4426
J. Phys. Chem. B 1998, 102, 4426-4431
Soret Coefficients of Organic Solutions Measured in the Microgravity SCM Experiment and by the Flow and Be´ nard Cells S. Van Vaerenbergh* and J. C. Legros Chemical Physics Department, MicrograVity Research Centre CP 165, UniVersite´ Libre de Bruxelles, Brussels, Belgium ReceiVed: NoVember 17, 1997; In Final Form: March 17, 1998
Soret coefficients of aqueous solutions of methyl, ethyl, isopropyl, and n-butyl alcohols and of solutions of methyl and ethyl alcohols in benzene have been measured in the Soret coefficient measurement (SCM) experiment under microgravity conditions on board the orbital platform EURECA at a mean temperature of 37.5 °C. These reference measurements will allow us to improve the understanding of the ground based results and to calibrate the ground based setup. This point is discussed with the values that we obtained by the flow cell technique and for systems that exhibited a hysteretic loop in the Schmidt-Milverton plots in the Be´nard cell at a mean temperature of 37 °C.
1. Introduction In a binary solution the mass diffusion flux which is induced by temperature (T) and mass fraction (N) gradients only may be written1 as a first approximation as
J ) -FD∇N - FDTN0(1 - N0)∇T
(1)
where N0 is the mean mass fraction, F is the specific mass, and D and DT are the mean isothermal diffusion and thermodiffusion coefficients of the solute. It is assumed that the gradients are small enough to consider that the phenomenological coefficients are constant. In the ideal situation where a steady state without convection is reached between impervious and rigid walls, the species diffusion flux vanish, so that the solute gradient is
DT ∇N ) - N0(1 - N0)∇T D
(2)
The convention that the solute refers to the denser component is used; i.e., the Soret coefficient DT/D of the solution is positive when the denser component migrates toward the cold side. The largest Soret coefficients2 reported in the literature for organic solutions are up to 4 × 10-2 K-1, but they rarely exceed3 10-2 K-1. Even so, the thermodiffusion may deeply influence the hydrodynamic of non-isothermal liquid layers because of the large dependence of density on the mass fraction and of the slow relaxation of solute inhomogeneities. To illustrate important practical consequences, let us just mention the influence of thermodiffusion in the distribution of components in the geothermal gradient of the natural reservoirs of oil.4-7 The large discrepancies,8,9 even on the sign, appearing in the published ground based measurements performed by different techniques, show how difficult it is to obtain reliable values of the Soret coefficients. The reason for such discrepancies is attributed to convective disturbances. Indeed, significant variations of density are induced by the temperature and concentration gradients. The resulting buoyancy forces induce natural convection and may also induce Rayleigh-Be´nard instabilities. The
Figure 1. Sketches of the techniques using the flow cell (a, top) and the Be´nard cell (b, bottom) with Schmidt-Milverton plots.
