Sorption desorption, and diffusion

In the first stage, unfixed dyes, salt and alkali present in the liquor phase must be removed and this is best done by replacing this liquor with fresh water. Sorption, desorption and diffusion processes play only subordinate roles in this stage, the key factors being liquor flow, mechanical action and liquor exchange. The dilution laws are generally applicable. 

Scow, K. M. (1993)- Effect of sorption-desorption and diffusion processes on the kinetics of biodegradation of organic chemicals in soil. In Sorption and Degradation of Pesticides and Organic Chemicals in Soil, ed. D. M. Linn, T. H. Carski, M. L. Brusseau F-H. Chang, pp. 73-114. Madison, WI Soil Science Society of America, American Society of Agronomy. 

Water Vapor Sorption, Desorption, and Diffusion in Excised Skin Part I. Technique... 

A gravimetric technique to study the sorption, desorption, and diffusion characteristics of uxiter vapor in excised skin under dynamic conditions is described. The technique features a continuously recording microbalance and a humiditygenerating apparatus which provides a stream of air with any given relative humidity. The diffusion coefficient is determined from the kinetics of sorption and desorption. The technique can be used to study other polymeric films, fibers, and powders. 

Figure 21-2. Sorption, desorption and diffusion processes across a polymer film.

Equation (57) is empirical, except for the case where v = 0.5, then Eq. (57) is similar to the parabolic diffusion model. Equation (57) and various modified forms have been used by a number of researchers to describe the kinetics of solid phase sorption/desorption and chemical transformation processes [25, 121-122]. 

Grathwohl, P. (1998). Diffusion in natural porous media contaminant transport, sorption/desorption and dissolution kinetics, Kluwer Publishers, Boston, MA. 

We will return now to the three independent random processes that underlie migration and induce zone spreading molecular diffusion, sorption-desorption, and flow-diffusion processes in the mobile phase. 

The second stage features the moisture sorption of fibers, which is relatively slow and takes a few minutes to a few hours to complete. In this period, water sorption into the fibers takes place as the water vapor diffuses into the fabric, which increases the relative humidity at the surfaces of fibers. After liquid water diffuses into the fabric, the surfaces of the fibers are saturated due to the film of water on them, which again will enhance the sorption process. During these two transient stages, heat transfer is coupled with the four different forms of liquid transfer due to the heat released or absorbed during sorption/desorption and evaporation/condensation. Sorption/ desorption and evaporation/condensation, in turn, are affected by the efficiency of the heat transfer. For instance, sorption and evaporation in thick cotton fabric take a longer time to reach steady states than in thin cotton fabrics. 

Grathwohl, P. (1998) Diffusion in Natural Porous Media Contaminant Transport, Sorption, Desorption and Dissolution Kinetics, Kluwer Academic Publishers. 

Heat and mass transfers in porous media are coupled in a complicated way. On the one hand, heat is transported by conduction, convection, and radiation. On the other hand, water moves under the action of gravity and pressure gradient whilst the vapor phase moves by diffusion caused by a gradient of vapor density. Thus, the heat transfer process can be coupled with mass transfer processes with phase changes such as moisture sorption/desorption and evaporation/condensation. 

Besides electrokinetic transport, chemical reactions also occur at the electrode surfaces (i.e., water electrolysis reactions with production of at the anode and OH at the cathode). Common mass-transport mechanisms like diffusion or convection and physical and chemical interactions of the species with the medium also occur. In a low-permeable porous medium under an electrical field, the major transport mechanism through the soil matrix during treatment for nonionic chemical species consists mainly of electro-osmosis, electrophoresis, molecular diffusion, hydrodynamic dispersion (molecular diffusion and dispersion varying with the heterogeneity of soils and fluid velocity [8]), sorption/ desorption, and chemical or biochemical reactions. Since related experiments are conducted in a relatively short period of time, the chemical and biochemical reactions that occur in the soil water are neglected [9]. 

Fig. 5.12 Fluid weight gain (or weight-loss) curves for initial sorption, desorption and resorption processes, as calculated by the equivalent diffusivity model, plotted vs. /time (Weitsman and Guo 2002)...

