Mass transfer nonspherical bubble

Mass Transfer Between Nonspherical Particles or Bubbles and Flow 185... 

The dependence (4.12.3) can also be used to estimate the intensity of transient mass transfer for nonspherical particles, drops, and bubbles at Pe 1. In this case, all dimensionless variables r, Sh, Shst, and Pe must be defined on the basis of the same characteristic length a. Under this condition, the expression (4.12.3) provides valid asymptotic results for small as well as large times. Equation (4.12.3) can be rewritten as follows ... 

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