Thermal Diffusion and Convective Stability Experimental study of the Carbon Tetrachloride + Chlorobenzene System BY ANTONIO SPARASCI AND H. J. VALENTINE TYRRELL* Department of Chemistry, Chelsea College, Manresa Road, Chelsea, London SW3 6LX Received 17th April, 1974 The thermal diffusion behaviour of carbon tetrachloride + chlorobenzene mixtures has been studied (at a mean temperature of 25°C) in horizontal liquid films confined between two rigid, thermally conducting, surfaces 0.923 mm apart. The heavier component (CCI,) migrated to the cold wall for all mixtures studied. Soret coefficients, thermal diffusion factors and heats of transport have been calculated from experiments where the upper plate was heated with respect to the lower one and also from experiments where the direction of the thermal gradient was reversed.Provided that the gradient in the second group of experiments was below a critical limit the results from the two sets of experiments were in good agreement. When the lower surface was heated with respect to the upper one, there was a critical limit to the applied temperature interval above which the apparent Soret coefficient decreased. The observed critical limits agree quite well with the predictions of a recent linear stability analysis. The type of convection which sets in above this limit has not hitherto been directly demonstrated because it does not contribute to the total heat flux across the liquid layer. If a horizontal fluid layer, thickness d, is heated from below, the fluid shows no convective motion as long as the temperature gradient across it (p ; taken as positive when the layer is heated from below) is less than a certain minimum va1ue.l This minimum depends upon the thickness of the layer, the experimental conditions employed, and the physical properties of the fluid.For a single component system, the critical limit is usually related to a dimensionless number R (Rayleigh or Rayleigh- BCnard number) defined as : R - gpapd4/Ky. (1) In eqn (1) g is the gravitational acceleration, p the density, a the volume coefficient of expansion, K the thermal diffusivity and y the dynamic viscosity. When /3 is large enough for R to exceed 1708 (assuming the layer to be conhed between two rigid, plane, horizontal surfaces) regular patterns of convective motion can be seen in the fluid (BCnard cellules).l The onset of this convective motion can either be detected optically or, more commonly, by studying the heat transfer rate across the fluid.When the critical value of R is exceeded this rate shows a sharp increase, that is, the apparent thermal conductivity increases suddenly at the critical value of p. of the components under the influence of the temperature gradient (Soret phenomenon). The density gradient associated with the temperature gradient will be modified by the establishment of concentration gradients, and the question of convective stability in such layers becomes more complicated. The problem has been considered by several Schechter, Prigogine and Hamm pointed out that the thermal diffusivity of a liquid is very much greater than the diffusion coefficient D(K/Dw lo2).Conse- quently, thermal equilibrium is attained much more rapidly than concentration 42 In liquid systems of more than one component there may be partial separationA. SPARASCI A N D H . J . V . TYRRELL 43 equilibrium, and as a result, convective flow may occur even under conditions where the overall density gradient would be such as to stabilise the layer in the gravitational field. Such flows were earlier suggested as a possible reason for certain discrepancies in results of experiments on thermal diffusion in aqueous electrolytes. A linear stability analysis for the case where KID is large (2 100) has led to some interesting conclusions. If the heavier component (subscript 1) migrates to the cold wall, the Soret coefficient (a) is defined to be positive : where Xi, Ni are respectively the molar and weight fractions of component i and the suffix " stat " indicates that dX,/dT, dNl/dTare measured in the stationary state.A dimensionless separation parameter S with the same sign as Q is defined as : where y = (a In p/dN,), and a is the volume coefficient of expansion, - (8 In p/aT),. Since : then, When the heavier component migrates to the cold wall ( S positive) the density gradient due to the temperature gradient is reinforced. The sign of this gradient is however changed when the heavier component migrates to the hot wall provided that the separation is large enough ( S < -1). The fluid layer then becomes gravitationally unstable. Experiments on unequally heated fluid layers can be classified into four groups as follows.