Time-dependent sorption

Aochi, Y. O., and W. J. Farmer, Role of microstructural properties in the time-dependent sorption/desorption behavior of 1,2-dichloroethane on humic substances , Environ. Sci. Technol., 31,2520-2526 (1997). 

Kookana, R.S., L.A.G. Aylmore, and R.G. Gerritse (1992). Time-dependent sorption of pesticides during transport in soils. Soil Sci., 154 214-225. 

Kookana, R.S., R.D. Schuller, and L.A.G. Aylmore (1993). Simulation of simazine transport through soil columns using time-dependent sorption data measured under flow conditions. J. Contam. Hydrol., 14 93-115. 

Ryden, J.C., J.R. McLaughlin, and J.K. Syers. 1977. Time dependent sorption of phosphate by soils and hydrous ferric oxides. J. Soil Sci. 28 585-595. 

Case n transport is an interesting special case of sorption because the linear time dependence of the relaxation process means that a constant swelling rate could be observed [119,121,128,129,132-135], Mechanistically, case II transport... 

Ionization, sorption, volatilization, and entrainment with fluid and particle motions are important to the fate of synthetic chemicals. Transport and transfer processes encompass a wide variety of time scales. Ionizations are rapid and, thus, usually are treated as equilibria in fate models. In many cases, sorption also can be treated as an equilibrium, although somtimes a kinetic approach is warranted (.2). Transport processes must be treated as time-dependent phenomena, except in simple screening models (.3..4) ... 

Most of the sorption/desorption transformation processes of various solid phases are time-dependent. To understand the dynamic interactions of organic pollutants with solid phases and to predict their fate with time, knowledge of the kinetics of these processes is important [20,23]. 

Beigel, C., Barriuso, E., and Di Pietro, L. Time dependency of triticonazole fungicide sorption and consequences for diffusion... 

Fig. 8.45 Sorption of Cu on montmoriilonite as a function of (a) pH and (b) time-dependent release of soil-absorbed Cu by EDTA, citrate, and oxalate. (Lehman and Harter, 1984)...

Fig. 19.9 Time-dependent change of enzymatic activity of catalase immobilized within PNIPA gel by sorption (1) and in aqueous solution (2) at temperature interval 25-40°C...

Concern about fission-product release from coated reactor fuel particles and fission-product sorption by fallout particles has provided stimulus to understand diffusion. In a fallout program mathematics of diffusion with simple boundary conditions have been used as a basis for (1) an experimental method of determining diffusion coefficients of volatile solutes and (2) a calculational method for estimating diffusion profiles with time dependent sources and. time dependent diffusion coefficients. The latter method has been used to estimate the distribution of fission products in fallout. In a fission-product release program, a numerical model which calculates diffusion profiles in multi-coated spherical particles has been programmed, and a parametric study based on coating and kernel properties has provided an understanding of fission product release. 

Because of the assumed dual sorption mechanism present in glassy polymers, the explicit form of the time dependent diffusion equation in these polymers is much more complex than that for rubbery polymers (82-86). As a result exact analytical solutions for this equation can be found only in limiting cases (84,85,87). In all other cases numerical methods must be used to correlate the experimental results with theoretical estimates. Often the numerical procedures require a set of starting values for the parameters of the model. Usually these values are shroud guessed in a range where they are expected to lie for the particular penetrant polymer system. Starting from this set of arbitrary parameters, the numerical procedure adjusts the values until the best fit with the experimental data is obtained. The problem which may arise in such a procedure (88), is that the numerical procedures may lead to excellent fits with the experimental data for quite different starting sets of parameters. Of course the physical interpretation of such a result is difficult. 

Figure 9-2 Several sorption (A) and desorption (D) curves, a) normal diffusion with constant D-value b) increasing D-value with increasing permeant concentration c) decreasing D-value with increasing permeant concentration d) sorption with pronounced swelling e) concentration- and time-dependent diffusion coefficient.

Through the uptake of a substance in a polymer matrix, time dependent changes in the polymer matrix can take place, particularly at high concentrations. As a consequence, the diffusion coefficient can be time- as well as concentration-dependent. One observes such behavior for example by the sorption of substances that lead to swelling at temperatures below the Tg. After a relatively rapid approach to an apparent state of equilibrium one observes a slow change towards the actual equilibrium (Fig. 9-2e). These two-step processes are caused by a gradual loosening of the cohesive forces between the macromolecules. 

Xing B, Pignatello JJ (1996) Time-dependent isotherm of organic compounds in soil organic matter implications for sorption mechanism. Environ Toxicol Chem 15(8) 1282-1288... 

Conventionally, molecular uptake is recorded gravi-metrically [18-20]. Alternatively, for a limited supply of adsorbate, molecular uptake may also be calculated from a knowledge of the time dependence of the pressure (piezometric method [21, 22]) or composition of the gas phase. Changing the sorbate pressure by a step change of the gas volume has proved to be a very efficient method for following fast sorption processes (single step method [23, 24]). The sorption uptake may also be measured volumctrically by mans of a gas burette arrangement [25]. 

To obtain quantitative information about sorption processes controlled by time-dependent diffusion Crank (1953) solved numerically Eq. (1), coupled with Eqs. (4), (5) and (14), for some assumed forms of >i(Cj), De(Cl) and a(cj. His results agreed reasonably with many typical non-Fickian features known at that time (Park (1953)]. However, when a new type of non-Fickian behavior, now generally called the "two-stage type, was discovered in 1953 by Long and his coworkers, it soon became evident that the concept of time-dependent diffusion was too simple to explain every non-Fickian behavior. This situation remains unaltered at present, and so we shall not go further into this subject. 

The region of "Case II sorption (relaxation-controlled transport) is separated from the Fickian diffusion region by a region where both relaxation and diffusion mechanisms are operative, giving rise to diffusion anomalies time-dependent or anomalous diffusion. 

The movement of chemicals undergoing any number of reactions with the soil and/or in the soil system (e.g., precipitation-dissolution or adsorption-desorption) can be described by considering that the system is in either the equilibrium or nonequilibrium state. Most often, however, nonequilibrium is assumed to control transport behavior of chemical species in soil. This nonequilibrium state is thought to be represented by two different adsorption or sorption sites. The first site probably reacts instantaneously, whereas the second may be time dependent. A possible explanation for these time-dependent reactions is high activation energy or, more likely, diffusion-controlled reaction. In essence, it is assumed that the pore-water velocity distribution is bimodal,... 

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