Fluid activities mass balance equations

An example of a phenol adsorption isothenn onto an activated carbon cloth is given in Fig. 3. Experimental data are modeled with the Langmuir and Freundlich equations. A graphical construction is presented the slope of the adsorption path is equal to - Vim according to the mass balance equation between fluid and solid phases. From a given Co, this graphical construction enables the final concentration Cf to be determined. 

Thermodynamic activity information is required in the dilute solution regime where Henry s law is applicable. For an ideal mixture, activities are synonymous with mole fractions, and the slope of ua vs. xa is unity at infinite dilution. Hence, the thermodynamic derivative in the denominator of equation (25-91) is approximated by unity. Since fluid B is quiescent, the mass-average velocity of the mixture is essentially zero. The consequences of this condition are that v 0 and the pressure gradient balances the gravitational force on fluid B, as expected for a hydrostatic situation. Since there is no acceleration or forced diffusion for the continuum of fluid B, it is reasonable to set gs 0. Under these conditions, equation (25-91) yields ... 

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