effects of the latter have been recognized since the 1970s8 and demonstrated experimentally.10 The horizontal gradients, unavoidable when lateral walls are considered, induce natural convection. Their perturbing action on measurements of Soret coefficients were suspected since the first measurements by Soret.11 This has, however, been demonstrated only recently thanks to the microgravity measurements performed in tin alloys.12,13 These results also allowed precise quantification of the convective perturbations14 in diluted solutions. For concentrated solutions, however, the density varies significantly because of the Soret effect, and without the knowledge of its amplitude, it is not possible to quantify the perturbing action of the lateral gradients on the measurements. To overcome this problem inherent to the measurement of Soret coefficients, it has been thought for a long time that cells with large aspect ratios (lateral extension/thickness) should be used. For organic solutions, such conditions can be best satisfied in the techniques using the flow cells15 and in the Be´nard cells.16,17 This is the reason we selected both cells for measurements in organic solutions. Parts a and b of Figure 1 provide sketches of these techniques. In the Be´nard cell used for these measurements, the liquid layer is in contact with the horizontal, parallel, and good heat conducting impervious walls. The upper plate is maintained at
S1089-5647(98)00232-6 CCC: $15.00 © 1998 American Chemical Society Published on Web 05/05/1998
Soret Coefficients of Organic Solutions a constant temperature, while the fluid is heated from the bottom plate by a controlled heating power. The temperature difference so obtained between the plates is plotted as a function of the heat flux (Schmidt-Milverton plots18). The transition from the purely diffusive transport of heat to the convectodiffusive transport after the onset of convection is revealed by a decrease of the slope. The onset of convection is initiated by the Rayleigh-Be´nard hydrodynamic instability. The onset conditions are obtained by a normal modes linear stability analysis. It shows19 that the critical temperature difference for the onset of convection is very sensitive to the value of the Soret coefficient. This is understandable since the thermal expansion and the contribution of the Soret effect to the density gradient are often of the same order of magnitude. If the Soret coefficient is positive (the denser component migrates toward the cold side), the two contributions add, and the convection starts for a lower temperature gradient than in a hypothetical pure liquid having the same viscosity, thermal diffusivity, and thermal expansion as the solution. To the contrary, when the Soret coefficient is negative, the two contributions compete and the flow will initiate at higher temperature gradients.19 In the Schmidt-Milverton plots, the stabilization by the solute field that appears for negative Soret coefficients is observed.20,21 A hysteresis21 is most frequently observed when this constraint is decreased back below its critical value. This hysteretic loop corresponds to an inverted Hopf bifurcation. To the contrary, for positive Soret coefficients, experiments show22 that the transition to the convectodiffusive regime seems to appear in these plots at critical temperature differences corresponding to fluids without the Soret effect. The reason can be understood using a nonlinear study of the RayleighBe´nard problem in solutions with the Soret effect.23 This study showed that the amplitude of the convective instability becomes significant only when the thermal Rayleigh number, whose definition is recalled below in formula 5, reaches the critical value of the pure liquid. Therefore the Nusselt number (ratio of the total heat flux crossing the layer to the one of the purely conductive state) becomes significant enough to be detected by a conventional thermal diagnostic, only for an imperfect supercritical bifurcation. Thus, the Schmidt-Milverton plotting appears to be better suited for measuring negative Soret coefficients, while another technique should be used for positive values. The approach of combining24 the Be´nard cell to another technique has been used in the past for NaCl aqueous solutions, a system for which the sign of the Soret coefficient changes with concentration.24,25 The flow cell was used in the ground measurements that are presented here for the above-mentioned reasons. The concentration gradient is established in a very thin layer (smaller than 0.5 mm) to minimize the possibility of onset of RayleighBe´nard convective instabilities. Still unexplained experimental results26 show, however, that the hydrodynamics of forced Poiseuille flow on binary mixtures heated from the top is far from being qualitatively understood. Other techniques could have been used for these measurements. However, they each lead to specific problems. For instance, recent developments show the possibility of performing measurements by velocimetry in a thermogravitation column.27 In this technique,3 natural convection is produced in a vertical channel by transverse heating. The convective velocity is then progressively amplified by the Soret effect, up to the point where it reaches a stationary value. The convective enhancement is therefore related to the Soret coefficients. However, the
J. Phys. Chem. B, Vol. 102, No. 22, 1998 4427 TABLE 1: Summary of the Soret Coefficients Measurements in the Flow Cell (at 35 °C), in the Be´ nard Cell (at 35-37 °C) and in the Microgravity SCM Experiment (at 37.5 °C)a Soret coeff × 103 (K-1) obtained by given conditions
system components water-isopropyl alcohol
no.
