There has been a considerable difference in opinion as to what is the proper exponent m. The two relations most often considered are m = -2/3 and m = -3/4. These are usually justified by recognizing that the concentration boundary layer is so thin for large Sc that the velocity field within 6, can be represented as a Taylor series expansion in terms of the dimensionless distance from the wall yf. By using an analogy between momentum transfer and mass transfer, it is argued that the eddy diffusivity is given as E / V 'y f n , where n is an integer greater than or equal to 3. (See pages 343-7 of the book by Monin and Yaglom, 1965.) In order to establish the correct exponent m, it is necessary to obtain very precise measurements over a wide range of Schmidt numbers, since the difference between the Sc-2'8 and the Sc-314 relations is not great. A considerable number of experimental studies have been directed toward this goal. However, there is enough disagreement among the results of different investigators that the problem has not been conclusively resolved.During the course of a study on the influence of Schmidt number on the frequency of mass transfer fluctuations, we obtained the very extensive set of measurements of f(Sc) presented here. Because of the care given to the execution of these experiments, we feel that a greater precision was attained than in previous investigations.

Measurements are presented on the influence of Schmidt number on the frequency of the mass transfer fluctuations at a solid boundary. The shape of the spectral function is similar at all Schmidt numbers. A relation between the mass transfer fluctuations and the fluctuating velocity field can be obtained only at high frequencies. A comparison of the scale and the frequency of the mass transfer fluctuations and the velocity fluctuations suggests that the rate of mass transfer is controlled by convective motions in the flow oriented eddies described by a number of previous investigators. However, the concentration fluctuations caused by these convective motions are greatly dampened close to the wall by molecular diffusion. Thus the mass transfer fluctuations reflect only the scale and not the frequency of the convective motions in the flow oriented eddies.