Biosorption rate

The values of pseudo-second-order equation parameters together with correlation coefficients are listed in Table 1. The correlation coefficients for the pseudo-second-order equation were 0.999. The calculated q values also agree very well with the experimental data. This strongly suggests that the biosorption of Cu + onto aminated ephedra waste is most appropriately represented by a pseudo-second-order rate process and the biosorption rate is controlled by chemical biosorption. 

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). 

The term biosorption is given to adsorption processes, which use biomaterials as adsorbents (or biosorbents). Chitosan is a biopolymer and has an extremely high affinity for many classes of dyes, including disperse, direct, reactive, acid, vat, sulfur, and naphthol dyes (Figure 39.3). The rate of diffusion of dyes in chitosan is similar to that in cellulose. Only for basic dyes has chitosan a low affinity. 

Figure 5.17. Diagram of the mathematical model describing the relationship between the specific growth rate jx (or specific rate of substrate utilization, q ) and the limiting substrate concentration s (A. Moser, 1978b) 1, Monod kinetics 2, Monod with S inhibition 3, Monod with S inhibition at high X 4, as 3 with P inhibition 5, as 4 with endogenous metabolism 6, as 4 with sequential metabolism of two substrates, that is, biosorption and 7, transients such as lag phase.

Figure 5.38. Kinetics of adsorption (biosorption) in biological waste water purification. Time course of chemical and biological oxygen demand expressed as eliminated substrate and degraded substrate following the reaction scheme of substrate degradation and substrate elimination, and evaluation of the rate of adsorption from the difference in chemical and biological rates (Theophilou et al., 1978). The final level Si represents the undegradable substrate. The value of S a represents the maximal capacity of cells (sludge) to adsorb substrate (phenomenon of biosorption ).

Figure 5.39. Consequences of biosorption effect for kinetics of biological waste water treatment shown in a plot of specific consumption rate versus substrate concentration s with the resulting zero-order kinetics.

The appearance of this zero-order rate (BOD with respect to S) is seen in Fig. 5.39 (A. Moser, 1974). Several authors have developed a formal kinetic approach to biosorption effects (Busby and Andrews, 1975 A. Moser, 1977 Theophilou et al., 1978). Figure 5.40 illustrates the reaction scheme thought to be adequate as a starting point for the following set of model equations ... 

The appearance of an overall reaction order one as the sum of several uptake rates was explained by such approaches (Wuhrmann et al., 1958), and it was later quantified (Wolfbauer et al, 1978). This fact is indicated in Fig. 5.48c. However, it seems to be possible to use the simple Monod equation for modeling, and an increased value of apparent will be the consequence. A case of parameter estimation with double substrate limitation is shown in Fig. 5.49 using the Walker plot (see Fig. 4.21b) for the integrated form of the rate equation (Wilderer, 1976). Difficulties arise due to overlapping and to the phenomenon of biosorption (cf. Sect. 5.3.9), leading to a zero-order behavior even if the overall order of S utilization is unity (see Equ. 5.36). 

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