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Institute of Process Chemical Fundamentals Czechoslovak Academy of sciences Prague, Czechoslouakia
V. HanEil* V. Vacek‘
’ Institute of Inorganic Chemistry.
Response to Comments on “Determlnatlon of Diffusion Coefflclents by Frequency Response In Taylor Flow”
Sir: We thank Hancil and Vacek for their valuable comments. The paper was intended to draw attention to a method of determining diffusion coefficients which, while not new in principle, seems to have been overlooked by others who have used Taylor flow. In the authors’ eyes a sinusoid is more satisfactory than a pulse or step because the physical system can be made to correspond rigorously to the defining equations and boundary conditions. There are thus fewer uncertainties. There is also greater experimental freedom both because of the absence of a tube-length condition and because of the availability of another parameter &e., frequency) that can be adjusted to suit the circumstances. The example quoted in the paper was intended to give experimenters an idea of the apparatus and procedure to be used. Potassium chloride was chosen because its diffusivity was known and because its concentration could be easily measured and recorded by electrical means-or so it was thought. The scatter in the results was discussed in the original manuscript but excised in the interests of brevity. The main cause was thought to be the unexpectedly large drift of the measuring-cell electrodes, a fact only realized toward the end of a master’s degree course. Ideally, the measurements should have been repeated, but it was considered that the results would serve the purpose of demonstrating the technique. It should be appreciated that these measurements were spread over about five weeks and that the results represented ten combinations of five tube lengths (counting zero length), using four frequencies per length and at least three
cycles per frequency. On the other hand, if a similar structure of measurements to those of, say, Hancil, Rod, and Rosenbaum had been adopted, namely by using four cycles of one sinusoid, with nothing else changed, the scatter would have been equal to or better than that claimed by these authors. With regard to other specific comments by Hancil and Vacek and their references to the paper by Hancil et al., the following replies may be made. (a) The sensitivity of the detection system is a matter common to both sinusoids and pulses, of course. On the other hand, for a given sensitivity and noise level the ratio of concentrations, namely the maximum at the inlet to the minimum at the exit, is smaller for a sinusoid than for a pulse, and the more the input signal of a pulse approaches the theoretical ideal of a Dirac impulse the worse the comparison becomes. (b) To compensate for end and other effects in their apparatus, Hancil et al. ran a substance of known diffusivity. Back-calculation then gave an “effective* tube diameter to be used in subsequent determinations, in place of the actual diameter. It is not clear that this correction is constant under all circumstances. On the other hand, a sinusoid does not require a calibrating substance, and end effects are determined for each case. Hence the measurements are, in this sense, absolute. Department of Chemical Engineering University of Waterloo Waterloo, Ontario, Canada N2L 3Gl
0196-4313/83/1022-0270$01.50/0@ 1983 American Chemical Society
G. A. Turner* M. S. Chong
