Question 10.21: Experiments have been carried out on the mass transfer of ac...
Experiments have been carried out on the mass transfer of acetone between air and a laminar water jet. Assuming that desorption produces random surface renewal with aconstant fractional rate of surface renewal, s, but an upper limit on surface age equal to the life of the jet, \tau , show that theage frequency distribution function, ϕ(t)
, for this case is given by:
ϕ(t) = s exp(-st/[1 – exp(-st)]) for 0 <t<\tau
ϕ(t) =0 for t >\tau .
Hence, show that the enhancement, E, for the increase in value of the liquid-phase mass transfer coefficient is:
E = [(πs\tau )^{1/2} erf(s\tau )^{1/2}]/{2[1 – exp(-s\tau ]}
where E is defined as the ratio of the mass transfer coefficient predicted by conditions described above to the mass transfer coefficient obtained from the penetration theory for a jet with an undisturbed surface. Assume that the interfacial concentration of acetone is practically constant.
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