1 2 3 4 benzene-methanol 5 6 water-methanol 7 water-ethanol 8 benzene-ethanol 9 water-n-butyl 10 alcohol 11
mean mass Be´nard fraction flow cell cell 0.4 0.6 0.8 0.9 0.4 0.8 0.1 0.1 0.5 0.95 0.97
0.3 0.5 -1.0 -3.1 -1.4 4.0 1.0 -2.0 -2.5
SCM
+ 5.2 ( 0.6 + 5.0 ( 0.6 -2.4 -2.1 ( 0.3 -21 -2.2 ( 0.3 + 4.1 ( 0.5 + 19.1 ( 2.1 -26 -25 ( 4.5 + 3.7 ( 0.7 + 7.3 ( 0.8 -9.2 -6.8 ( 2.0 -11 -2.8 ( 1.3
a The mean mass fraction N0 given in the third column is for the first component (the densest). The numbers in column 2 refer to Figure 2.
theoretical or numerical correlations depend on many physical and geometrical parameters so that the accuracy of the obtained Soret coefficients is easily affected by experimental errors. Other techniques try to avoid the problems linked to convection by the introduction of porous media.28-30 It has, however, been shown that, in such media where the ratio contact surface/ volume may be large, the Soret effect mixed with effects linked to polarization at solid walls in the case of very fine grained media, known as thermodyalisis.29 For these reasons, any measurement performed at very low levels of gravity can be considered as reference measurements when it can be ensured that the convective remixing is reduced to a level below the accuracy of the measurement. Such reference data can be used to understand the origins of discrepancies obtained in the several ground based techniques. This has motivated the realization of fine microgravity experiments.31 After long delays, such measurements have been performed for the first time in 1992-3 in organic solutions, on board of the EUropean REtrievable CArrier (EURECA) during the Soret coefficient measurement (SCM) experiment.31,32 The results are reported in extenso for the first time in this paper. These standard values obtained are used to evaluate the coupling between the convection and the measured concentration gradients in the flow cell and the Be´nard cell by studying a common set of systems at mean temperatures between 35 and 40 °C. 2. Microgravity Measurements The results of the SCM experiment are listed in Table 1. The studied systems have been prepared with “proanalysis” components and with tridistilled water. The solutions have been carefully outgassed before filling the cells under vacuum. The samples were processed for 5 months in a microgravity environment at a mean temperature of 37.5 °C and with a mean temperature difference of 5 K in tubular cells having a length of height centimeters. They were recovered after a flight of nine months and analyzed on the ground by densitometry. The asymptotic steady state was evaluated to be attained at nearly 99%. The way to account for the specific experimental conditions has been detailed elsewhere,32 together with the detailed description of the experiment. Among the twenty measurements
4428 J. Phys. Chem. B, Vol. 102, No. 22, 1998 foreseen, nine failed due to corrosion of the volume compensators’ membranes. Upon further investigation, it was determined that the corrosive degradation was activated by space radiation. For the other eleven cells we have to conclude from accurate postflight inspection and from recovered volumes that the measurements are reliable. A weak remixing in these microgravity measurements has to be considered because of a low level of time dependent residual acceleration field. The measurements performed by eight accelerometers placed on the satellite shows that the component of the acceleration spectrum below 50 Hz remained under 10-5 of the ground level of gravity. The model14 developed for capillaries to evaluate the weak convective remixing on board satellites shows that it is the radial component of the residual accelerations that is the most dangerous. They combine with the radial density gradient that exists in the liquid due to the difference of conductivity of the walls to produce slow motions. The radial thermal difference in the cells of the SCM experiment has been evaluated with ESATAN, a thermal analysis software. It provides values below 0.35 K. The estimate of the convective perturbation on the value of the Soret coefficient is smaller than 5% in the worst case. This rough estimate has to be improved, however, to account for instance for variable gravity levels. After the recovery of the experiment, the Soret coefficients have been deduced from density measurements. Their densities and the density/composition curves are determined with a vibrating density meter.33 A cascade of two 15 L thermostatic water baths ensures a temperature stability of the densitometer better than 0.05 K. The constants of the instrument are obtained with air and tridistilled water densities. The accuracy on the value of the initial mass fraction is better than 1%. The manipulations of volatile liquids are probably the main source of error on the Soret coefficients deduced from the chemical separation. The latter is estimated to 0.5%, while the relative error on the thermal gradient is 5%. The resulting accuracies of the SCM measurements are obtained by the formula
