Adsorption internal diffusion

Adsorption equilibrium of CPA and 2,4-D onto GAC could be represented by Sips equation. Adsorption equilibrium capacity increased with decreasing pH of the solution. The internal diffusion coefficients were determined by comparing the experimental concentration curves with those predicted from the surface diffusion model (SDM) and pore diffusion model (PDM). The breakthrough curve for packed bed is steeper than that for the fluidized bed and the breakthrough curves obtained from semi-fluidized beds lie between those obtained from the packed and fluidized beds. Desorption rate of 2,4-D was about 90 % using distilled water. 

It ought to be verified, however, in all cases, that the experimental Q-9 curve truly represents the distribution of surface sites with respect to a given adsorbate under specified conditions. The definition of differential heats of adsorption [Eq. (39) 3 includes, in particular, the condition that the surface area of the adsorbent A remain unchanged during the experiment. The whole expanse of the catalyst surface must therefore be accessible to the gas molecules during the adsorption of all successive doses. The adsorption of the gas should not be limited by diffusion, either within the adsorbent layer (external diffusion) or in the pores (internal diffusion). Diffusion, in either case, restricts the accessibility to the adsorbent surface. 

The most reliable method for detecting the influence of internal diffusion upon the profile of Q-6 curves would be to determine calorimetrically and to compare the differential heats of adsorption of a given gas on the surface of similar samples with different porosities. But it would be very difficult... 

When chemisorption is involved, or when some additional surface chemical reaction occurs, the process is more complicated. The most common combinations of surface mechanisms have been expressed in the Langmuir-Hinshelwood relationships 36). Since the adsorption process results in the net transfer of molecules from the gas to the adsorbed phase, it is accompanied by a bulk flow of fluid which keeps the total pressure constant. The effect is small and usually neglected. As adsorption proceeds, diffusing molecules may be denied access to parts of the internal surface because the pore system becomes blocked at critical points with condensate. Complex as the situation may be in theory,... 

Figure 3. Breakthrough curves for adsorption of nitrogen—internal diffusion...

A common method of assessing the relative importance of internal diffusion and point adsorption resistances is to measure, as a function of time, the uptake of adsorbent from a solution containing solid particles. Batch data of this type taken at different temperatures and particle sizes can usually be analyzed so as to establish the importance of internal resistances. However, some types of diffusion have relatively high activation energies so that the separation is complex. Also, in such methods care must be taken to ensure rapid motion of the fluid with respect to the particles, for example by stirring, in order to eliminate external diffusion... 

For sample EAAw-m/b although the external area was 120 m g the dynamic capacity was only c. 50% of the micropore volume. However, this sample had a narrow threshold diameter (0.9 pm) compared to the previous two series. Thus, it would appear that the presence of wide pores that aid internal diffusion into the monolith walls was also important. This was confirmed by the results with samples EAN-m/b and EAN-m/c that only gave dynamic adsorption capacities of 50% and 1% of their micropore volumes, respectively. These samples had low external areas 90 m g and 50 mV and narrow threshold diameters (0.3 pm). 

The dynamic adsorption capacity of activated carbon containing monoliths has been shown to be equivalent to the micropore volume. However, this condition can only be met when the external area is above c. 100 m g" and the threshold diameter wide. In systems with no micropore volume or poor internal diffusion due to a low external surface area and narrow threshold diameter the breakthrough point is reached when c. 9% of the external area is covered. Future work will concentrate on using higher linear velocities and adsorption temperatures md different monolith geometries (wall thickness and channel width) in order to study the internal diffusion limitations of these types of adsorption units. 

Kinetic studies of ion exchange on partially ion-exchanged type A zeolites of Mg Ca and Mn " revealed that mini-mums and maximums characterize the differential coefficients of internal diffusion for every exchange of 2 Na " ions for one divalent cation per unit cell of the zeolite. On the basis of these observations, assuming definite interactions between the cations and the zeolite lattice, predictions can be made concerning the distribution and arrangement of cations in the unit cells of a type A zeolite. Research on liquid phase adsorption of n-alkanes on partially ion-exchanged type A zeolites indicated that the differential diffusion coefficients for alkane adsorption are influenced likewise by cation distribution in the unit cells of the zeolite. 

Figure 3. Coefficients of internal diffusion in adsorption of n-decane from n-decane-toluene solution by type A magnesium zeolites and calcium zeolites at a zeolite uptake of qt in grams n-decane/grams zeolite = 0.120...

Thus, in spite of a satisfactory agreement of Equation 17 with experimental data for systems with weakly convex adsorption isotherms, the internal diffusion coefficients, evaluated for these cases according to Equation 17, are in fact below their actual value. 

