Статья
2019

Eddy Diffusivity in the Viscous Sublayer

John Newman John Newman
Российский электрохимический журнал
https://doi.org/10.1134/S1023193519100069
Abstract / Full Text
Newman, J. Eddy Diffusivity in the Viscous Sublayer. Russ J Electrochem 55, 1031–1033 (2019). https://doi.org/10.1134/S1023193519100069

An attempt is made to resolve a long standing difference in the predicted distribution of the eddy diffusivity in the viscous sublayer, where the literature shows a dependence on either the cube or the fourth power of the distance from a solid wall. The resolution suggested is that a y3 dependence prevails very close to the wall while a y4 dependence may prevail in the outer part of the viscous sublayer near the border with the outer turbulent flow. However, at high values of the Schmidt number, the overall mass-transfer rate will show behavior corresponding to the y3 dependence, and any hints of the y4 dependence would be very hard to observe experimentally.

Author information

  • Department of Chemical and Biomolecular Enginering, University of California, 94720-1462, Berkeley, California, USA

    John Newman

References
  1. Murphree, E.V., Relation between heat transfer and fluid friction, Ind. Eng. Chem., 1932, vol. 24, pp. 726–736. https://doi.org/10.1021/ie50271a004
  2. Levich, B., The theory of concentration polarization, I, Acta Physicochim. U.R.S.S., 1942, vol. 17, pp. 257–307.
  3. Levich, B., The theory of concentration polarization, II, Acta Physicochim. U.R.S.S., 1944, vol. 19, pp. 117–132.
  4. Martemianov, S.A., Statistical theory of turbulent mass transfer in electrochemical systems, Russ. J. Electrochem., 2017, vol. 53, pp. 1076–1086.
  5. Hubbard, D.W., Mass transfer in turbulent flow at high Schmidt numbers, Dissertation, Univ. of Wisconsin, 1964.
  6. Chilton, T.H. and Colburn, A.P., Mass transfer (absorption) coefficients. Prediction from data on heat transfer and fluid friction, Ind. Eng. Chem., 1934, vol. 26, pp. 1183–1187.
  7. Lin, C.S., Moulton, R.W., and Putnam, G.L., Mass transfer between solid wall and fluid streams. Mechanism and eddy distribution relationships in turbulent flow, Ind. Eng. Chem., 1953, vol. 45, pp. 636–640.
  8. Vielstich, W., Der Zusammenhang zwischen Nernstscher Diffusionsschicht und Prandtlscher Strömungsgrenzschicht, Z. Elektrochim., 1953, vol. 57, pp. 646–655.
  9. Levich, V.G., Physicochemical Hydronamics, Englewood Cliffs, NJ: Prentice-Hall, 1962, Sections 4, 25, 26.
  10. Newman, J. and Thomas-Alyea, K.E., Electrochemical Systems, Hoboken, NJ: Wiley-Intersci., 2004.
  11. Wasan, D.T., Tien, C.L., and Wilke, C.R., Theoretical correlation of velocity and eddy viscosity for flow close to a pipe wall, AlChE J., 1963, vol. 9, pp. 567–568.
  12. Nikuradse, J., Gesetzmässigkeiten der turbulenten Strömung in glatte Rohren, Forschungsheft 356 Beilage zu Forschung auf dem Gebiete des Ingenieurwesens, Berlin: VDI-Verlag GMBH, Sept./Oct. 1932, ed. B, vol. 3. Translated as Nikuradse, J., Laws of turbulent flow in smooth pipes, NASA TT F-10, Washington: National Aeronautics and Space Administration, Oct. 1966, no. 359.
  13. Newman, J., Theoretical analysis of turbulent mass transfer with rotating cylinders, J. Electrochem. Soc., 2016, vol. 163, pp. E191–E198.
  14. Vorotyntsev, M.A., Martem’yanov, S.A., and Grafov, B.M., Closed equation of turbulent heat and mass transfer, J. Exp. Theor. Phys., 1980, vol. 52, pp. 909–914.