The coupled heat and liquid moisture transport of porous material has wide industrial applications. Heat transfer mechanisms in porous textiles include conduction by the solid material of fibers, conduction by intervening air, radiation, and convection. Meanwhile, liquid and moisture transfer mechanisms include vapor diffusion in the void space and moisture sorption by the fiber, evaporation, and capillary effects. Water vapor moves through porous textiles as a result of water vapor concentration differences. Fibers absorb water vapor due to their internal chemical compositions and structures. The flow of liquid moisture through the textiles is caused by fiber-liquid moleeular attraction at the surface of fiber materials, whieh is determined mainly by surface tension and effective capillary pore distribution and pathways. Evaporation and/or condensation take plaee, depending on the temperature and moisture distributions. The heat transfer proeess is coupled with the moisture transfer processes with phase ehanges sueh as moisture sorption/desorption and evaporation/condensation. 

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. 

The Elovich model was originally developed to describe the kinetics of heterogeneous chemisorption of gases on solid surfaces [117]. It describes a number of reaction mechanisms including bulk and surface diffusion, as well as activation and deactivation of catalytic surfaces. In solid phase chemistry, the Elovich model has been used to describe the kinetics of sorption/desorption of various chemicals on solid phases [23]. It can be expressed as [118] ... 

Most researchers attribute slow kinetics to some sort of diffusion limitation (e.g., diffusion is random movement under the influence of a concentration gradient [193]), because sorbing molecules are subject to diffusive constraints throughout almost the entire sorption/desorption time course due to the porous nature of particles. Particles are porous by virtue of their aggregated nature and because the lattice of individual grains in the aggregate may be fractured. 

Kinetic models proposed for sorption/desorption mechanisms including first-order, multiple first-order, Langmuir-type second-order, and various diffusion rate laws are shown in Sects. 3.2 and 3.4. All except the diffusion models conceptualize specific sites to or from which molecules may sorb or desorb in a first-order fashion. The following points should be taken into consideration [ 181,198] ... 

Pignatello and Xing [107] used two models, the organic matter diffusion model (OMD) and the sorption-retarded pore diffusion model (SRPD), in order to understand better the meaning of slow sorption/desorption observations and mechanisms and to explore the most likely causes of such slow process in natural solid particles. These authors reported that both OMD and SRPD mechanisms operate in the environment, often probably together in the same particle. OMD may predominate in soils that are high in natural OM and low in aggregation, while SRPD may predominate in soils where the opposite conditions exist. 

Sorption/desorption is the key property for estimating the mobility of organic pollutants in solid phases. There is a real need to predict such mobility at different aqueous-solid phase interfaces. Solid phase sorption influences the extent of pollutant volatilization from the solid phase surface, its lateral or vertical transport, and biotic or abiotic processes (e.g., biodegradation, bioavailability, hydrolysis, and photolysis). For instance, transport through a soil phase includes several processes such as bulk flow, dispersive flow, diffusion through macropores, and molecular diffusion. The transport rate of an organic pollutant depends mainly on the partitioning between the vapor, liquid, and solid phase of an aqueous-solid phase system. 

Apparent hysteresis occurs mainly when complete equilibrium is not reached. Diffusion into the solid matrix or into micropores of aggregates is considered a main cause of apparent hysteresis. In a transitory state, sorption occurs concurrently with desorption and the concentration of contaminant in the liquid phase is erroneously low because some fraction is associated with sorption. 

The purpose of most experimental studies of diffusion is to obtain accurate diffusion coefficients as a function of temperature, pressure, and composition of the phase. For this purpose, the best approach is to design the experiments so that the diffusion problem has a simple anal3hical solution. After the experiments, the experimental results are compared with (or fit by) the anal3hical solution to obtain the diffusivity. The method of choice depends on the problems. The often used methods include diffusion-couple method, thin-source method, desorption or sorption method, and crystal dissolution method. 

Tracer diffusivities are often determined using the thin-source method. Self-diffusivities are often obtained from the diffusion couple and the sorption methods. Chemical diffusivities (including interdiffusivity, effective binary diffusivity, and multicomponent diffusivity matrix) may be obtained from the diffusion-couple, sorption, desorption, or crystal dissolution method. 

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