Batch competitive adsorption

Adsorption of an impurity onto a porous solid such as activated carbon, alumina, or silica is often used to purify gases and liquids. Adsorption usually is reversible, but if the heat of adsorption is high then the tendency to desorb may be low. Typically adsorption is done in a continuous process. It also may be done in a batch process for small-scale separations or to determine the parameters that control the adsorption process for a given adsorbate (the adsorbing molecule) and a given adsorbent (the porous solid). 

In this problem we will simulate a batch adsorption process that takes place with two adsorbate components. The simulation will allow us to do computational experiments with the aim of learning how the adsorption and desorption parameters affect the behavior of this process. Building the simulation will provide new experience in developing the model equations, utilizing more complex constitutive relationships, finding numerical solutions to these equations, and displaying the results graphically. 

Adsorption and desorption can be considered to be analogous to a reversible chemical reaction. By way of this analogy there must be a forward rate corresponding to adsorption and a reverse rate for desorption. The net rate of adsorption is the difference between these two rates. 

When a molecule descends to a solid surface and comes to rest we consider this an adsorption event. The time a molecule spends in this state may be very short (10 sec) or it may be long ( hours). Because molecules have real bulk, volume, and dimensions, when they rest at the surface they occupy some area. Thinking of a flat plane as the surface, then the cross-sectional area (shadow area) of the molecule is the area of the surface that is occupied. The locus of points beneath this molecule can be termed the adsorption site. The area of the surface divided by the area of the site gives the theoretical number of sites present at the surface  

Dividing this number by Avogadro s number L and the volume occupied by the surface, that is, by the volume of the high surface area solid H gives the concentration of adsorption sites  

When a molecule descends to a solid surface and comes to rest we consider this an 

The locus of pointsbeneath this molecule canbe termed the adsorption site. The area of 

Therateofadsorptionisproportionaltotheconcentrationoftheadsorbateinthebulkphase (gas or solid) surrounding the solid and the difference between the total concentration of sites in the adsorbentphase(poroussolid)andthenumberofsitesalreadyoccupiedbythe adsorbatemolecules  

Thesurfaceconcentrationsaregiveninawaythatisanalogoustotheadsorptionsiteconcen-tration,thatis,asthenumberofmolesoftheadsorbedspeciespervolumeofthe adsorbent solid. 

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We have developed a compact photocatalytic reactor [1], which enables efficient decomposition of organic carbons in a gas or a liquid phase, incorporating a flexible and light-dispersive wire-net coated with titanium dioxide. Ethylene was selected as a model compound which would rot plants in sealed space when emitted. Effects of the titanium dioxide loading, the ethylene concentration, and the humidity were examined in batches. Kinetic analysis elucidated that the surface reaction of adsorbed ethylene could be regarded as a controlling step under the experimental conditions studied, assuming the competitive adsorption of ethylene and water molecules on the same active site. 

Optimal operating conditions and catalysts Acetylation of phenyl ethers was generally carried out in the absence of solvents, which makes easier the recovery of the acetylated product from the reaction mixture. On the other hand, because of the high melting point of substrate and acetylated products, solvents were always used in the acetylation of 2-methoxynaphthalene. Flow reactors (e.g. fixed bed tubular reactors), in which the detrimental effect of competitive adsorption of substrate and products on the acetylation yield is lower than in the batch reactors, should be preferred. However although the set up of fixed bed reactors for liquid phase reactions is relatively simple, their substitution to the batch reactors, which are the only system used in academic organic chemistry, remains essentially limited to commercial units. 

Batch competition experiments v ith equal vv eights of desorbent and DMN heart-cut v ere run to determine the effect of desorbent on selectivity for adsorption of 2,7-DMN over 2,6-DMN. The relative strength v ith v hich desorbent or any other component of a mixture is adsorbed can be shovv n by p factor, p Factor is defined as the ratio of component x in the adsorbed phase over component x in the unadsorbed phase divided... 

