Freundlich-type isotherms

Figure 11. Peak Distortion Caused by a Freundlich Type Isotherm...

Freundlich-Type Relations A binary Freundlich isotherm, obtained from the ideal adsorbed solution theory in loading-explicit closed form [Crittenden et al., Environ. Sti. TechnoL, 19,1037 (1985)], is... 

The linear equilibrium isotherm adsorption relationship (Eq. 11) requires a constant rate of adsorption, and is most often not physically valid because the ability of clay solid particles to absorb pollutants decreases as the adsorbed amount of pollutant increases, contrary to expectations from the liner model. If the rate of adsorption decreases rapidly as the concentration in the pore fluid increases, the simple Freundlich type model (Eqs. 8 and 9) must be extended to properly portray the adsorption relationship. Few models can faithfully portray the adsorption relationship for multicomponent COM-pollutant systems where some of the components are adsorbed and others are desorbed. It is therefore necessary to perform initial tests with the natural system to choose the adsorption model specific to the problem at hand. From leaching-column experimental data, using field materials (soil solids and COMs solutions), and model calibration, the following general function can be successfully applied [155] ... 

Sheindorf, C., Rebhun, M., and Sheintuch, M. Organic pollutants adsorption from multicomponent systems modeled by Freundlich type isotherm. Water Res., 16(3) 357-362, 1982. 

Hashimoto et al. (1977) studied the removal of DBS from an aqueous solution in a carbon fixed-bed adsorber at 30 °C. The dimensions of the bed were D = 20 mm and Z = 25.1 cm. Carbon particles of 0.0322-cm radius were used, with 0.82 g/cm3 particle density, and 0.39 g/cm3 bulk density. The concentration of the influent stream was 99.2 rng/L and the superficial velocity was 0.0239 cm/s. The fixed bed was operated under upflow condition. Furthermore, the isotherm of the DBS-carbon system at 30 °C was found to be of Freundlich type with Fr = 0.113 and = 178 (mg/g)(L/mg)0113. Finally, the average solid-phase diffusion coefficient was found to be 2.1 X 10 10 cm2/s. The approximate value of 10 9 m2/s could be used for DBS liquid-phase diffusion coefficient. 

Murillo et al. (2004) studied the adsorption of phenanthrene (polycyclic aromatic hydrocarbon -PAH) from helium as carrier gas on a coke fixed-bed adsorber, at 150 °C. The isotherm of the phenanthrene-coke system at 150 °C was found to be of Freundlich type with Fr = 0.161 and KF = 1.9 (mol/kg)(m3/mol)0161. The isotherm has been derived for phenanthrene concentrations between 1.71 X 10 4 and 1.35 X 10-2 mol/m3. Finally, the average solid-phase diffusion coefficient, calculated from several experimental runs, was found to be 6.77 X 10-8 cm2/s. 

Diffusion-type models are two-parameter models, involving kt or Ds and La, while BDST models are one-parameter models, involving only 0, as gmax is an experimentally derived parameter. The determination of La requires the whole experimental equilibrium curve, and in case of sigmoidal or other non-Langmiur or Freundlich-type isotherms, these models are unusable. From this point of view, BDST models are more easily applied in adsorption operations, at least as a first approximation. 

Adsorption Isotherms of Langmuir Type and Freundlich Type... 

In practice, the following Freundlich-type empirical isotherm can be used for many liquid-solid adsorption systems ... 

An adsorbate A is adsorbed in a fixed-bed adsorber that is of 25 cm height and packed with active charcoal particles of 0.6 mm diameter. The concentration of A in a feed solution is 1.1 mol m , and the feed is supplied to the adsorber at an interstitial velocity of 1.6 m h L The adsorption equilibrium of A is given by the following Freundlich-type isotherm. 

Estimate the equilibrium concentration of the solution. An adsorption isotherm of the Freundlich type is given as... 

Experimental studies of the partitioning of sodium into aragonite, calcite, and dolomite have been carried out by White (1977, 1978), who concluded that the mode of substitution was as Na2CC>3 rather than as Na bicarbonate or hydroxide. The behavior of Na+ does not follow that normally described by a simple partition coefficient, but rather coprecipitation is better described by a Freundlich-type adsorption isotherm equation, implying that adsorption is important. 

Secondly, the adsorption equilibrium on a sparsely covered surface is approximately proportional to the square root or to the cube root of the equilibrium pressure, tending, however, to follow a lesser power of the equilibrium pressure at higher coverage. This nearly corresponds to the Freundlich type of adsorption isotherm. From this Kwan suggests... 

For certain continuous distribution functions and a Langmuir type local isotherm it is possible to solve Eq. (79) analytically. The thus obtained overall isotherm equations are normalised Freundlich type equations [32, 52, 53,102,107 110], for instance ... 

Some theoretical proton adsorption isotherms based on Eq. (87) and different types of surface groups are reported in [32,102]. Benjamin and Leckie [86] and Kinniburg et al. [14, 15] used Freundlich type equations to describe metal ion binding to ferrihydride. A discussion of this work has been given by Van Riemsdijk et al. [52, 53]. 

The correlation coefficient indicates that 99.95 percent of the data variation is explained with the Freundlich type isotherm. The Freundlich fit hypothesis looks very good. 

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