Immobile adsorbed

In one dimension the truncation of the equations of motion has been worked out in detail [59]. This has allowed an accurate examination of the role of diffusion in desorption, and implications for the Arrhenius analysis in nonequilibrium situations. The largest deviations from the desorption kinetics of a mobile adsorbate obviously occur for an immobile adsorbate... 

The presence of an immobile adsorbed film or layer on the particle surface may lead to the formation of still stronger interparticle van der Waals bonds (R6). First, surface roughness is smoothed out, increasing the apparent particle size and contact area, and second, the separation distance is effectively... 

The pressure dependence of the concentration of sorbed gas was consistent with the dual mode model while the relaxation data addressed itself to the validity of the assumptions made by the model. The assumption of rapid interchange was found to be valid for this system while the assumption of an immobile adsorbed phase could introduce a small error in the analysis It should be possible to reduce this error by more exact measurements of the concentration of sorbed gas as classical pressure experiments could... 

Waugh et al.131 discussed the selective oxidation of benzene to maleic anhydride on the basis of a detailed study of maleic anhydride and benzene adsorption on a V-Mo oxide catalyst supported on a-Al203. Hydroquinone is found to be an intermediate in this reaction and p-benzoquinone, formed from the hydroquinone, is the main intermediate in the non-selective pathway. The maleic anhydride is observed to be immobile adsorbed and the surface oxidation reaction has a relatively low activation energy. From this the authors conclude that it is not lattice oxygen but weakly bound molecular 02 which is responsible for the selective oxidation and a detailed mechanism, in which use is made of orbital symmetry arguments, is presented. 

Various adsorbents have been examined for their potential to increase in situ product separation in plant cell culture. Suspended solid adsorbents were popular, and the use of immobilized adsorbent has been investigated recently [17-20]. The advantages of immobilized adsorbent are that it is easy to use in a bioreactor operation and that it allows adsorbents to be easily separated from culture broth for the repeated use of cells and adsorbents [21, 22]. The design and optimization of in situ separation process for phytochemicals using immobilized adsorbent required a detailed mathematical model. It was difficult to achieve an optimal design based on purely empirical correlations, because the effects of various design parameters and process variables were coupled. 

In this review the use of adsorbent for the in situ separation of product in plant cell culture is discussed, and a mathematical model which describes immobilized adsorbent coupled with selective separation is presented. Several examples of the application of the technique are also provided. 

Reviews (9, 63, 64) of the reactions between hydroxylated mineral surfaces and aqueous solutions brought out the richness of variety found in surface phenomena involving natural particles. Isolated surface complexes, the principal topic of this chapter, are expected when reaction times are short and the adsorbate content is low [Figure 6, inspired by Schindler and Stumm 63)]. Thus, surface complexes occupy a reasonably well-defined domain in the tableau of reaction time scale versus sorbate concentration. Localized clusters of adsorbate (47, 48, 65, 66) that contain two or more adsorbate ions bonded together can form if the amount sorbed is increased by accretion or bv the direct adsorption of polymeric species (multinuclear surface complexes). Surface clusters can erase the hyperfine structure in the ESR spectrum of an immobilized adsorbate (33, 67) or produce new second-neighbor peaks from ions like the absorber in its EXAFS spectrum (47, 66). 

Nigam, S. Sakoda, A. Wang, H. Y. "Bioproduct recovery from unclarified broths and homogenates using immobilized adsorbents" Biotech. Prog. 1988,4, pp 166-172. 

The purpose of this article is to formulate a model which considers simultaneous diffusion and binding reaction within the immobilized adsorbent particles. The model has been developed for batch adsorption processes. It can however be easily modified to predict product adsorption in other reactor configurations. 

Several assumptions are made to mathematically model the immobilized adsorbent. The small adsorbent particles are assumed to be distributed uniformly inside the hydrogel bead. The external mass transfer resistance due to the boundary layer is assumed to be negligible if the bulk solution is well stirred. This assumption is supported by the experimental observations of Tanaka et al. who studied diffusion of several substrates from well stirred batch solutions into Ca-alginate gel beads (4), However, the boundary conditions can be easily modified to incorporate external diffusion effects if needed. Furthermore product diffusion in both the hydrogel and the porous adsorbent is considered to follow Fickian laws and its diffusivity in each region is assumed to be constant. 

Several simulation runs were carried out to gain insight into the effect of bead design parameters on the adsorption characteristics of immobilized adsorbent beads. The physical parameters (rate constant, diffusivity etc.) for the simulation studies were determined from experimental data on the adsorption of cycloheximide, a low molecular weight antibiotic, onto XAD-4 non-ionic polymeric resin (10.11) (Table I). The fit between the model and the experimentally determined adsorption curves is quite good (Figure 3). 

Figure 3. Concentration profile of cycloheximide in a batch adsorber employing immobilized adsorbent beads (see Table I for experimental conditions).

Two component diffusion and binding. There is a frequent possibility of having one or more oompounds present in the fermentation broth which may compete for the available ligands in the adsorbent particles. The objective here is to optimize the bead design so as to maximize the purity of the desired product adsorbed onto the adsorbent particles. In order to numerically simulate such a situation it was assumed that two compounds are being adsorbed onto the immobilized adsorbents a desired product 1 and an undesired by-product 2. The adsorption rate constant for the desired product, K., is assumed to be 10 times that of the undesired product, K,. The diffusivities for both of these products are assumed to be similar. Two additional parameters are defined to study the dynamic behavior of such systems. 

Figure 7 shows the variation of selectivity with respect to time for three types of affinity beads (Cases (a), (b) and (c)). In all three cases, selectivity decreases from the initial maximum value as time progresses. Due to identical diffusivities, the two products have very similar concentration profiles within the immobilized adsorbent bead at initial time. Thus the initial selectivity is just the ratio of their adsorption rate constants. However, since product... 

Figures 6a,b. Effect of bioproduct diffusivity in hydrogel (D) and in adsorbent matrix (D ) on ligand consumption using immobilized adsorbent beads.

It was found that the decline in selectivity was least in case (c) because of a smaller overall diffusional resistance of the bead. Figure 8 shows the variation of product purity (Pu) as a function of time for these three cases. The product purity curves show the same general trend as the selectivity curves. Final product purity was also found to be highest for case (c). By virtue of their lower overall mass transfer resistance case (c) immobilized adsorbent beads not only display a higher adsorption rate but also offer a higher selectivity for the desired product. 

Fignre 7. (left) Selectivity as a function of time for competitive adsorption of two compounds, (right) Concentration profiles within the immobilized adsorbent head and the bulb solution. 

Immobile adsorbate any variation of —/ H with increase of coverage q Mobile adsorbate —AH decreases with increase of q... 

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