Isothermal application

The equation can be fitted to a wide range of isotherms with quite small residual errors over the entire range of concentrations of interest. It is a liquid liquid analogue of the Langmuir adsorption isotherm applicable to... 

Reaction rates for the start-of-cycle reforming system are described by pseudo-monomolecular rates of change of the 13 kinetic lumps. That is, the rates of change of the lumps are represented by first-order mass action kinetics with the same adsorption isotherm applicable to each reaction step. Following the same format as Eq. (4), steady-state material balances for the hydrocarbon lumps are derived for a plug-flow, fixed bed catalytic reformer. A nondissociation, Langmuir-Hinshelwood adsorption model is employed. Steady-state material balances written over a differential fractional catalyst volume dv are the following ... 

Gileadi combined adsorption isothenn, 340, 342, 344 Gileadi isotherm, application to electrode kinetics, 344, 347 Gouy-Chapman theory, 190, 193, 200 Graphical representation, (of impedance data), 431... 

Stiiwe K., White L., and Brown R. (1994) The influence of eroding topography on steady-state isotherms application to fission track analysis. Earth Planet. Sci Lett 124, 63-74. 

Fig. 19. Adsorption isotherm correlation, showing Freundlich isotherm application.

The generalised adsorption isotherms, Eqs. (50), can be used to generate simpler isotherms applicable to real systems. Here, for simplicity we examine the following adsorption processes at monolayers of constant thickness a) the single adsorption of a neutral or ionic adsorbate which possess a constant orientation at the monolayer, (b) the reorientation from a flat position to a normal one of a neutral adsorbate, and c) the co-adsorption of two adsorbates. 

Ideal Model, Nonlinear Isotherm Application of the method described so far becomes more complicated when the isotherms are no longer linear and the migration velocities of the components are strongly influenced by fluid concentrations. One approach for determining the operating parameters is the explicit solution of the ideal TMB process model (Equations 6.204 and 6.205), as proposed by Storti, Mazzotti, and Morbidelli. By introducing the dimensionless time... 

Equation (15) can also be considered as a general form of adsorption (excess) isotherms applicable for liquid free surfaces. For example, let us suppose that the differential function of the measured relationship y versus a can be expressed in the following explicit form ... 

Brunauer, Emmett, and Teller (1938) successfully extended the Langmuir adsorption isotherm applicable to monolayer adsorption to multilayer adsorption. While the assumptions made contain some serious deficiencies, the reproducibility of the BET method has made it the standard procedure for determining total surface area. In addition to the assumptions involved in the Langmuir adsorption, the BET method assumes that heats of adsorption for the multilayer adsorption are the same for the second and subsequent layers and are equal to the heat of liquefaction of the adsorbate. Adsorption and desorption rate constants are assumed to be the same for all layers except for the first layer, which is in contact with the... 

In this seetion, we intend to present some simple and straightforward aspects of adsorption of nonelectrolytes from binary liquid solutions on to mineral surfaces. Owing to the vast literature on this subject, we limit the presentation to a description of some frequently observed adsorption isotherms applicable to experimental data represented by the adsorption of polar molecules on to mineral oxide surfaces from dilute nonaqueous solutions. 

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