| Abstract |
Mass transfer of solutes from/to
a solid immersed in a fluid can often be described by analytical solutions
of Fick's second law. The important parameters of these solutions are
the diffusion coefficient and the external mass transfer coefficient,
the former related to the internal resistance and the latter related to
the external resistance to mass transfer. Estimation of parameters considering
both internal and external resistances is cumbersome, due to the high
correlation between the model parameters, which jeopardises regression
procedures. An alternative solution consists in describing the process
as being controlled by internal resistance only, and estimating an apparent
diffusion coefficient, lower than the true one, that accounts for the
effects of the external resistance and that might be used for predictive
purposes provided the same hydrodynamic conditions prevail. The main objective
of this work was to theoretically evaluate the predictive ability of such
approach. Apparent diffusion coefficients were estimated, using a design
based on equally spaced values of fractional mass loss/uptake (Mt/M )
generated by the model that accounts for both internal and external resistances
to mass transfer. Values of Mt/M predicted by the simplified model, using
the apparent diffusion coefficients, were compared with the "true"
values of Mt/M . The average of the absolute values of the relative errors
of Mt/M was lower than 5% for Biot numbers above 17.5, and lower than
1% for Biot numbers above 102. The absolute values of the relative errors
were found to be higher in the initial part of the uptake/loss process,
that is, for low values of Mt/M . For example, for a Biot number of 30,
the absolute values of the relative errors were around 5% and 45% for
values of Mt/M equal to 0.5 and 0.1, respectively.
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