) (a) K. A. Stacey, “Light Scattering in Physical Chemistry,” Butterworths Scientific Publications, London, 1956, p. 106. (b) M. ILL Fiahman, “Light Scattering by Colloidal Systems,” Technical Service Laboratories, New Jersey, 1957,p. 22.
there still appears need for improvement in design in order t o measure accurately molecular weights of 10,000 or less. Moreover, the use of light scattering as a means of following kinetics processes, with half-lives of the order of a few seconds, does not appear to have been developed to any extent. Recent investigations, in these laboratories, employing light scattering as a means of measuring the micellar weights of cationic detergents2and the (2) R. H. Ottewill and H. C. Parreira; t o be published.
b
