Sorption rates

Sorption Rates in Batch Systems. Direct measurement of the uptake rate by gravimetric, volumetric, or pie2ometric methods is widely used as a means of measuring intraparticle diffusivities. Diffusive transport within a particle may be represented by the Fickian diffusion equation, which, in spherical coordinates, takes the form... 

There was studied dependence of sorption rate values of microamounts high listed elements from time of their contact with sorbents, pH media and means of equilibrium concentration. It is shown that owing to exchange of sorbents surface characteristics, its hydrating rate value and heterogeneity of sorbate and hydrolyzed forms of metals investigated interaction with surface can simultaneously proceed on several mechanisms. The contributions of various factors into adsorption of elements-analogues are depended from sorption conditions and nature of sorbent surface. 

AT is intended to include any and all of the effects of the sorption rate of monomer on the surface, steric arrangement of active species, the addition of the monomer to the live polymer chain, and any desorption needed to permit the chain to continue growing. We assume a steady state in which every mole of propylene that polymerizes is replaced by another mole entering the shell from the gas, so that all of the fluxes are equal to Ny gmol propylene reacted per second per liter of total reactor volume. The following set of equations relates the molar flux to each of the concentration driving forces. 

The values of kj calculated by Bacon and Anderson (1982), and used in most models of Th scavenging, varied with particle concentration and ranged from 0.2 to 1.2 Such values are appreciably longer than expected from sorption rates onto particle surfaces. The discrepancy can be explained if dissolved Th is initially sorbed to surfaces of very small particles (colloids) that pass through the typical filters (0.1-0.4 im) used to separate dissolved from particulate fractions (Santschi et al. 1986). 

Recent reports on biosorbents based on diverse types of macrophytes are found widely in the literature. Free-floating aquatic plants from the genera Salvinia, Azolla, Eichhornia, Lemna, and Pistia have been described the most. S. natans biomass was able to uptake As(V) at low initial concentrations from 0.25 to 2 mg/L (74.8% and 54%, respectively). The experimental data fitted well to both Langmuir and Freundlich isotherms. The effect of pH and biomass quantities on sorption rate has also been investigated along with some metabolic parameters.105... 

The data of Loukidou et al. (2004) for the equilibrium biosorption of chromium (VI) by Aeromonas caviae particles were well described by the Langmuir and Freundlich isotherms. Sorption rates estimated from pseudo second-order kinetics were in satisfactory agreement with experimental data. The results of XAFS study on the sorption of Cd by B. subtilis were generally in accord with existing surface complexation models (Boyanov et al. 2003). Intrinsic metal sorption constants were obtained by correcting the apparent sorption constants by the Boltzmann factor. A 1 2 metal-ligand stoichiometry provides the best fit to the experimental data with log K values of 6.0 0.2 for Sr(II) and 6.2 0.2 for Ba(II). 

Loukidou et al. (2005) fitted the data for the equilibrium sorption of Cd from aqueous solutions by Aeromonas caviae to the Langmuir and Freundlich isotherms. They also conducted, a detailed analysis of sorption rates to validate several kinetic models. A suitable kinetic equation was derived, assuming that biosorption is chemically controlled. The so-called pseudo second-order rate expression could satisfactorily describe the experimental data. The adsorption data of Zn on soil bacterium Pseudomonas putida were fit with the van Bemmelen-Freundlich model (Toner et al. 2005). 

Van Campen et al. [31] developed models describing the rate of moisture uptake above RH0 that consider both the mass transport of water to the solid substance and the heat transfer away from the surface. For the special case of an environment consisting of pure water vapor (i.e., initial vacuum conditions), the Van Campen et al. model is greatly simplified since vapor diffusion need not be considered. Here, only the rate at which heat is transported away from the surface is assumed to be an important factor in limiting the sorption rate, W. For this special case, an expression was derived to express the rate of moisture uptake solely as a function of RHj, the relative humidity of the environment, and RH0. 