|δ
DT DT δN0 δ∇T δ∇N / |)| |+| | + |(1 - 2N0) |+ D D ∇T ∇N N0 DT DT |δ / |convection (3) D D
The numerical values are given in the sixth column of Table 1 along with the values of the Soret coefficients. The accuracy of the microgravity measurements is smaller than 40% in the worst case of diluted solutions and of the order of 10% for concentrated solutions. One may appreciate such an achievement by comparing these values to others in published literature where even the direction of separation often differs from paper to paper. 3. Be´ nard Cell and Flow Cell Measurements The systems of SCM have been studied on ground laboratory with the flow cell and the Be´nard cell. The systems are prepared with the same bottles as those for the SCM experiment. The angle with the horizontal plane of the rigid walls of the flow cell is better than 1 arc min, and the stability of the temperature difference between the horizontal plates, better than 0.1 K. The Soret coefficient is deduced from the chemical separations between the upper and lower outgoing flows by the
Van Vaerenbergh and Legros
Figure 2. Example of Schmidt-Milverton plots obtained in the Be´nard cell in systems presenting a hysteretic loop, here a mixture of 90 wt %/0.9 wt % isopropyl alcohol and water at 35 °C. The figure shows the temperature differences considered in the derivation of eqs 15 and 16.
following formula:15
Nup - Nlow ) -
3 DT N (1 - N0)(Tup - Tlow) 8 D 0
(4)
These flow cell measurements have been carried out at a mean temperature of 35 °C and with a temperature difference of 4.5 K. It corresponds to a thermal Rayleigh number of about -50. This number is defined by
Ra ) -g
∂ ln F 3 d (Tup - Tlow)/Kν ∂T
(5)
where d is the thickness of the layer, here equal to 0.31 ( 0.05 cm, and K and ν the thermal diffusivity and kinematic viscosity, respectively of the order of 10-4 cm2/s and 10-2 cm2/s for organic solutions. The pressure inside the liquid is maintained higher than the atmospheric pressure. The flow is regulated in such a way that the fluid residence time is about 5 times the diffusion relaxation time, so that the separation has nearly attained the asymptotic value. The resulting variations of the viscosity with temperature and composition do not induce departure from the parabolic profile of the horizontal velocity of more than 1%. This flow is therefore characterized with one additional dimensionless Reynolds number defined with the mean velocity 〈V〉 by
Re ) 〈V〉/νd
(6)
In our experiments, the value of Re is about 35. At the present time, little is known about the stability of a flowing binary mixture heated “from the top”. Only the limiting case where Re ) 0 has been studied, and it may be unstable for systems with negative Soret coefficient. This question of the influence of the Soret effect on the Be´nard stability of a layer at rest has been extensively studied theoretically. These results are frequently used in the measurement of Soret coefficients in Be´nard cells with standard Schmidt-Milverton plots (temperature difference versus heating power). A typical plot for systems with negative Soret coefficients is shown in Figure 2. We obtained such plots with a fixed temperature of 38 °C at the top plate and increasing the heat flux by steps at the bottom plate. The accuracy of the temperature measurements is 0.01 K and 5% for the heat flux measurements. However, for the reasons mentioned above, only the systems presenting a hysteresis can be used for a quantitative determination of the Soret coefficient. The absence of hysteresis has been interpreted
Soret Coefficients of Organic Solutions
J. Phys. Chem. B, Vol. 102, No. 22, 1998 4429
TABLE 2: Data for the Evaluation of the Soret Coefficients from the Schmidt-Milverton Plotsa solute-solvent
N0 (%)
-R × 105 (K-1)
-β × 100
δ∆T/∆T (%)
δ′∆T/∆T (%)
ψ × 100
Le × 1000
water-isopropyl alcohol
80 90 10 95 97
17 13 8 7 7
18 11 20 19 19
4.0 19 53 8.2 12
2.8 13 47 9.1 10
4.2 17 26 8.3 12
5 23 140 23 21
water-methanol water-n-butyl alcohol
a The symbols are defined in the text. The last columns are the separation factor and Lewis number as deduced by eqs 7 and 8 from the temperature difference ratios given in the two previous columns. The expansion coefficients provided in the third and fourth columns are obtained with a density meter and the viscosity and thermal diffusivity are from ref 36.