(i) p negative, S positive. The density gradient always stabilises the layer against convective flow (if wall effects are neglected). (ii) p negative, S negative. From eqn (5) it is possible for the density gradient to become inverted, although even when this does not happen, bulk flow may occur because K % D. This seems to be the reason for some of the anomalous results reported for thermal diffusion experiments on systems where the heavier compon- ent migrates to the hot wall.9 (iii) /3 positive, S positive. In respect of the type of convective flow considered here the system is essentially the same as the preceding one provided that fl is relatively small. (iv) p positive, S negative.In this instance the temperature gradient gives rise to an inverted density gradient which is opposed by the migration of the heavier compon- ent towards the lower (hotter) surface. When KID is large, as in liquid systems, oscillatory instabilities (" overstable " states) have been predicted independently by Hurle and Jakeman and by Velarde and Schechter.6 Finite amplitude temperature oscillations have been shown 4* 21 to occur at the centre of a horizontal cell, heated from below, when filled with a water + methanol mixture for which S was negative.44 THERMAL DIFFUSION AND CONVECTIVE STABILITY The instabilities were observed for the experimental conditions predicted by the theory. At low temperatures (< 10°C), an 0.5 mol dm-3 aqueous sodium chloride solution has a negative Soret coefficient.Caldwell 22 has examined the heat flux across a horizontal layer of this solution as a function of the temperature interval (with #l positive). The apparent thermal conductivities showed a sudden increase at Rayleigh numbers above the theoretical value for a single component system (1708). From these observations, and the theoretical treatment of Hurle and Jakema~~,~ Soret coefficients were calculated 22 which agreed well with those obtained by more con- ventional methods. There was, additionally, some evidence of finite amplitude instabilities near the critical point. Experiments with positive values of p are extensions of the Rayleigh-BCnard type of experiment to two component systems. If S is positive, theory 6* predicts that convective instability should occur for smaller values of /3 than would be required to induce instability in a one-component fluid layer having the same dimensions and physical properties.This is not solely due to the fact that the migration of the heavier component to the upper (colder) surface of the cell reinforces the inverted density gradient associated with a positive value of B, because an identical limit is predicted for the conditions described under (ii) above. In these conditions, the stabilising density gradient associated with the temperature gradient is opposed by a de-stabilising gradient associated with the migration of the heavier component to the heated upper surface. Even if the overall density gradient is such as, apparently to stabilise the system in the gravitational field, convective instability can occur because of the fact that K $ D.Consider, for example, a small volume element in the two component liquid film for which both p and S are negative and the density is greatest at the bottom of the cell. If a fluctuation occurs and the volume element rises slightly, it should, at first sight, sink back to its original position in a short time. Though less rich in the heavier component, it is colder, and therefore heavier, than the fluid surrounding it in the new position. However, since K 9 D, the volume element may reach thermal equilibrium with these new surroundings before its composition changes substantially, and it will then be lighter than its surroundings. Consequently, it will tend to rise further, the original fluctuation being thereby reinforced rather than damped out.In this way, slow convection currents may be set up even when the overall density gradient seems adequate to prevent them. A similar phenomenon is found in oceanology as the '' salt fountain effect ", c.f. ref. (7). The Velarde-Schechter theory predicts that convective instability should occur when p and S have the same sign if a thermal Rayleigh number a reaches a critical value of 720. a is defined as (RSKID), which, from the definitions (1) and (3), is equivalent to : = R*aNlN2#l where R* is defined as the dimensionless quantity the temperature gradient (Pcrit) above which this served is therefore given by (7) (gpyd4/Dy). The critical value of type of convection should be ob- When this critical temperature gradient is reached the wavelength of the convective cell will be large.Theoretically it should be infinite but R varies little with wave- number at small wavenumbers,6 and there may be a number of long wavelength modesA. SPARASCI AND H. Y. V. TYRRELL 45 operative together. If so, definite tessellated patterns similar to those observed for one component systems at the critical point would not be seen. The velocity of such non-regular convective motion is very small.6 The onset of convection in binary systems with both p and S positive has hitherto been examined by the technique of measuring the heat flux across the fluid layer as a function of p. Suitable systems are carbon tetrachloride +benzene and carbon tetrachloride + chlorobenzene. In both cases the heavier component (carbon tetrachloride) migrated to the cold wall in a thermal gradient O.contrary to an earlier report.12 However, no change in the apparent thermal conductivity occurred in a cell heated from below until the normal Btnard limit was reached.3* ' 9 l3 Jt was originally suggested that this was because no thermal diffusion separation can occur in a two component liquid layer heated in this l 1 but such a separation was later observed for the toluene+ethanol system l4 in a pure Soret effect cell. The true explanation seems to be 6* '* l5 that the convective instability described by eqn (6), (7) and (8) involves a very slow bulk motion of the liquid. Because of the large value of KID for liquids, this motion does not contribute to the heat flux across the cell, and its onset cannot therefore be detected in thermal conduction experiments.Beltoa and Tyrell l4 noted in their experiments that the apparent Soret coefficient observed in an inverse temperature gradient (in the toluene +ethanol system with S positive) was reduced when p became large. A systematic study of the apparent Soret coefficient of a binary system with S positive, using a range of positive and negative values of p has therefore been carried out to search for the existence of a critical limit below the normal Bknard limit, and to test the theoretical conclusions of Velarde and Schechter summarised in eqn (6)-(8). In particular, eqn (8) shows that Pcrit should be dependent upon composition and, if both 6 and R* vary little with composition, it should be a minimum when N1 = N2 = 0.5.The system chosen for the study was carbon tetrachloride + chlorobenzene, partly because there had been some dispute about the sign of the separation in a thermal gradient, and partly because this system had been used in some of the heat flux experiments carried out by Legros, van Hook and Thomaes. EXPERIMENTAL The design of the Soret cell and the experimental techniques have been described ear- lier.lou9 l6 In the present work the plate separation in the reference cell was 0.918 mm and in the test cell 0.923 mm. The method of controlling the temperature interval across the cell used earlier was equally suitable for positive or negative values of p. Because the tempera- ture gradient was to be applied in both directions, and both components have relatively large refractive index increments with temperature, the optical system used limited the useful temperature interval which could be used across the cell to about +O.5O0C, for normal Soret effect studies ( p negative) temperature intervals of up to 0.8"C were used earlier ; in principle, the necessity of using a smaller temperature interval reduces the accuracy with which the Soret coefficient can be measured.Refractive index increments with temperature for the NaD line at constant composition were measured at a mean temperature of 25°C using a Rayleigh refractometer and the technique described earlier. Oa Unpublished data on the refractive index of these mixtures as a function of composition for the mercury green line (2 = 546.1 nm) had been found l7 to fit the curve (valid at 23.5"C) : n:z& = A+ BX2 + kXq(1- X,)"'.