So far in this section we have considered only the adsorption, desorption, and surface reaction. Let us next set these in the context of the transfer and diffusion steps for the same reaction. As has been mentioned above, the catalyst will often be held on porous particles so that the reactants and products have to diffuse to and from the surface of the particle and also within it. For external transfer from the flowing reaction mixture to the exterior of the particle we shall reserve the term mass transfer (more particularly, external mass transfer), and for the diffusion within the particle the term diffusion (or internal diffusion). Both are, of course, concurrently examples of mass transfer and of diflTusion so that the choice of language is an arbitrary one but it draws a useful distinction. 

Although there may have been some adsorption and desorption on the pore walls during the molecule s passage into the interior of the pellet, we do not consider this the third stage until adsorption occurs at a reactive catalytic site. This, and the next two, are the steps we have been considering above, so that within the pellet the concentrations of A and which were denoted by a and b above, will be fl(r) and h(r). All that we have done above has local validity and only if the internal diffusion is very rapid, so that a(r) and 6(r) are effectively uniform, will the reaction rate expression be valid for the pellet as a whole. The rate of adsorption is given by fad, Eq. (6.2.11). 

Now if the internal diffusion is rapid and the adsorption-desorption and reaction are all very fast, the concentrations throughout the pellet are and and from the equilibrium of Eq. (6.2.18)... 

The previous equations describing the adsorption/desorption behavior of gases lead to models describing sink effects in indoor environments. In addition, transport of molecules within the sink material can have a major impact on desorption rates thus, models accounting for internal diffusion have been developed for indoor sinks. Models based on fundamental theories are preferred over empirical approaches, but some studies rely on experimental data to fit empirical models [21-23]. 

These conclusions differ somewhat from those of Pirkle and Siegell in their analysis of adsorption chromatography in a crossflow magnetically fluidized bed (14). They found the dominant effects to be the width of the feed band and the external mass transfer resistance. It is not surprising that the effect of internal diffusion would be more important in size exclusion chromatography with macromolecular solutes. 

We see that at small particle sizes internal diffusion is no longer the sir step and that the surface reaction sequence of adsorption, surface reaction, a desorption Steps 3. 4, and 5) limit the overall rate of reaction. Consider nc one more point about internal diffusion and surface reaction. These steps through 6) are not at all affected by flow conditions external to the pellet. 

J0.2.2 Step 2 Overview Internal Diffusion 660 /0,2. Adsorption Isotherms 661... 

The effective diffusion coefficient depends on the particle porosity, the pore diameter, the tortuosity, and the nature of the diffusing species. For gas-filled pores, the above factors can be allowed for to make a reasonable estimate of the effective diffusivity in the gas phase. However, diffusion of adsorbed molecules along the pore walls, called surface diffusion, often contributes much more to the total flux than diffusion in the gas phase. This is particularly evident in the adsorption of water vapor on silica gel and the adsorption of hydrocarbon vapors on carbon, where the measured values of correspond to internal and external coefficients of comparable magnitude or even to external film control, For adsorption of solutes from aqueous solutions, surface migration is much less important, and the internal diffusion resistance generally dominates the transfer process. 

FAVORABtE ADSORPTION. For favorable adsorption, the break point occurs between the values predicted for linear adsorption and irreversible adsorption. Solutions are available for certain isotherm shapes and different values of internal and external resistances. These solutions have found use for the design of ion exchangers, where the sohd-fiuid equilibria and the internal diffusivities are more readily characterized than for adsorption. 

The actual length of the adsorption zone may be much greater than the estimated value of L,ni of 11.1 cm because of internal diffusion resistance, which is hard to predict. However, even if the length of unused bed is 25 cm, the time to breakthrough would be about 10 years. 

However, the two-sink model as well as other existing adsorption (sink) models do not seem to be able to describe the strong asymmetry between the adsorption/desorption of VOCs on/from indoor surface materials (the desorption process is much slower than the adsorption process). Diffusion combined with internal adsorption is assumed to be capable of explaining the observed asymmetry. Diffusion mechanisms have been considered to play a role in interactions of VOCs with indoor sinks. Dunn and Chen (1993) proposed and tested three unified, diffusion-limited mathematical models to account for such interactions. The phrase unified relates to the ability of the model to predict both the ad/absorption and desorption phases. This is a very important aspect of modeling test chamber kinetics because in actual applications of chamber studies to indoor air quality (lAQ), we will never be able to predict when we will be in an accumulation or decay phase, so that the same model must apply to both. Development of such models is underway by different research groups. An excellent reference, in which the theoretical bases of most of the recently developed sorption models are reviewed, is the paper by Axley and Lorenzetti (1993). The authors proposed four generic families of models formulated as mass transport modules that can be combined with existing lAQ models. These models include processes such as equilibrium adsorption, boundary layer diffusion, porous adsorbent diffusion transport, and conveetion-diffusion transport. In their paper, the authors present applications of these models and propose criteria for selection of models that are based on the boundary layer/conduction heat transfer problem. 

---