In fluid and molecular dynamics, the Batchelor scale, determined by George Batchelor (1959),[1] describes the size of a droplet of fluid that will diffuse in the same time it takes the energy in an eddy of size η to dissipate. The Batchelor scale can be determined by:[2]

where:

Similar to the Kolmogorov microscales – which describe the smallest scales of turbulence before viscosity dominates – the Batchelor scale describes the smallest length scales of fluctuations in scalar concentration that can exist before being dominated by molecular diffusion. It is important to note that for Sc > 1, which is common in many liquid flows, the Batchelor scale is small when compared to the Kolmogorov microscales. This means that scalar transport occurs at scales smaller than the smallest eddy size.

References

  1. G.K., Batchelor. (1959), "Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity", Journal of Fluid Mechanics, 5: 113–133, Bibcode:1959JFM.....5..113B, doi:10.1017/s002211205900009x, S2CID 122304345
  2. Paul, Edward L.; Atiemo-Obeng, Victor A.; Kresta, Suzanne M. (2004), Handbook of industrial mixing: science and practice (1st ed.), Wiley-IEEE, pp. 49–52, ISBN 0-471-26919-0
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.