(9) In this equation, A was the refractive index of pure carbon tetrachloride, B the difference between the refractive indices of pure chlorobenzene and pure carbon tetrachloride, and Xz the mole fraction of chlorobenzene. The third term on the right contains three empirical46 THERMAL DIFFUSION AND CONVECTIVE STABILITY constants (k,p, rn) determined by a least squares fitting procedures as : k = 2.116~ rn = 0.7698, p = 0.5891. This third term represents the deviation of n&!l from linearity in mole fraction, and it is here assumed that the parameters k, rn, p can be used unchanged to describe the curvature of the plot of nk5 with composition provided that appropriate values of A and B were used.Using a precision Pulfrich refractometer on our purified samples the following results were obtained : carbon tetrachloride : nk5 = 1.457 56 c hlor o benzene : nk5 = 1.521 86, hence Bi5 = 0.064 30. Differentiation of eqn (9) gives : (a~~A~/ax~)~ = B ; ~ + kxq( 1 - x2)"(p/x2 - mix,). (10) This equation was tested by comparing the value of (dn&5/dX2)T predicted from (10) for X2 = 0.2862 with a directly measured value using the techniques described earlier.loa* 16, l8 The calculated value was 7.19 x The agreement is good, and no further direct measurements of (anis/dX2), were undertaken. Carbon tetrachloride (AnalaR grade) was purified by initially refluxing over mercury for two hours. This was followed by washing with concentrated sulphuric acid to remove traces of sulphides, 5 % sodium hydroxide solution and water. After drying over fused calcium and the experimental value 7.08 x 8.4- 8 . 2 - 8.0 7.8 7.6 7.4 7.2 7.0- 6.8 El B E l El - - - - - I 5.2 4.8 4.4 4.0- 3.6 3.2 2.8 2.4 2.0 Xi = 0.1982 - r;] El - I3 - - - - - !3 I I Xi = 0.51 6.A 6.2 5.6- 5.2 4.8 4.4 4.0 3.6 Xi = 0.8059 El u m w n % I3 - - - - , FIG.1 .-The onset of convection in thin (0.923 mm) liquid films of carbon tetrachloride+ chloro- benzene solutions heated from below as shown by the change in apparent Soret coefficient as the temperature interval across the cell is increased.A. SPARASCI AND H. J . V . TYRRELL 47 chloride the sample was fractionally distilled through a 50 cm column packed with alternate 3 cm bands of multiple Fenske and single turn helices.A reflux ratio of 4 : 1 was employed, the middle fraction (66 %) being retained. This fraction was distilled twice more, the middle fraction being retained at each stage. The final product was collected in a specially designed vessel which enabled storage and dispensing to be achieved without contamination by atmospheric water vapour (ni5 = 1.457 56 ; lit., ni5 = 1.457 59). Chlorobenzene was shaken with portions of concentrated sulphuric acid until the latter was substantially colourless. This was followed by washing with water, 5 % potassium bicarbonate solution and water. After drying over fused calcium chloride the chlorobenzene was distilled in the column mentioned above. The middle fraction (66 %) was dried over phosphorus pentoxide for twenty four hours and distilled twice more, the middle fraction being retained at each stage.The refractive index of the final product was measured on a Pulfrich refractometer (nio = 1.524 61 ; lit., ni0 = 1.524 59). RESULTS For both positive and negative values of p the heavier component, carbon tetra- chloride, was found to migrate to the cold wall as reported by Legros, van Hook, and Thomaes l1 from flow-cell data i.e. S is positive for this system. Hence, for positive values of fl, there should be a critical value at which the observed Soret coefficient TABLE 1 .-THERMAL DIFFUSION FACTORS (298.1 0) FOR CARBON TETRACHLORIDE+ CHLORO- BENZENE MIXTURES IN HORIZONTAL LIQUD FILMS HEATED (a) FROM ABOVE ( p NEGATIVE), (6) FROM BELOW (p POSITIVE) WITH AN APPLIED TEMPERATURE GRADIENT LESS THAN THE CRITICAL VALUE FOR CONVECTION (MEAN TEMPERATURE 25°C) molar fraction carbon tetrachloride X I O.oo00 0.0989 0.1000 0.1982 0.2000 0.3000 0.3180 0.3730 0.3917 0.4OoO 0.5000 0.5024 0.5150 0.5896 0.5957 0.6000 0.6050 0.6977 0.7000 0.7172 0.7220 0.8Ooo 0.8059 0.8173 0.8921 0.8955 0.9000 1 .m 104( - a n & 5 / a ~ ) / K-1 5.73 5.69 5.65 5.61 - - - - - 5.57 5.54 - - - - 5.50 - - 5.48 - - 5.46 - - - - 5.44 5.43 thermal diffusion factor (02") negative values of B - 2.88( 0.1 9) 2.25(+ 0.09) - - - 1.69( + 0.04) 1.50(+ 