Figure 1.17 The sorption rates of mercaptopropyl-functionalized ORMOSIL depend on the relative long-range versus short-range structural order/disorder and their intrinsic hydrophobicity. Ordered materials with 20-30% alkylation perform best. (Reproduced from ref. 38, with permission.)...

Condition 1 Direct determination of diffusivities in ZSM-5 via sorption rate measurements showed Dp/DQ > 103 and and DQ Dm. 

The zeolites and catalysts used in this study were prepared as described previously (1,16,18,20). The ortho-xylene sorption rate data, obtained on a computer-controlled Du Pont 951 TGA, were measured at 120°C and P(o-xylene) 3.8 torr. The isomerization and disproportionation data were obtained using a... 

The surfactant bioconcentration data available in the literature show considerable variability, due mainly to the different compounds, species, environmental characteristics and analytical procedures used to determine the BCF. Physicochemical properties of surfactants, such as molecular structure, molecular weight, partitioning coefficients (Kom Kqc), water solubility and sorption rate constants all influence their BCF [47]. 

The source term in equation (2.22) requires a separate differential equation for Sp, which would incorporate the concentration of the compound in solution. We would thus have two equations that need to be solved simultaneously. However, most sorption rates are high, relative to the transport rates in sediments and soil. Thus, local equilibrium in adsorption and desorption is often a good assumption. It also simplifies the solution to a transport problem considerably. If we make that assumption, Sp changes in proportion to C alone, or... 

Model Predictions. The rate for desorption of americium from the fissure surfaces into solution was assumed to equal the rate for the adsorption of americium from solution by the fissure surfaces. The sorption rate and the equilibrium fractionation of americium that were determined in the static experiments were used to determine input parameters to the ARDISC model. The ARDISC model predictions for the distributions of americium on the fissure surfaces in both sets of experiments are presented in Figures 5 through 10 along with the autoradiographs and the experimental histograms representing the various distributions of americium on the fissure surfaces. 

Assuming first order reaction kinetics, the sorption rate that was determined for adsorption and desorption was 0.187 sec . A reaction rate of 0.187 sec implies a half time of reaction of 3.7 seconds. 

Schlautman, M. A., and J. J. Morgan, Sorption of perylene on a nonporous inorganic silica surface - Effects of aqueous chemistry on sorption rates , Environ. Sci. Technol., 28, 2184-2190 (1994). 

In this equation dW/dt is the rate of sorption, k. is the experimental rate constant for sorption, W, is the equilibrium sorption, W is the amount of sorption at time t = t, and h is the experimental rate constant for desorption. Thus, the sorption rate was found to be proportional to the square of the concentration of unoccupied sites, and the desorption rate was proportional to the square of the concentration of occupied sites. These rate equations are not general solutions to Fick s law of diffusion. The experimental rate constants for sorption were found to be non-linearly dependent on methanol pressure and seemed to correlate with the amount of surface sorbed methanol in different ways for coals of various rank. 

Purity of Covellite Hg(0) Saturation Cone. Hg(0) Sorption Rate... 

An intriguing aspect of these measurements is that the values of D determined from NMR and from sorption kinetics differ by several orders of magnitude. For example, for methane on (Ca,Na)-A the value of the diffusion coefficient determined by NMR is 2 x 10 5 cm2 sec-, and the value determined for sorption rates only 5 x 10"10 cm2 sec-1. The values from NMR are always larger and are similar to those measured in bulk liquids. The discrepancy, which is, of course, far greater than the uncertainty of either method, remained unexplained for several years, until careful studies (267,295,296) showed that the actual sorption rates are not determined by intracrystalline diffusion, but by diffusion outside the zeolite particles, by surface barriers, and/or by the rate of dissipation of the heat of sorption. NMR-derived results are therefore vindicated. Large diffusion coefficients (of the order of 10-6 cm2 sec-1) can be reliably measured by sorption kinetics... 

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