Mixture isotherm Extended Langmuir

For multicomponent adsorption the most commonly used isotherm is the extended Langmuir isotherm (Eq. 18). Another, frequently used approach is the Ideal Adsorption Solution theory (IAS theory), which was developed by Prausnitz [53] and applied to mixtures of gases by, for example, Kaul [54] and Rees [52,55]. 

In the case of extended Langmuir isotherm, which is the simplest case of dealing with multicomponent mixtures, the isotherm expression of the component i... 

When the system consists of a gas mixture containing N components, the overall adsorption equilibrium is described by the general integral equation, Eq. (16). Kapoor et al. applied the extended Langmuir equation as a local isotherm and a uniform energy distribution. The uniform distribution function is... 

The MPSD model can be conveniently extended to describe the adsorption equilibria of a gas mixture with N components. The generalized MPSD model simply takes the extended Langmuir equation as the local isotherm while using the MPSD information obtained from pure component data ... 

The Langmuir isotherm for pure-component adsorption can readily be extended to an n-component mixture, known as the extended Langmuir isotherm (Yang, 1987) ... 

For systems following the Langmuir isotherm, the IAS theory is identical to the extended Langmuir equation for mixtures, if the saturated amounts are equal... 

The extended Langmuir (Markham-Benton) isotherm has limited applicability especially for liquid phase adsorption, since even singlecomponent isotherms in liquid phase are rarely explained by the Langmuir equation. There have been several trials to extend the Freundlich type equation to mixture isotherms. Fritz and Schliinder (1974) gave the following equation. 

The theory of the hodograph transform and the relationship derived between the equations of the two lines given by this transform in the case of a binary mixture and those of the competitive equilibrium isotherms were briefly presented in Section 8.1.2. The theory is easily extended to multicomponent mixtures, although in this case we must represent the hodograph transform in an n-dimensional coordinate system, Ci, C2, , C , or in its planar projections. If the solution presents a constant state (Figure 8.1), it is a simple wave solution, and there is a relationship between the concentrations of the different components in the eluent at the column exit (Figure 8.2). This result is valid for any convex-upward isotherm. In the particular case in which the competitive Langmuir isotherm apphes, these relationships are linear. 

A revised set of Eqs. 17.75a to 17.75c can be written to extend these separation conditions to nonlinear SMB operation [59]. In the case of a set of colimms having different porosities, and on the basis of the triangle model, the separation area in the case of a binary mixtures the components of which follow competitive Langmuir isotherm behavior becomes defined by the set of equations... 

Frequently, adsorption applications involve mixtures rather than pure gases. If the adsorption of two or more components of the mixture is significant, the situation can become quite complicated, depending upon the interactions of the adsorbed molecules. Assuming no interactions, the Langmuir isotherm can be extended to a multicomponent mixture of j components ... 

The Langmuir isotherm is thermodynamically correct for single conponent systems. It has also been used as the basis for a variety of other isotherms such as the BET isotherm (multiple layers of adsorbate), the Langmuir-Freundlich isotherm, and the linear-Langmuir isotherm (add a linear isotherm and a Langmuir isotherm Eq. (18z6c) with different values of a). The Langmuir isotherm is also commonly extended to the adsorption of multiconponent mixtures. For exanple, for the simultaneous adsorption of conponents A... 

---