0.10) 1.51(+ 0.1 1) 1.46( + 0.06) 1.56(+0.09) 1.47( + 0.05) 1.55(+ 0.07) 1.60( + 0.06) - - - - - - 1.58( & 0.05) - - 1.64(+0.09) 2.14(+ 0.07) 2.15(&0.07) - - positive values of B - 2.39(+0.08) - - .69(+0.08) .47( + 0.05) .42( + 0.12) .61( & 0.1 1) .53( & 0.05) - - - - - - - - 1.70( & 0.05) - - 1.78(+0.11) -48 THERMAL DIFFUSION AND CONVECTIVE STABILITY should begin to fall because of the onset of convection.According to the Velarde- Schechter theory [eqn (6)-(8)] this critical point should be composition-dependent. Fig. (1) shows results obtained in this work at three compositions. In each case, there is a fairly clearly defined critical temperature interval above which the measured Soret coefficient decreases, and, as predicted, this is less for Xl = 0.515 than for X , = 0.198 or X , = 0.806. Soret coefficients (0) have been calculated both for positive values of /3 less than Pcrit, and for negative values of p where Q was essentially independent of p as expected.Results are shown in table 1, along with the refractive index increment values used in the calculations. There was no significant difference between thermal diffusion factors (or Soret coefficients) measured with negative values of /3 and those with positive values of p, provided Pcrit was not exceeded. The precision with which Q could be measured was essentially the same for the two groups of measurements and similar to that achieved in other work using a similar technique. DISCUSSION The Soret coefficients found for this system are comparable in magnitude with those K-I for an Since the Soret coefficient is related to the heat of transport found for the system carbon tetrachloride+benzene lo (Q = 6.4 x equimolar mixture).by the relationship : (1 1) Q,* RT2x,(1 +d In f2/d In XZ)T,P changes in 0 with concentration may be due to changes in Q*/X, or to the thermo- dynamic term, or both. Measurements of the total vapour pressure over chloro- benzene +carbon tetrachloride mixtures have been obtained by Bittrich and his co-workers 23 at 40°C but they have not tabulated activity coefficients (f) for the individual components. Although the total pressure data are given only at mole fraction intervals of 0.1, we have calculated partial pressures by the Boissonnas method,24 and estimated activity coefficients from these without correcting for vapour phase non-ideality. Values of (1 + a Inf/a In X)j- were obtained from these using a simple finite-difference method and combined with Soret coefficients inter- polated from a smoothed curve, constructed from data in table 1, to give values of Q$/Xl (table 2).Although the activity coefficient terms are inevitably not very accurate, and strictly apply only at 40°C, it seems certain that the observed changes in CT with concentration cannot be explained in terms of a variation of (1 +a lnf/ d In X)T,p with composition. Fig. 1 illustrates the sharpness of the transition at the critical temperature interval at which the apparent Soret coefficient began to fall off in the experiments where /? was positive (fluid layer heated from below). The three plots are representative and clearly there is little doubt about the value of the limiting temperature interval for Xl = 0.8059. Iii all cases, the horizontal line can be regarded as well-established being derived from a smoothed plot of Soret coefficient against composition based on all the data in table 1 .The individual experimental points were obtained from several independent experiments and show the kind of scatter expected from experimental errors of measurement, which are particularly severe for small values of AT and sol- utions dilute in either component. In most cases (cf. data illustrated for Xl = 0.1982, 0.8059), the fall in the apparent Soret coefficient with increasing AT was apparently linear, and the critical temperature interval could be determined to a few 1- Later confirmed by communication from Professor Bittrich of his own activity data. Q =A . SPARASCI A N D H. J . V .TYRRELL 44 tenths of a degree with some certainty. In the centre of the composition range (cf. plot shown for X , = 0.5150) the fall was not linear in AT, and extrapolation to the critical limit was more difficult. In these cases we took the critical limit as being the highest value of AT at which the Soret coefficient, as measured with p positive, coincided closely with the value based on data in table 1. TABLE 2.