Interstitial flow

Computational fluid dynamics (CFD) is rapidly becoming a standard tool for the analysis of chemically reacting flows. For single-phase reactors, such as stirred tanks and empty tubes, it is already well-established. For multiphase reactors such as fixed beds, bubble columns, trickle beds and fluidized beds, its use is relatively new, and methods are still under development. The aim of this chapter is to present the application of CFD to the simulation of three-dimensional interstitial flow in packed tubes, with and without catalytic reaction. Although the use of... 

An alternative and complementary use of CFD in fixed bed simulation has been to solve the actual flow field between the particles (Fig. lb). This approach does not simplify the geometrical complexities of the packing, or replace them by the pseudo-continuum that is used in the first approach. The governing equations for the interstitial fluid flow itself are solved directly. The contrast is thus between the interstitial flow field type of simulation and the superficial flow... 

The focus of the remainder of this chapter is on interstitial flow simulation by finite volume or finite element methods. These allow simulations at higher flow rates through turbulence models, and the inclusion of chemical reactions and heat transfer. In particular, the conjugate heat transfer problem of conduction inside the catalyst particles can be addressed with this method. 

This article has attempted to review the issues in applying CFD to simulate interstitial flow in packed tubes, with an emphasis on low-A tubes. The rapid changes in computational capability of today s computers mean that the problems and limitations discussed here will also change rapidly. All we can do is to try to extrapolate where the needs and areas of interest are likely to be in the near future. 

Na, which refers to unit superficial area, may be expressed in terms of an interstitial flow... 

Levick, J.R. (1994) An analysis of the interaction between interstitial plasma protein, interstitial flow, and fenestral filtration and its apphcation to synovium. Microvasc. Res., 47, 90-125. 

An important issue, particularly in light of the symposium goals, is that of interstitial flow. The RMFE framework should be compatible with a biphasic... 

Bubbling leads immediately to the concept of two phases with part of the gas flowing interstitially amongst closely spaced particles and the rest flowing in the form of bubbles. The interstitial flow remains constant at the minimum fluidisation value although fine powders may expand a little and permit a rather larger flow. The bubble flow is therefore easily evaluated from... 

Chemical reactor models invariably start from the two-phase theory (12). The interstitial flow is assumed to be in good and continuous contact with solids whilst some by-passing occurs in the bubble phase. There is, however, very little axial or radial mixing of the gas. There may be some exchange between the two phases and Figure 4 depicts this kind of model. 

Fig. 2a, b Development of a concentration boundary layer along the NAPL-water interface in uniform interstitial flow for a zero bulk aqueous phase (background) concentration b constant nonzero background concentration (adopted from Chrysikopoulos and Lee [30])... 

In electrochromatography with porous particles, a (3 factor for the pore volume (Pta) as well as for the interstitial volume (Poul) can be defined. (Note For monolithic or continuous columns, only a single EOF screening factor can be defined for the pore volume.) An important parameter in the discussion of the effects of pore flow on the separation efficiency is the pore-to-interstitial flow ratio (0, which is defined as [18]... 

In a more detailed study, the influence of the pore size and the ionic strength on the pore-to-interstitial flow ratio was investigated with this SEEC method. Measurements were performed with ionic strengths in the range from 10 pM to 100 rriM and with particles with pore sizes ranging from 5 to 100 nm... 

This expression is more satisfying than Eq. (9) in that it predicts more or less expected behavior at all possible pore-to-interstitial flow ratios. Therefore, at the moment Eq. (10) appears to be the most appropriate solution for the Cs term for capillary electrochromatography in the presence of pore flow obtained so far. 

Figure 8 Illustration of the interstitial flow profiles in (A) pressure-driven chromatography (B) electrochromatography with nonporous particles and (C) electrochromatography at fully perfusive conditions. The length of the arrow represents the local velocity.

The effects of pore flow in size-exclusion electrochromatography (SEEC) are even more apparent than in reversed-phase CEC. The solutes typically separated in SEEC are slowly diffusing macromolecules such as synthetic polymers. For these solutes the enhanced diffusion effect becomes relevant even at low pore flow velocities and at low pore-to-interstitial flow ratios. 

For slowly diffusing solutes, a significant improvement in the separation efficiency can be expected when a high intraparticle EOF is created. At low pore-to-interstitial flow ratio this may be accomplished by, e.g., the application of a high electrical field strength. 

When the pore size, ionic strength, and electrical field strength are optimized for a high pore flow velocity and a high pore-to-interstitial flow ratio, reduced plate heights well below unity can be achieved in CEC of low-molecular-mass compounds. When such conditions can be created in combination with the use of small particles (dp < 1 pm), plate heights below 1.0 pm will be possible. 

The filtered conditionally averaged measurements picks up the flow between the bubbles. Far from the test bubble, the filtered conditionally averaged velocity tends to a constant value which corresponds closely to the interstitial flow concept introduced in 7.3.3, i.e. 

The factors that affect phase separation discussed in this section include anion effect, divalent effect, alkaline effect, mixing effect of interstitial flow, and the synergy of mixed surfactants. 

The compatibility of ASP fluids is not consistent with ultralow IFT. Generally, if the surfactant is more soluble in water, and the ASP fluids are more compatible, having ultralow IFT would be more difficult. If the surfactant is more hydrophobic, and the ASP fluids are less compatible, it would be easier for the IFT to reach ultralow levels. If ASP fluids are less compatible, causing phase separation would be easier. Then phase separation would cause IFT to be increased. Fortunately, Yang et al. (2002b) observed that interstitial flow has a mixing effect so that phase separation can be reduced when ASP fluids flow in the core. 

---