Also A =
2835eDqL/[ 1
+ 5670 (
90w4/3g
~
Dq
)‘I
43s (aT )
T h e term 5 6 7 0 ( D q ) * / [ w 3 & ( A T ) ] *increases as 2w, the distance between the hot and the cold walls, decreases, and thus for each mixture and temperature difference there is a value of 2w, below which it can no longer be neglected: In practice, for liquid systems, this value is of the order of magnitude of 0.05 cm. This discussion does not, of course, invalidate the authors’ conclusions, but merely qualifies and extends the applicability of their above mentioned equations. Equations 7 and 8 are not strictly comparable with Equations 9 and 39. Debye’s result is valid for short experimental separation times and for X > Kd (2-4). O u r neglect of the Kd term throughout our derivation reflects this tacit assumption. Hoivever, since others may legitimately apply the equation to gaseous pairs, Romero’s qualification is important. \Ye feel that one statement is open to discussion. H e states that, for liquids, the value of 2w below which Kd can no longer be neglected is of the order of magnitude of 0.05 cm. While this is possible, our experience shows that it is an easy matter to make the error introduced into the thermal diffusion constant for liquid systems by neglecting Kd insignificant. If a large temperature difference is maintained, which is often dictated by practical considerations of separation, time, or analytical techniques available, one can safely work with annuli less than 0.03 cm. For example, in a study of the relative degree of separability of several hydrocarbon pairs, using 0.0292- and 0.0343-cm. annuli columns, the value of the correction factor introduced by accounting for Kd was 1.0072 f 0.0064 (standard deviation, 33 measurements). The maximum correction factor in any one case was 1.0242. Vsing our data, we calculated the annuli required to produce 1, 3, and 57, errors, respectively, as 0.028 f 0.003, 0.023 =k 0.002, and 0.021 f 0.002 cm. For heuristic purposes, Table I gives data leading to the correction factor of 1.0242. \Ve discuss this point a t length for two reasons. First, if K d were always required, the possible unavailability of viscosity and temperature coefficient of density data for a liquid mixture would prevent one from determining a reliable thermal diffusion constant (within the limitations of the forgotten effect).
288
l&EC FUNDAMENTALS
Table I.
Experimental and Calculated Data for the System
Cyclohexane-n-Octadecane .4nnulus, cm. 0.0292 Average temperature, O K. 323 Correction factor 1 ,0242 Linear regression coefficient 6.373 X 10-5 Ordinary diffusion coefficient, sq. cm./sec. 7 351 X Temperature coefficient of density, g./(cc. O C.) - 7 . 0 6 7 X Temperature difference, ’ C. 40 Thermal diffusion constant 0.0157 Viscosity, poise 0.0243 Initial mole fraction n-octadecane (hot wall prod.) 0.7513
Second, the annular spacing of a popular commercially available thermal diffusion column, the Jones-Hughes column (7), is of the order of 0.03 cm. T h e columns which we used were Jones-Hughes columns. Romero’s 0.05-cm. value places the Jones-Hughes column within the range where Kd is required. O u r contention is merely that possession of thermal diffusion columns with annuli as small as say 0.025 cm., or the lack of viscosity or temperature coefficient of density data, or both, need not prevent one from obtaining useful thermal diffusion constants. literature Cited
( 1 ) Jones, A. L., Hughes, E. C. (to Standard Oil Co.), U. S. Patents 2,541,069-70-71 (Feb. 13, 1951) (available from M. Fink Co., 7520 IVinding IYay, Brecksville, Ohio). (2) Lorenz. M., Emery, A. H., Jr., Chem. Eng. Sci. 11, 16 (1959). (3) Powers, J. E., Ind. En?. Chem. 53, 577 (1961). (4) Tyrrell, H. J. V., “Diffusion and Heat Flow in Liquids,”
p. 210, Butterworth. London, 1961.
Thomas C. Ruppel‘ James Coull University of Pittsburgh Pittsburgh, Pa. 1
Present address, U. S. Bureau of Mines, Pittsburgh, Pa.