-HEATS OF TRANSPORT (@/xi), THERMODYNAMIC FACTORS, AND SORET COEFFICIENTS (0) DERIVED BY INTERPOLATION ON A SMOOTHED CURVE molar fraction carbon tetrachloride, XI 0.85 0.75 0.65 0.55 0.45 0.35 0.25 0.15 (l+8 InfP In WT.P 1.10 1.10 1.10 1.09 1.06 1.08 1.02 1.06 103x alK-1 tQt/Xl)/kJrnol-' 6.60 5.60 5.13 5.00 5.00 5.38 6.50 8.58 5.4 4.6 4 . 2 4.0 3.9 4.3 4.9 6.7 However, in order to calculate K, other data are needed.Eqn (6) can be re-written : Rcrit = (gd 3 / ~ ~ ) ( a ~ I a ~ 1) 1 X2ATc (12) The variation of density with composition for this system was studied by Das and Roy l9 at 10°C intervals between 10 and 60°C. In each case we have found that the density could be represented as a linear function of mole fraction of carbon tetra- chloride (X,), the correlation coefficients being greater than 0.9999 in each case. Thus ap/a XI was effectively independent of concentration, the following values (g ~ m - ~ ) being obtained from the least squares analysis at each temperature : 0.496 24 (10°C) ; 0.487 72 (20°C) ; 0.479 42 (30°C) ; 0.470 31 (40°C) ; 0.462 33 (50°C) ; 0.452 26 (60°C). These values vary linearly with temperature to a good approximation and a least squares analysis gave (correlation coefficient 0.9996) : At 25°C the best estimate of dp/i?X, was therefore 0.483 43 g ~ r n - ~ , and this was used in the subsequent calculations of 8.The diffusion coefficient presented more serious difficulties since no experimental diffusion work seems to have been undertaken on these mixtures. Self diffusion coefficients for the pure components Dr were estimated by assuming that : 2o (i?p/i?X1)T = 0.505 23-8.719 x (T-273.15) g CM-~. (13) D*q = kT/4nrW. (14) For eqn (14) to apply, a suitable method of calculating the van der Waals' radius Y, is required. Using the technique described by Edward,20 rw was found to be 0.283 nm for chlorobenzene and 0.275 nm for carbon tetrachloride.This made it possible to estimate DT for carbon tetrachloride and DZ for chlorobenzene with a reasonable degree of accuracy. The simplest possible relationship between the mutual diffusion coefficient D and the self diffusion coefficients is [ref. (2) p. 1341 : In the absence of more complete data the estimates of DT obtained from eqn (14) were D = X2D;+XlD;. (15)50 THERMAL DIFFUSION A N D CONVECTIVE STABILITY combined with eqn (15) to give the following estimate of Dy and its variation with composition : Hence Rcrit may be calculated at a series of compositions. The simple Rayleigh- Benard theory [eqn (l)] can be modified to take account of the increased de-stabilisa- tion due to the concentration gradient arising from the establishment of the Soret equilibrium, by replacing a by a( 1 + S ) in eqn (l), cf. eqn (5).The critical temperature interval in this case would then be given by : Dy = (1.1998 - 0.424XJ x lo-’ dyn. (16) 1708Ky pgd4a( 1 + s>. The definition of S in eqn (3) is equivalent to : Hence, in addition to the pbysical constants already discussed, it is necessary to know K, and (ap/dT),. To obtain K, thermal conductivity and heat capacity data are required. Frontas’ev and Gusakov have measured thermal conductivities for the pure components, and Mukhamedzyanov et aZ.26 have pointed out that, for nearly- ideal mixtures, the thermal conductivities of mixtures vary almost linearly with mass fraction, though not with mole fraction. Hence, values of the thermal conductivity of each mixture studied was estimated in this way.Excess heat capacities have been obtained for this system, together with heat capacities of the pure and reliable viscosity data are also available.27 Densities and values of (ap/aT), can be obtained from the data of Das and Roy l9 already referred to. s = - aX,X2(aP/aX,)*/(ap/aT)x. (1 8) TABLE 3 .-OBSERVED AND CALCULATED TEMPERATURE INTERVALS AND CRITICAL VALUES OF THE -k CHLOROBENZENE SOLUTIONS HEATED FROM BELOW (TWO RIGID BOUNDARIES 0.923 lTllll APART, THERMAL RAYLEIGH NUMBER (&.Tit) FOR HORIZONTAL LIQUID FILMS OF CARBON TETRACHLORIDE MEAN TEMPERATURE 25°C) critical temperature intervalslOC calculated molar fraction mpdified carbon Velarde-Schechter Rayleigh-B&nard tetrachloride, X I Rcrit. observed (eqn 12) (eqn 17) 0.8059 0.7172 0.5150 0.5000 0.3917 0.3730 0.3180 0.1982 1100 1 200 1000 900 1100 1100 1200 1200 0.35 0.24 0.34 0.21 0.26 0.18 0.24 0.18 0.27 0.18 0.28 0.19 0.32 0.19 0.32 0.19 6.8 6.8 6.9 7.0 7.3 7.3 7.5 8.8 Temperature intervals were obtained experimentally from the observed optical deflection produced by the reference cell subject to appropriate corrections, see ref.