Adsorption linear isotherm

Vlad, M. O. Cerofofini, G. F. Ross, J. Statistical fractal adsorption isotherms, linear energy relations, and power-law trapping-time distributions in porous media. Phys Rev. E 2000, 62, 837-844. 

Vlugt T J H, Krishna R and Smit B 1999 Molecular simulations of adsorption isotherms for linear and branched alkanes and their mixtures in silicalite J. Phys. Ohem. B 103 1102-18... 

A rather simpler situation arises when the bulk concentrations are sufficiently small that the adsorption isotherms approach linearity. Then (7,4), for example, shows that... 

The 2eohte and the resin adsorbents show different adsorption isotherm characteristics, particularly at higher concentration (51). The resin adsorbent isotherm is slightly concave upward, whereas the 2eohte isotherm is linear, or even slightly concave downward. Resins, therefore, have an advantage in a UOP Sarex operation that involves high feed-soHds concentration. 

For a linear isotherm tij = KjCj), this equation is identical to the con-seiwation equation for sohd diffusion, except that the solid diffusivity D,i is replaced by the equivalent diffusivity = pDj,i/ p + Ppi< ). Thus, Eqs. (16-96) and (16-99) can be used for pore diffusion control with infinite and finite fluid volumes simply by replacing D,j with D. When the adsorption isotherm is nonhnear, a numerical solution is... 

The major surfactant in the foam may usually be considered to be present at the bubble surfaces in the form of an adsorbed monolayer with a substantially constant F, often of the order of 3 X 10" (g mol)/ cm", for a molecular weight of several hundred. On the other hand, trace materials follow the linear-adsorption isotherm Tj = KiCj if their concentration is low enough. For a wider range of concentration a Langmuir or other type of isotherm may be applicable (Davies and Rideal, loc. cit.). 

In LC, at very low concentrations of moderator in the mobile phase, the solvent distributes itself between the two phases in much the same way as the solute. However, as the dilution is not infinite, the adsorption isotherm is not linear and takes the form of the Langmuir isotherm. 

The mobile phase was water in which the moderator alcohols were dissolved. It is seen that the linear relationship is completely validated and the data can provide the adsorption isotherms in the manner discussed. The mean surface area was found to be 199 m /g with a standard deviation between the different alcohols of 11 m /g. 

In addition, the concentration of solute in both phases increased almost linearly with the amount of solute added. This would indicate that the system was operating over that part of the adsorption isotherm that was linear. Thus, the solute was interacting... 

A countercurrent moving-bed adsorption column is used to remove benzene from a gaseous emission. Activated carbon is employed as the adsorbent. The flowrate of the gas is 1.2 kg/s and it contains 0.027 wt/wt% of benzene. It is desired to recover 99% of this pollutant. The activated carbon entering the column has 2 X 10 wt/wt% of benzene. Over the operating range, the adsorption isotherm (Yaws et al., 1995) is linearized to... 

Cost estimation and screening external MSAs To determine which external MSA should be used to remove this load, it is necessary to determine the supply and target compositions as well as unit cost data for each MSA. Towards this end, one ought to consider the various processes undergone by each MSA. For instance, activated carbon, S3, has an equilibrium relation (adsorption isotherm) for adsorbing phenol that is linear up to a lean-phase mass fraction of 0.11, after which activated carbon is quickly saturated and the adsorption isotherm levels off. Hence, JC3 is taken as 0.11. It is also necessary to check the thermodynamic feasibility of this composition. Equation (3.5a) can be used to calculate the corresponding... 

The low-coverage parts of the adsorption isotherms evaluated at different temperatures have shown a remarkable feature of linear dependence between the adsorption and the logarithm of gas pressure. This sort of behavior corresponds to the well-known Temkin equation of adsorption... 

For the case of a binary system with linear adsorption isotherms, very simple formulas can be derived to evaluate the better TMB flow rates [19, 20]. For the linear case, the net fluxes constraints are reduced to only four inequalities, which are assumed to be satisfied by the same margin /3 (/3 > 1) and so ... 

Fig. 9-7. Region for complete separation under Equilibrium Theory. Linear adsorption isotherms.

The competitive adsorption isotherms were determined experimentally for the separation of chiral epoxide enantiomers at 25 °C by the adsorption-desorption method [37]. A mass balance allows the knowledge of the concentration of each component retained in the particle, q, in equilibrium with the feed concentration, < In fact includes both the adsorbed phase concentration and the concentration in the fluid inside pores. This overall retained concentration is used to be consistent with the models presented for the SMB simulations based on homogeneous particles. The bed porosity was taken as = 0.4 since the total porosity was measured as Ej = 0.67 and the particle porosity of microcrystalline cellulose triacetate is p = 0.45 [38]. This procedure provides one point of the adsorption isotherm for each component (Cp q. The determination of the complete isotherm will require a set of experiments using different feed concentrations. To support the measured isotherms, a dynamic method of frontal chromatography is implemented based on the analysis of the response curves to a step change in feed concentration (adsorption) followed by the desorption of the column with pure eluent. It is well known that often the selectivity factor decreases with the increase of the concentration of chiral species and therefore the linear -i- Langmuir competitive isotherm was used ... 

Linear case This case is met when the adsorption isotherm is considered linear, which means operation under diluted conditions. Taking into account the saturation capacities of the CSP, this behavior is usually met for concentrations around or below 1 g for separation of enantiomers. 

A more general criterion for linearity can be derived noting that the denominator of the Langmuirian adsorption isotherms must approach 1, and consequently ... 

Calculation of TMB flowrates To calculate TMB flowrates, linear behavior of the adsorption isotherms for a feed concentration of 1 g is assessed. To check this point, we will use the criterion given in Equation (10). 

Langmuir adsorption isotherm, 93 Laser flash photolysis, 263-266 Least-squares regression, 37-40 linear, 37-39 nonlinear, 39-40 unweighted, 38 weighted, 38-39 Lifetime, 16... 

Equation (1) merely states that the general distribution law applies to the system and that the adsorption isotherm is linear. At the concentrations normally employed in liquid chromatographic separations this will be true. 

The upper curve shows the adsorption isotherm that normally occurs in liquid chromatography separations where the concentration of solute in the system is very low. The isotherm is linear and thus the distribution coefficient is constant at all concentrations of solute in either phase. It follows that as the peak velocity is inversely related to the distribution coefficient, all solute concentrations travel at the same velocity through the column and the peak is symmetrical. 

The adsorption isotherms for each chemical, Triton X-100 or phenanthrene, on the activated carbons were shown in Figs. 1 and 2. The adsorption isotherms are expressed as qg [g g ], the amount of compounds adsorbed per unit mass of adsorbent, as a fimction of Q [g l ], the concentration in solution at equilibrium [5, 6]. The best-fit parameters for Freimdlich isotherms (g = or linear isotherms (q - Kj C ) were summarized in Table 2. The... 

---