as corresponding to a very small or positive Soret coefficient, as shown in Table 1. The negative Soret coefficients are usually deduced from the value of the critical thermal Rayleigh number, which according to the theory, is a single-valued function of the separation factor. Deducing the Soret coefficients in such cases from the critical temperature differences has, however, not provided reliable results. This is not due to the principle of the technique but to the poor accuracies that one can obtain on the values of the dissipative coefficients of the solutions when extrapolated to nonstandard temperatures. To interpret the results obtained by the Be´nard cell at a nonstandard temperature, we needed therefore to derive also a simplified technique of interpretation of the Schmidt-Milverton plots for the measurement of negative Soret coefficients. For such cases, when the heat flux corresponds to high supercritical values, the strong convective motion makes the solution nearly homogeneous, without stabilizing the solute profile. Thus, the extrapolated line of the convective regime intersects the one of the purely diffusive regime at a temperature difference below the critical one (point B of Figure 2). The calculation of the onset of convection (point A on Figure 2) can be obtained by a classical linear analysis. The critical conditions for finite amplitude perturbations are obtained similarly by a stability analysis of the convected fields. In a first approximation, they can be described by a minimal representation34 with five parameters. The latter analysis will provide an estimate of the smaller temperature difference of the convective regime (point C on Figure 2). The results have been obtained34 analytically for a layer with stress-free boundaries but not for the actual rigid walls. Since in both cases the convective velocity is developed mainly in the bulk phase, we have assumed in a first approximation that the scaling laws obtained are not influenced much by the stressfree boundaries hypothesis. The scaling laws considered here are the ratios of critical Rayleigh numbers to the one corresponding to a pure fluid without Soret effect. These relations are a function of the “Rayleigh separation factor” (or Rayleigh ratio) and the Prandtl, Schmidt, and Lewis numbers respectively defined by
[
ψ)Pr ) ν/K
]
(7)
Le ) D/K
(8)
DT ∂F ∂F N0(1 - N0) / ∂N D ∂T Sc ) ν/D
For organic solutions, typical values are Pr ) 10 and Sc ) 1000, whereas the separation factors ψ range from 0.1 to 10. The expansion coefficients, measured with the above-mentioned densitometer, are given in Table 2. The results from ref 30 pertinent to this derivation are for a separation factor less than
-ψ* )
Le(1 + (1/Sc))
(9)
Le + (1 + Le)(1 + (1/Sc)) 2
This bifurcation separation factor has a value of the order of 0.01 for organic solutions. Then, in a layer with free, undeformable interfaces, the overstable modes set in at the critical value Raovcrit of Ra given by
Raovcrit Ra0crit
crit
(
) (1 + Le) 1 +
1 Pr Raov -ψ Sc Pr + 1 Ra crit
)
(10)
0
where Ra0crit is the critical Rayleigh number obtained when the separation factor vanishes. The description of the convective regime by its minimal expansion in sine and cosine functions leads to a critical Rayleigh number for finite amplitude modes (Rafacrit) determined by35
(
1 + Le 1/2 Le
a ) 1 - Le2 ( 2Le -ψa
)
(11)
where
a ) Rafacrit/Ra0crit
(12)
We neglect the terms of order 1 in Lewis number, which is around 0.01, and obtain
a - 1 ) (2[Le(-ψ)a]1/2 1-
Ra0crit Raovcrit
Pr ) -ψ Pr + 1
(13) (14)
The experimental quantities used are shown in Figure 2. ∆T is the temperature difference at the onset of convection (vertical distance origin of axissA); δ∆T is the increase of the solute stabilization (vertical distance B-A) and δ′∆T the vertical distance C-A. The latter is the maximal value of overstabilization by solute that is observed and is referred to here as the “amplitude of overstabilization”. If the measurements would have allowed us to resolve a hysteresis, these meanings would be unchanged. In the range of parameters of organic solutions, eqs 13 and 14 lead respectively to
