Mass transfer in the context of biological reactors typically involves the transport of a
gaseous species such as oxygen from a gas phase to a liquid phase. The rate at which gas dissolves
in a liquid (flux) at any particular time is proportional to the difference between the equilibrium
concentration and the concentration at that time. A departure from equilibrium can be considered a
"driving force" for mass transfer. When the equilibrium concentration is reached, the liquid is
saturated with the gas. Under this condition, no additional gas will dissolve, and the rate of transfer
is therefore zero. If the liquid is devoid of dissolved gas, then the rate of dissolution will be at a
maximum. We’ll come back to this point. The proportionality between the concentration difference
and the transfer rate is called a mass transfer coefficient.
A simple approach is to consider two important resistances to mass transfer from a gas to a
liquid: a gas film and a fluid film. The most convenient type of mass transfer coefficient is an
overall mass transfer coefficient (K), which encompasses both film resistances and uses both liquid
phase and gas phase concentrations in calculating an overall driving force. For gases like oxygen
which are sparingly soluble in water, the liquid film is the principal resistance to mass transfer, and
the overall mass transfer coefficient is approximately equal to the liquid phase mass transfer
coefficient (kL). The subscript “L” denotes that liquid phase concentrations will be used to describe
the overall driving force. The concentration difference used for the driving force is the concentration
of oxygen in the liquid at saturation (c*O2) and the actual liquid phase concentration of oxygen (cO2).
Thus, the molar oxygen flux (O2) can be written
Mass transfer in the context of biological reactors typically involves the transport of a
gaseous species such as oxygen from a gas phase to a liquid phase. The rate at which gas dissolves
in a liquid (flux) at any particular time is proportional to the difference between the equilibrium
concentration and the concentration at that time. A departure from equilibrium can be considered a
"driving force" for mass transfer. When the equilibrium concentration is reached, the liquid is
saturated with the gas. Under this condition, no additional gas will dissolve, and the rate of transfer
is therefore zero. If the liquid is devoid of dissolved gas, then the rate of dissolution will be at a
maximum. We’ll come back to this point. The proportionality between the concentration difference
and the transfer rate is called a mass transfer coefficient.
A simple approach is to consider two important resistances to mass transfer from a gas to a
liquid: a gas film and a fluid film. The most convenient type of mass transfer coefficient is an
overall mass transfer coefficient (K), which encompasses both film resistances and uses both liquid
phase and gas phase concentrations in calculating an overall driving force. For gases like oxygen
which are sparingly soluble in water, the liquid film is the principal resistance to mass transfer, and
the overall mass transfer coefficient is approximately equal to the liquid phase mass transfer
coefficient (kL). The subscript “L” denotes that liquid phase concentrations will be used to describe
the overall driving force. The concentration difference used for the driving force is the concentration
of oxygen in the liquid at saturation (c*O2) and the actual liquid phase concentration of oxygen (cO2).
Thus, the molar oxygen flux (O2) can be written
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