Dead-end

There are two approaches to explain physical mechanism of the phenomenon. The first model is based on the existence of the difference between the saturated vapor pressures above two menisci in dead-end capillary. It results in the evaporation of a liquid from the meniscus of smaller curvature ( classical capillary imbibition) and the condensation of its vapor upon the meniscus of larger curvature originally existed due to capillary condensation. 

At first we tried to explain the phenomenon on the base of the existence of the difference between the saturated vapor pressures above two menisci in dead-end capillary [12]. It results in the evaporation of a liquid from the meniscus of smaller curvature ( classical capillary imbibition) and the condensation of its vapor upon the meniscus of larger curvature originally existed due to capillary condensation. We worked out the mathematical description of both gas-vapor diffusion and evaporation-condensation processes in cone s channel. Solving the system of differential equations for evaporation-condensation processes, we ve derived the formula for the dependence of top s (or inner) liquid column growth on time. But the calculated curves for the kinetics of inner column s length are 1-2 orders of magnitude smaller than the experimental ones [12]. 

Thus it is necessary to find alternative approach to describe the physical mechanism of two-side filling of conical capillaries with hquids. Theoretical model of film flow in conical dead-end capillary is based on the concept of disjoining pressure II in thin liquid film [13]... 

Fig. 4 illustrates the time-dependence of the length of top s water column in conical capillary of the dimensions R = 15 pm and lo =310 pm at temperature T = 22°C. Experimental data for the top s column are approximated by the formula (11). The value of A is selected under the requirement to ensure optimum correlation between experimental and theoretical data. It gives Ae =3,810 J. One can see that there is satisfactory correlation between experimental and theoretical dependencies. Moreover, the value Ae has the same order of magnitude as Hamaker constant Ah. But just Ah describes one of the main components of disjoining pressure IT [13]. It confirms the rightness of our physical arguments, described above, to explain the mechanism of two-side liquid penetration into dead-end capillaries. 

To clear up a role of two-side filling with liquids of dead-end capillaries in the practice of PT, we ve carried out some special experiments. It was established some years ago that it s almost impossible to reveal small defects applying dry powder developer in the case when defect s hollows are completely filled with a penetrant. But just such a situation one... 

Physical mechanism of two-side filling of dead-end capillaries with liquids, based on liquid film flow along the wall, is proposed for the first time. Theoretical model correlates with experimental data. 

A well-understood catalytic cycle is tliat of the Wilkinson alkene hydrogenation (figure C2.7.2) [2]. Like most catalytic cycles, tliat shown in figure C2.7.2 is complex, involving intennediate species in tire cycle (inside tire dashed line) and otlier species outside tire cycle and in dead-end patlis. Knowledge of all but a small number of catalytic cycles is only fragmentary because of tire complexity and because, if tire catalyst is active, tire cycle turns over rapidly and tire concentrations of tire intennediates are minute thus, tliese intennediates are often not even... 

A drawback of this approach is that it typically generates enormous and imwieldy synthesis trees which contain a large number of dead-end branches which are not worth further consideration. Furthermore, the chemist is forced to follow a rigid scheme during the planning process, alternating between the application of transforms, the derivation of new precursors, and again the application of further transforms to these precursors. 

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. 

Dead-end micropores are excluded here, of course, since they carry no concentration gradients in steady non-reactive conditions. 

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. 

Here L is the thickness of the porous septum and jS the length of each dead-end micropore, the effective binary bulk diffusion coefficient... 

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. 

Depth filters are usually preferred for the most common type of microfiltration system, illustrated schematically in Figure 28. In this process design, called "dead-end" or "in-line" filtration, the entire fluid flow is forced through the membrane under pressure. As particulates accumulate on the membrane surface or in its interior, the pressure required to maintain the required flow increases until, at some point, the membrane must be replaced. The useful life of the membrane is proportional to the particulate loading of the feed solution. In-line microfiltration of solutions as a final polishing step prior to use is a typical apphcation (66,67). 

Fig. 28. Schematic representation of dead-end and cross-flow filtration with microfiltration membranes. The equipment used in dead-end filtration is simple, but retained particles plug the membranes rapidly. The equipment required for cross-flow filtration is more complex, but the membrane lifetime is...

Fig. 11. Types of piperack configurations (a) dead-end yard lines enter and leave one end of yard (b) straight-through yard lines can enter and leave both ends of the yard (c) L-shaped yard lines can enter and leave north and east of the plot (d) T-shaped yard lines can enter and leave on three sides of the plot (e) U-shaped yard lines can enter and leave all four sides of the plot (f) combination of I- and T-shaped yard and (g) complex yard piping...

Cross Flow Most membrane processes are operated in cross flow, and only a few have the option to operate in the more conventional dead-end flow. In cross flow, the retentate passes parallel to the separating membrane, often at a velocity an order of magnitude higher than the velocity of the stream passing through the membrane. Microfiltration is the major membrane process in which a significant number if apphcations may be run with dead-end flow. 

Because this mass-transfer step is so vital, conventional dead-end operation of ultrafilters is veiy rare. There are many ways to depolarize a membrane. Cross-flow is by far the most common. Turbulent flow is more common than laminar flow. 

Process Description Microfiltration (MF) separates particles from true solutions, be they liquid or gas phase. Alone among the membrane processes, microfiltration may be accomplished without the use of a membrane. The usual materi s retained by a microfiltra-tion membrane range in size from several [Lm down to 0.2 [Lm. At the low end of this spectrum, very large soluble macromolecules are retained by a microfilter. Bacteria and other microorganisms are a particularly important class of particles retained by MF membranes. Among membrane processes, dead-end filtration is uniquely common to MF, but cross-flow configurations are often used. 

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