∂′∆T /1+ ) 4Le(-ψ) (∂′∆T ∆T ) ( ∆T ) ∂∆T Pr /1+ ) -ψ (∂∆T ∆T ) ( ∆T ) Pr + 1 2
(15) (16)
As will be discussed in the next section, the use of eq 16 provides results that are in agreement with SCM measurements,
4430 J. Phys. Chem. B, Vol. 102, No. 22, 1998
Van Vaerenbergh and Legros
except for diluted solutions. The separation factors obtained are given in the seventh column of Table 2. Equation 15 has also been tested by comparing it with the Lewis numbers of the solutions, knowing their separation factor. The values obtained are reported in the eighth column of Table 2. 4. Discussion of the Results The agreement of the signs between the three techniques appears in Table 1. This validates the ground based method for the determination of the sign of the Soret coefficient. The discrepancies obtained for the amplitudes between the Be´nard cell and the microgravity measurements are not fully explained at this time: large discrepancies have been obtained in the Be´nard cell using eq 10 for highly diluted solutions of alcohol in water. A working hypothesis that we are now studying is that the solute flux description for high dilutions is not of the form given by eq 1, but rather
J ) -FD∇N - FDTN∇T
(17)
The consideration of such a form where the thermodiffusive contribution depends on the variable N has proved to have significant influence in solidification37,38 processes. The same has been predicted for the Marangoni-Be´nard instability with Soret effect.39 If this is true also for the Rayleigh-Be´nard problem with Soret effect, eqs 15 and 16 are obviously no more valid, and the overall stability problem should be reconsidered for diluted solutions. Note that a very high solute stabilization, far above the one predicted by classical analysis and currently unexplained, has been observed in solutions of 1 N LiI by other scientists.40 For concentrated solutions, formula 16 should be much more accurate than eq 15. One reason is the uncertainty of a factor of around 2 on the value of the Lewis number due to the approximate knowledge of the diffusion coefficients. Another experimental reason is that the onset of overstability is better resolved than the onset of finite amplitude modes. Even with this, it clearly appears from results shown in Table 2 that the theoretical approximations leading to eq 15 are too crude, and even out of range for the water-methanol system. Obviously, formula 15 involves a convective movement with large amplitude which cannot be insensitive to the boundary conditions and to the simplified representation of the convected fields. Thus, the relative amplitude of the overstabilization, expressed by eq 15 needs a much more accurate evaluation that cannot be performed analytically. On the contrary, eq 16 seems to provide very good results for concentrated solutions. Thus, for concentrated solutions, the relative solute stabilization expressed by eq 16 would be an accurate and straightforward measurement of the separation factor. This is because the Prandtl number is about 10 and uncertainties on its value have little influence. The Soret coefficient is deduced from the separation factor using only expansion coefficients, which are easily determined experimentally. The distinction between concentrated and diluted solutions, and the ability to directly measure the separation factor using eq 16 for concentrated solutions, would be valuable outcomes of the SCM measurements that must be investigated further. The reference measurements also show that the values obtained by the Be´nard cell for concentrated solutions are quite accurate.
Figure 3. Experimental correlation observed between the flow cell and the SCM microgravity experiment. The Y axis is the ratio of the SCM to the flow-cell Soret coefficients, and the X axis is the theoretical maximal value of the horizontal density gradient in the flow cell. The numbers refer to the solutions defined in Table 1.
