Two-stage sorption model

T. goesingense. The required input parameters were partly measured for the experimental conditions of the rhizobox experiment and partly obtained from literature data. The curves that matched best measured labile Ni were those obtained by the most simple initial model, the model including release from a fixed Ni phase and the two-stage sorption model. The simulation results for each of the three models were quite similar, indicating that the influence of the additionally included processes was relatively small under the assumptions of equilibrium between fixed phase and solution in the bulk soil. The models including both root hairs and exudation overestimated depletion of labile Ni close to... 

Model 5 model 1 including a two-stage sorption model... 

The values for the exudation rate F, interaction coefficient (A), buffer power of exudate in soil b and the decomposition rate constant for the exudate k were adopted from Kirk (1999). The value of the forward rate constant was estimated from Scheckel and Sparks (2001), who evaluated kinetic adsorption data of Ni to different minerals where ranged from 2.5 x 10 to 9.78 X 10 s For the simulation, an average value of 5.00 x 10 was used. This value also coincides with the values that Kirk and Staunton (1989) suggested for the kinetic adsorption of Q to soil, where the values ranged from lO" to 10 2 s f This same value was assumed for the rate constant for the two-stage sorption model, a2- The fraction of type 1 sites (F ) was assumed to be 0.3. Table 7 summarizes all input parameter values. 

Li, Y. and B. Holcombe, A two-stage sorption model of the coupled diffusion of moisture and heat in wool fabrics. Textile Research Journal, 1992, 62(4), 211-217. 

Fig. 2. Simulated curves of (a) labile and (b) dissolved Ni (NiJ vs. measurements. Model 1 initial model Model 2 plus root hairs Model 3 plus root exudation Model 4 plus slow reacting Ni Model 5 plus two-stage sorption Ni, initial concentration.

Fig. 7. Effect of varying the values of on (a) labile Ni and (b) dissolved Ni (Ni ) calculated by Model 4 including slow reacting Ni and a on (c) labile Ni and (d) dissolved Ni (Ni ) calculated by Model 5 including two-stage sorption.

De Wilde WP, Shopov PJ (1994) A simple model for moisture sorption in epoxies with sigmoidal and two-stage sorption effects. Compos Struct 27(3) 243-252 Derrien K, Gilormini P (2007) The effect of applied stresses on the equilibrium moisture content in polymers. Scr Mater 56(4) 297-299... 

In these equations, both and X are functions of the concentration of water absorbed by the fibers. Most textile fibers have very small diameters and very large surface/volume ratios. The assumption in the second equation of instantaneous thermal equilibrium between the fibers and the gas in the inter-fiber space does not therefore lead to appreciable error. The two equations in the model are not linear and contain three unknown, i.e., Cj-, T, and. A third equation should be established appropriately in order to solve the model. Researchers derived a third equation to obtain an analytical solution by assuming thatC is linearly dependent on T and C , and that fibers reach equilibrium with adjacent air instantaneously. Considering the two-stage sorption process of wool. Scientists proposed an... 

The assumptions in his model do not allow for the complexity of the moisture sorption isotherm and the sorption kinetics of fibers. Scientists presented two mathematical models to simulate the interaction between moisture sorption by fiber and moisture flux through the air spaces of a fabric. In the first model, they considered diffusion within the fiber to be so rapid that the fiber moisture content is always in equilibrium with the adjacent air. In the second model, they assumed that the sorption kinetics of the fiber follows Fickian diffusion. Their model neglected the effect of heat of sorption behavior of the fiber. Scientists developed a new sorption equation that takes into account the two-stage sorption kinetics of wool fibers, and incorporated this with more realistic boundary conditions to simulate the sorption behavior of wool fabrics. They assumed that water vapor uptake rate of fiber consists of a two components associated with the two stages of sorption identified by researchers. 

The First-Order Kinetic Model. Karickhoff (1, 68) has proposed a two-compartment equilibrium-kinetic model for describing the solute uptake or release by a sediment. This model is based on the assumption that two types of sorption sites exist labile sites, S, which are in equilibrium with bulk aqueous solution, and hindered sites, Sjj, which are controlled by a slow first-order rate process. Conceptually, sorption according to this model can be considered either as a two-stage process ... 

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. 

Li and Holcombe [31] developed a two -stage model, which takes into account water-vapor-sorption kinetics of wool fibers and can be used to describe the coupled heat and moisture transfer in wool fabrics. The predictions from the model showed good agreement... 

Scientists developed a two-stage model, which takes into account water-vapor-sorption kinetics of wool fibers and can be used to describe the coupled heat and moisture transfer in wool fabrics. The predictions fi om the model showed good agreement with experimental observations obtained from a sorption-cell experiment. More recently, Scientists further improved the method of mathematical simulation of the coupled diffusion of the moisture and heat in wool fabric by using a direct numerical solution of the moisture-diffusion equation in the fibers with two sets of variable diffusion coefficients. These researeh publieations were focused on fabrics made fi om one type of fiber. The features and differences in the physical mechanisms of coupled moisture and heat diffusion into fabrics made fi om different fibers have not been systematieally investigated. 

Fan and Luo [12] incorporated the new two-stage moisture sorption/ desorption model of fibers into the dynamic heat and moisture transfer model for porous clothing assemblies. They considered the radiation heat transfer and the efFect of water content of fibers on the thermal conductivity of fiber material. Further, Fan and his co-woricers improved the model by introducing moisture bulk flow, which was caused by the vapor-pressure gradients and supersaturation state [12]. This improvement made up for the ignorance of liquid water diffusion in the porous textile material in previous models. The equations of the model are listed as follows ... 

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