Sorption-diffusion-desorption process

The first order equation has also been used to describe sorption and desorption processes. Haggerty and Gorelick [43] showed that there is an equivalent distribution of first order rate constants for any distribution of diffusion coefficients. Other models that use distributions of first order rate constants are presented in the following references [44-47]. 

This solution is valid for the initially linear portion of the sorption (or desorption) curve when MtIM is plotted against the square root of time. These equations also demonstrate that for Fickian processes the sorption time scales with the square of the dimension. Thus, to confirm Fickian diffusion rigorously, a plot of MJM vs. Vt/T should be made for samples of different thicknesses a single master curve should be obtained. If the data for samples of different thicknesses do not overlap despite transport exponents of 0.5, the transport is designated pseudo-Fickian. ... 

While first-order models have been used widely to describe the kinetics of solid phase sorption/desorption processes, a number of other models have been employed. These include various ordered equations such as zero-order, second-order, fractional-order, Elovich, power function or fractional power, and parabolic diffusion models. A brief discussion of these models will be provided the final forms of the equations are given in Table 2. 

If the rate constants for the sorption-desorption processes are small equilibrium between phases need not be achieved instantaneously. This effect is often called resistance-to-mass transfer, and thus transport of solute from one phase to another can be assumed diffusional in nature. As the solute migrates through the column it is sorbed from the mobile phase into the stationary phase. Flow is through the void volume of the solid particles with the result that the solute molecules diffuse through the interstices to reach surface of stationary phase. Likewise, the solute has to diffuse from the interior of the stationary phase to get back into the mobile phase. 

Since the fraction of empty sites in a zeolite channel determines the correlation factor (Section 5.2.2), as is well known from single-file diffusion in the pores of a membrane, the strong dependence of the diffusion coefficients on concentration can be understood. This is why a simple Nernst-Planck type coupling of the diffusive fluxes (see, for example, [H, Schmalzried (1981)]) is also not adequate. Therefore, we should not expect that sorption and desorption are symmetric processes having identical kinetics. Surveys on zeolite kinetics can be found in [A. Dyer (1988) J. Karger, D.M. Ruthven (1992)]. 

Without knowing the effect of the surfactants on the distribution coefficient for TCE sorption to the peat soil, it is not possible to determine what mechanism caused the reduction in TCE removal. It is possible that the addition of sodiumdodecylsulfate, sodiumdodecylbenzenesulfonate, Tween 20, or Triton X-405 may have enhanced the sorption of TCE to the peat soil. If this were the case, the reduction in TCE removal would be attributable to a decrease in the magnitude of the concentration gradient driving the desorption process. Another possibility is that the addition of these surfactants may have inhibited the diffusion of the TCE from the peat soil to the aqueous phase. This last hypothesis could result if the surfactant... 

Many of the early studies on kinetics of soil chemical processes were obviously concerned with diffusion-controlled exchange phenomena that had half-lives (r1/2) of 1 s or greater. However, we know that time scales for soil chemical processes range from days to years for some weathering processes, to milliseconds for degradation, sorption, and desorption of certain pesticides and organic pollutants, and to microseconds for surface-catalyzed like reactions. Examples of the latter include metal sorption-desorption reactions on oxides. 

Karickhoff (1980) and Karickhoff et al. (1979) have studied sorption and desorption kinetics of hydrophobic pollutants on sediments. Sorption kinetics of pyrene, phenanthrene, and naphthalene on sediments showed an initial rapid increase in sorption with time (5-15 min) followed by a slow approach to equilibrium (Fig. 6.7). This same type of behavior was observed for pesticide sorption on soils and soil constituents and suggests rapid sorption on readily available sites followed by tortuous diffusion-controlled reactions. Karickhoff et al. (1979) modeled sorption of the hydrophobic aromatic hydrocarbons on the sediments using a two-stage kinetic process. The chemicals were fractionated into a labile state (equilibrium occurring in 1 h) and a nonlabile state. 

Recent research has shown that HOCs, particularly aromatic compounds, may be biodegraded by microorganisms to a residual concentration that no longer decreases or which decreases only very slowly over years [ 18]. It is widely believed that further reductions are limited by the availability of hydrocarbons to microorganisms and all the more so for aged contaminants [19, 20]. The bioavailability of a chemical is controlled by a number of physical-chemical processes such as sorption and desorption, diffusion, and dissolution [21]. In particular, for aged soils a fraction of the contaminant appears to be inaccessible for biodegradation. The pollutant, not nutrient availability, seems to be the... 

A fundamental advantage of the frequency response method is its ability to yield information concerning the distribution of molecular mobilities. For example, a bimodal distribution of diffusivites, which is difficult to detect by conventional sorption measurements, leads to two different resonances [49], Moreover, from an analysis of the frequency response spectrum it is even possible to monitor molecular diffusion in combination with chemical reactions [45]. As in conventional sorption experiments, however, the intrusion of heat effects limits the information provided by this technique for fast adsorption-desorption processes [50]. 

Thermal desorption is a dynamic (non-equilibrium) technique in which a sample of hydrated corneum is heated at a constant rate in a dry atmosphere. The water desorption rate is plotted as a function of temperature. The general shape and temperature maxima of the desorption rate vs. temperature curves (Figure 12) are characteristic of the material s diffusion and equilibrium sorption behavior as well as experimental conditions such as heating rate. In a simple desorption process where... 

The results of numerous investigations on the kinetics of sorption of pure substances in zeolites have since then appeared in the literature and the field has been reviewed recently by Walker et al. 42). The total uptake or loss of sorbate in a large number of crystallites is commonly observed, and it is generally assumed that the rate of these processes is controlled by diffusion in the solid. Variable diffusion coefficients were sometimes observed by this method, and it appears possible that other processes than diffusion in the solid had some influence on the rate in these cases. The apparent diffusivity will depend only on concentration (besides temperature) if the migration of sorbate particles in the solid is rate controlling. A simple criterion whether this condition exists can be obtained by measuring sorption or desorption rates repeatedly for various initial concentrations and boundary conditions, as described by Diinwald and Wagner 43). 

However, the two-sink model as well as other existing adsorption (sink) models do not seem to be able to describe the strong asymmetry between the adsorption/desorption of VOCs on/from indoor surface materials (the desorption process is much slower than the adsorption process). Diffusion combined with internal adsorption is assumed to be capable of explaining the observed asymmetry. Diffusion mechanisms have been considered to play a role in interactions of VOCs with indoor sinks. Dunn and Chen (1993) proposed and tested three unified, diffusion-limited mathematical models to account for such interactions. The phrase unified relates to the ability of the model to predict both the ad/absorption and desorption phases. This is a very important aspect of modeling test chamber kinetics because in actual applications of chamber studies to indoor air quality (lAQ), we will never be able to predict when we will be in an accumulation or decay phase, so that the same model must apply to both. Development of such models is underway by different research groups. An excellent reference, in which the theoretical bases of most of the recently developed sorption models are reviewed, is the paper by Axley and Lorenzetti (1993). The authors proposed four generic families of models formulated as mass transport modules that can be combined with existing lAQ models. These models include processes such as equilibrium adsorption, boundary layer diffusion, porous adsorbent diffusion transport, and conveetion-diffusion transport. In their paper, the authors present applications of these models and propose criteria for selection of models that are based on the boundary layer/conduction heat transfer problem. 

Sorption, diffusion, and desorption processes across a plastic sheet... 

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