Analytic Solution for Irreversible Equilibrium

The earliest solution for the breakthrough curve for an irreversible system appears to be due to Bohart and Adams who used a quasi-chemical kinetic rate expression. 

The solutions for linear rate expressions with either solid or fluid driving force are readily obtained. In contrast to the situation with a linear isotherm, where the solution for a linear rate expression is the same with either fluid or solid phase driving force, in the case of an irreversible isotherm the response curves for these two models are quite different. 

The rate expression for solid diffusion control is obtained directly by. differentiation of the expression for the uptake curve for a spherical adsorbent particle subjected to a step change in sorbate concentration at the external surface [Eq. (6.4)]. Pore diffusion control with an irreversible isotherm leads to the shrinking core model and the uptake rate is therefore given by the differential of Eq. (6.27). 

A summary of some of the available solutions for irreversible systems is given in Table 8.2. All solutions assume plug flow. The limiting cases of solid diffusion control and pore diffusion control were solved by Cooper - and by Cooper and Libermann while the solution for the case of combined pore diffusion and external mass transfer resistance was obtained by Weber and Chakravorti using the method of Cooper and Libermann. Weber and 

FIGURE 8.15. Comparison of theoretical breakthrough curves for a system with irreversible equilibrium, calculated according to linear rate models with solid and fluid resistances and the solid and pore diffusion models (models 2-5 of Table 8,2). 

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Analytic Solution for Irreversible Equilibrium (One Adsorbable Component)... 

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