The same conclusion cannot be made for the flow cell. The sign is good, but the discrepancies on the amplitude with respect to SCM results appear somewhat erratic. Taking into account the uncertainties on the measurements, it appears that the microgravity measurements are never smaller than the measurements performed in the ground based technique, excepted system no. 4. It also clearly appears from Table 1 that the larger the “true” Soret coefficient (the one obtained in SCM) is, the smaller the ratio of a 1 g flow cell to microgravity measurements is. Figure 3 shows the experimental correlation between the ratio of microgravity to the flow cell measurements and the following quantity:
DT |∇T| D
|∇TF| ) -FβN0(1 - N0)
(18)
where the Soret coefficient is the “true” one and the temperature gradient is the one used in the flow cell. The correlation appears to be quite good given the uncertainties and range of variation of the parameters. It can hardly be attributed to a classical Be´nard instability because the Rayleigh number is very small and also because this happens in both stabilizing (positive Soret coefficient) and destabilizing (negative Soret coefficient) solute fields. One possible cause would be the solute gradient along the flow, which appears due to the progressive establishment of the solute profile. Indeed, the quantity appearing in eq 12 can be equated to driving force of such a perturbation, which is the theoretical horizontal density gradient given by
DT |∇T| D
max(|∇horizontalF|) ) -FβN0(1 - N0)
(19)
Such an effect has never been taken into account in the literature, and we are presently analyzing its influence. This effect may partly explain the dependence of separations on the mean flow observed in the flow cell. To conclude, the large variations of the Soret coefficients with composition and the frequent dependence of its sign on composition should be emphasized. It is the sign of the obvious large departure from a crude model of dense gases. Trying to apply some existing predictive model, one faces the heavy problem of the lack of data at nonstandard conditions. Such
Soret Coefficients of Organic Solutions
J. Phys. Chem. B, Vol. 102, No. 22, 1998 4431
an analysis lies out of the scope of this paper and will be performed elsewhere.
ity” with the support of the Commission, in the frame of the network CHRX-CT930106 and of the Prodex program of ESA.
5. Conclusions
References and Notes
To obtain reliable measurements of the Soret coefficients of organic solutions, the flow cell, Schmidt-Milverton plots, and microgravity conditions were employed. The reasons for this selection is to minimize the convective perturbations. At the present time there is no clear evidence that ground based techniques could provide a reliable value for any system. The signs of the Soret coefficients obtained by the three techniques are the same for all of the eleven organic solutions so studied. For the large Soret coefficients obtained in SCM, it seems that a convective phenomenon appears in the flow cell for both positive and negative separation factors. The discrepancies with measurements performed in the flow cell appear to be perturbed proportionally to the theoretical horizontal density gradient. This appears to be the first experimental observation to provide some explanation for the discrepancies observed in the flow cell. The Be´nard cell has been used for measurements of the separation factor of systems presenting a hysteresis loop in the Schmidt-Milverton plots. We have derived expressions of the separation factor as a function of ratios of the measured characteristic temperature differences. This expression is very simple, and only the expansion coefficients are to be known with accuracy to determine the Soret coefficients. For dilute systems (N ) 0.1 or 0.9) there are important and still unexplained discrepancies with the SCM measurements. These may be due to a form of the mass flux which could be not valid for diluted solutions. The SCM results have helped to understand the discrepancies between the Be´nard cell and flow cell techniques and microgravity measurements observed for eleven organic binary solutions. A general understanding of all ground based measurements performed with these techniques is obviously not achieved. The reason is that organic solutions may exhibit a wide variety of hydrodynamic behaviors whose spectrum has surely not been fully explored with the single SCM experiment. There is a subtantial need not only for theoretical and experimental ground based investigations but also for microgravity data. Acknowledgment. This paper presents results partly obtained in the framework of the Belgian program on Interuniversity Poles of Attraction 4-06 initiated by the Belgian State, Prime Minister’s Office, Federal Office for Scientific, Technological and Cultural Affairs. The scientific responsibility is assumed by its authors. It also represents research results of the European Community Program “Human Capital and Mobil-
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