Figure 6.28 compares measured and simulated profiles for the batch separation of EMD53986. Very good agreement between theory (solid lines) and experiment (symbols) is achieved using the multi-component modified-Langmuir isotherm (Fig. 6.21). Also shown are the simulation results neglecting component interaction by using only the single-component isotherms (dashed line), which deviate strongly from the observed mixture behavior. Typical for competitive adsorption is the displacement of the weaker retained R-enantiomer and the peak expansion of the stronger adsorbed S-enantiomer.

Ghaee et al. [80] studied the adsorption property of copper and nickel on macroporous CS membranes. Batch adsorption experiments were carried out with mono- and bicomponent solutions on CS membrane. In monocomponent adsorption, the copper ion adsorption was 19.87 mg/g, which was higher than those of nickel (i.e., 5.21 mg/g). Maximum adsorptions for copper and nickel were 25.64 and 10.3 mg/g, respectively. Compared to monoadsorption, the amount of adsorption for individual component in bicomponent mixtures showed a decrease. That is due to the competitive adsorption and coordination site limitation. Aliabadi et al. [81] prepared electro-spun nanofiber membrane of PE oxide/CS for the adsorption of nickel, cadmium, lead, and copper ions from aqueous solutions. The maximum adsorption capacity of nickel, copper, cadmium, and lead ions by the PEO/CS nanofiber membrane followed the descending order nickel(II) > copper(II) > cadmium(II) > lead(II). 

Finally, S0 et al. (2012) studied the competitive adsorption of arsenate and phosphate onto calcite in batch experiments and modeled the results using the CCM and the CD-MUSIC model. It was found that both models predicted well the separate adsorption of both anions, but the CCM underpredicted the competition when combining the models for single sorbate systems instead the CD-MUSIC model predicted satisfactorily the competitive adsorption of phosphate and arsenate onto calcite in the binary systan by combining the parameters of the separate systems. 

Perhaps the hypersorption process (7) of recent years may be thought new and it is new in applying the mechanical principle of continuous operation to charcoal adsorption, but such adsorption on a batch process was in use more than 25 years ago and became obsolete in competition with absorption. Now the continuous hypersorption method appears to be finding a real field of usefulness, especially in making very high recoveries of propane and in recovering substantial amounts of ethane. Recovery of ethane is beginning to be important, in connection with its use as a chemical raw material for the reactions mentioned previously in this paper. 

The adsorption properties of natural clinoptilolite toward Co were investigated by batch equilibration technique [07S2], The kinetic data were fitted by pseudo-second-order reaction model, and the adsorption isotherms were defined by the Langmuir equation. The adsorption capacity of the natural clinoptilolite was decreased by the competition among the metal ions in solution. The adsorption capacity reached 2.34 mg/g for Co. The adsorption of Co was low, at low pH, but increased remarkably with increasing pH and precipitated at pH > 8. The presence of EDTA hindered the adsorption of Co on clinoptiloUte. 

The disadvantage of the broad PSD in the effluent from a CSTR can actually prove to be an asset if one wishes to study competitive growth and transport rates among the particles. Kinetic model components for particle growth, free radical adsorption and free radical desorption must be of the proper form if one is to be able to predict the PSD of the effluent latex. Batch data will not provide an analysis of the same sensitivity. Hence, measurement of feed and effluent PSD s from a CSTR can be an effective way of measuring fundamental kinetic constants. 

Finally to gain a deeper understanding of the bisolute batch adsorption process, models of various significant physical phenomena taking place in the adsorber (e.g., interaction between adsorbates as well as competition) should be incorporated into the present model. Investigations of these phenomena are, however, outside the scope of the present study. 

In the adsorption calorimetry experiment, a small amount n" of the stock solution injected during a given injection is diluted in the supernatant liquid inside the cell and some of the resulting species subsequently adsorb onto solid particles. They displace a certain amount of solvent molecules and can exchange with some pre-adsorbed molecules or ions, because of the limited extent of the adsorption space. The effects of desolvation and re-solvation of various compounds taking part in the displacement process contribute to the competitive character of adsorption at the solid-solution interface. The flow chart of the batch displacement experiment is shown in Fig. 6.22. Since the enthalpy effects accompanying dilution of the stock solution inside the cell should be known, both the dilution and adsorption experiments are carried out under the same conditions (cf.. Fig. 6.19). 

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