(1Oa). The results of these calculations are shown in table 3. Obviously the onset of convective re-mixing occurs at much smaller temperature intervals than would be predicted from the modified Rayleigh-BCnard eqn (17). The observed value of Rcrit (mean value 1100) is 53 % higher than the Velarde-Schechter prediction of 720, though it does remain, as predicted, substantially independent of concentra tion. The uncertainty in the experimental value of ATcrit is not large enough to explain this apparent discrepancy, but, in deriving acrit from the experimental data, a number ofA .SPARASCI A N D H. J . V. TYRRELL 51 assumptions have had to be made, the effects of which are impossible to judge. In addition, the theory assumes that K/D= lo2, though for the mixture considered here, this ratio appears to be about 50. In any event, this apparent discrepancy between theory and practice is relatively unimportant in comparison with the unequivocal evidence we have now obtained for the existence of a critical limit for the onset of very slow convective motion in a two- component system for which both p and S are positive. This limit is far below that associated with the normal Rayleigh-B6nard motion at which increased heat flow has been observed for this ~ystern.~ The convective velocity in our experiments must be low enough for no excess heat flow to be associated with it, as predicted by theory, and it can only be observed, as here, by studying changes in the concentration distri- bution across the fluid layer.This kind of convective motion is almost certainly responsible for many of the discrepancies in the published literature on Soret coeffi- cients since it may start at the vertical boundary walls of the Soret cell, as was sug- gested originally by Agar and Turner.* We are indebted to Dr. M. G. Velarde, Professor J. Thomaes and Dr. J-C. Legros One of us (A. S.) is indebted for useful discussions and access to unpublished data.to the S.R.C. for the award of a studentship. cf. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford, 1961). cf. H. J. V. Tyrrell, Diflusion and Heat Flow in Liquids (Butterworth, London, 1961). J-C. Legros, W. A. van Hook and G. Thomaes, Chem. Phys. Letters, 1968,1, 696. D. T. J. Hurle and E. Jakeman, J. Fluid Mech., 1971, 47, 667. R. S. Schechter, I. Prigogine and J. R. Hamm, Phys. Fluids, 1972, 15, 379. M. G. Velarde and R. S. Schechter, Phys. Fluids, 1972, 15, 1707. J-C. Legros, J. K. Platten and P. G. Poty, Phys. Fluids, 1972, 15, 1383. J. N. Agar and J. C. R. Turner, Proc. Roy. SOC. A, 1960,255, 307. M. G. Velarde and R. S. Schechter, Chem. Phys. Letters, 1971, 12, 312. Turner, Trans. Faraday SOC., 1969, 65, 1523. lo cf. (a) L. Guczi and H. J. V. Tyrrell, J. Chem. SOC., 1965, 6576 ; (b) M. J. Story and J. C. R. l 1 J-C. Legros, W. A. van Hook and G. Thomaes, Chem. Phys. Letters, 1968,2,251. l 2 G. Thomaes, J. Chim. phys., 1956, 50,407. l3 J-C. Legros, D. Rasse and G. Thomaes, Chem. Phys. Letters, 1970,4, 632. l4 P. S. Belton and H. J. V. Tyrrell, Chem. Phys. Letters, 1970, 4, 619. l 5 M. G. Velarde and R. S. Schechter, Chem. Phys. Letters, 1971, 12, 312. l6 G. Farsang and H. J. V. Tyrrell, J. Chem. SOC. A , 1969, 1839. J. Demichowicz-Pigonawa and H. J. V. Tyrrell, Roczniki Chem., 1969,43,433. l 9 L. M. Das and S. C. Roy, Indiaiz J. Phys., 1930,5,441. quoted in J. Timmermanns, The Physico- chemical Constants of Binary Mixtures in Concentrated Solutions (Interscience, New York, 2o J. T. Edward, J. Chem. Educ., 1970,47, 261. 21 J. K. Platten and G. Chavepeyer, J. Fluid Mech., 1973, 60, 305. 22 D. R. Caldwell, J. Phys. Chem., 1973, 77, 2004. ’ J-C. Legros, personal communication. 1959-60), V O ~ . 1, p. 321. 23 R. Kind, G. Kahnt, D. Schmidt, J. Schumann and H-J. Bittrich, Z. phys. Chem. (Leipzig), 1968, 230, 277. 24 C. G. Boissonnas, Helu. Chim. Acta, 1939, 22, 341. 25 V. P. Frontas’ev and M. Y. Gusakov, Uch. Zap. Saratovsk. Gos. Uniu., 1960, No. 69, 237 ; see 26 G. K. Mukhamedzyanov, A. G. Usmanov and A. A. Tarzanimov, Izvest. V. U. Z., Neft i Gaz, 27 R. J. Fort and W. R. Moore, Trans. Faraday Soc., 1966, 62, 1112. Chem. Abs., l963,58,1923b. 1964, 7(10), 70; see Chem. Abs., 1965, 62, 7142f.