Unsteadystate Mass Transfer

In the previous sections, only steady-state mass transfer phenomena were dealt with. In practice, mass transfer al-

In the previous discussion, the mass transfer of one phase was considered. The concentration gradient of the other phase was assumed to be zero (the system was assumed either well stirred or very dilute). In most practical prob lems, however, concentration gradients may exist on both sides of the interface of the system. For example, consider that solute A is being transferred from a gas to a liquid phase. In such a case, A must travel from the bulk volume into the boundary layer of the gas phase, through the interface, into the boundary layer, and finally into the bulk volume of the liquid phase. The concentration profile of A is shown in Figure 3. Defining PA as the partial pressure of A in the gas phase, CA as the concentration in the liquid phase, PAi as the partial pressure of A in the gas boundary layer, and CAi as the concentration in the liquid boundary layer, the rate of transfer of A from the gas phase to the interface is

The rate of transfer of A away from the interface and into the liquid phase is

where kg and kL are transfer coefficients for the gas and liquid boundary layer, respectively. At steady state, the rate of transfer to the interface must be equal to the rate of transfer away, so that k. =

For a substance A diffusing through a stagnant layer of B, comparing equation 17 with equation 52, and equation 25 with equation 53 gives

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