Dead end pores

Another important distinction relating to pore geometry is that between "through" pores, with two open ends, and "dead-end" pores with only one. 

Now suppose e(a) denotes the total void volume associated with pores of radii < a, per unit volume of the porous medium. This includes the contributions of any dead-end pores. Chough these are not taken into account in the distribution function f(a,ri). Then we shall write... 

Furthermore, if there are no dead end pores it is not difficult to show from equation (8.16) that under the assumption of... 

Since the void fraction distribution is independently measurable, the only remaining adjustable parameters are the A, so when surface diffusion is negligible equations (8.23) provide a completely predictive flux model. Unfortunately the assumption that (a) is independent of a is unlikely to be realistic, since the proportion of dead end pores will usually increase rapidly with decreasing pore radius. 

Thus dynamic tests will be influenced by the existence of the dead-end pores and, in principle, they offer the possibility of obtaining quantitative inforiuation on diffusion in these pores. 

The first thing to notice about these results is that the influence of the micropores reduces the effective diffusion coefficient below the value of the bulk diffusion coefficient for the macropore system. This is also clear in general from the forms of equations (10.44) and (10.48). As increases from zero, corresponding to the introduction of micropores, the variance of the response pulse Increases, and this corresponds to a reduction in the effective diffusion coefficient. The second important point is that the influence of the micropores on the results is quite small-Indeed it seems unlikely that measurements of this type will be able to realize their promise to provide information about diffusion in dead-end pores. 

Dead-end Pores Dead-end volumes cause dispersion in unsteady flow (concentration profiles ar> ing) because, as a solute-rich front passes the pore, transport oceurs by molecular diffusion into the pore. After the front has passed, this solute will diffuse back out, thus dispersing. 

Pinner A, Nye PH. 1982. A pulse method for studying effects of dead-end pores, slow equilibration and soil structure on diffusion of solutes in soil. Journal of Soil Science 33 25-35. 

In Equation 7, solute concentrations are area averaged with the subscripts referring to the mobile or stationary phase, I Is the length of the dead end pores, and the dlffuslvltles and D... 

Stationary electro-osmosis in a dead-ended pore adjacent to a dense permselective surface. 

Figure 25.1 Heterogeneity is one of the main properties of porous media it not only characterizes the scales shown in the figure, but also occurs on larger scales up to the size of the whole porous system. Three important mechanisms of transport and mixing in porous media are (a) interpore dispersion caused by mixing of pore channels (b) intrapore dispersion caused by nonuniform velocity distribution and mixing in individual channels (c) dispersion and retardation of solute transport caused by molecular diffusion between open and dead-end pores as well as between the water and the...

Further, when electric field is applied to a capillary that is closed at one end, EOF as shown in Fig. 1.15 is set up in the tube. This situation is very similar to that of a dead end pore in a packing particle in CEC, where flow is generated at the pore wall and causes the electrolyte to accumulate at the dead end, followed by pressure driven flow at the center in the reverse direction. Unlike in pressure driven flow where mass transfer through such a pore would depend entirely on the diffusive flux, in CEC this flow would greatly enhance the mass transfer. 

Coats, K. H., and Smith, B. D. (1964). Dead-end pore volume and dispersion in porous media. 

Blind pore (Dead-end pore) Pore with a single connection to the surface... 

Table 1.3. In addition to closed pores and open pores, we may distinguish between blind pores (or dead-end pores) and interconnected pores. Pores which are open at both sides of a membrane or porous plug are termed through pores.

The available transport models are not reliable enough for porous material with a complex pore structure and broad pore size distribution. As a result the values of the model par ameters may depend on the operating conditions. Many authors believe that the value of the effective diffusivity D, as determined in a Wicke-Kallenbach steady-state experiment, need not be equal to the value which characterizes the diffusive flux under reaction conditions. It is generally assumed that transient experiments provide more relevant data. One of the arguments is that dead-end pores, which do not influence steady state transport but which contribute under reaction conditions, are accounted for in dynamic experiments. Experimental data confirming or rejecting this opinion are scarce and contradictory [2]. Nevertheless, transient experiments provide important supplementary information and they are definitely required for bidisperse porous material where diffusion in micro- and macropores is described separately with different effective diffusivities. 

Adsorption Dipsersion by tidsoiplioii is another unsteady-stale plicnomcnon. As with dead-end pores, a coiicciilralion front deposits or... 

Now consider the total material flux in a porous solid. We postulate a thoroughly cross-linked main pore network with singly attached dead-end pore branches. 

In chromatographic separations using flat sheet membranes, compact porous disks, fibers, tubes, or rods, the interaction between the ligate molecule and the immobilized ligand takes place in the through-pores of the matrix and not in the dead-end pores of the conventional packed-bed particles. This method resembles affinity membrane separation with a very short affinity chromatography column [2]. 

FIGURE 4.16 Schematic illustration of pore types in porous solid with open pores (c,d), locked-in (a) and dead-end pores (b,e,t). (From Rouquerol J., Avnir D., Fairbridge C.W., Everett D.H., Haynes J.H., Pemicone N., Ramsey J.D.F., Sing K.S.W., Unger K.K., Pure Appl. Chem., 66, 1739, 1994. With permission.)... 

One of the most important factors influenced by the physical adsorbent parameters is the available surface area. Within an ideal adsorbent the surface area is high so as to offer a multitude of adsorption sites. All adsorption sites should be equal and accessible within short distances, thus keeping diffusion pathways short. This prerequisite leads to the consequence that all pores should be of equal size, that no deep dead-end pores are present and that the accessibility of the pores from the area of convective flow within a packed bed should be equal for all pores. 

Fig. 2.3. Schematic picture of pore types in a porous membrane, a Isolated pore b,f dead end pore c,d tortuous and/or rough pores (d) with constrictions (c) e conical pore.

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