Parallel capillaries

In the bed of spheres, the film thicknesses should be appreciably greater than in the parallel capillary model, perhaps by a factor of 2 or so. 

A number of publications (6-10) have demonstrated that the size separation mechanism In HDC can be described by the parallel capillary model for the bed Interstices. The relevant expression for the separation factor, Rj., (ratio of eluant tracer to particle mean residence times) Is given by. 

Separation factors predicted by the partition model are compared with the experimental data from reference (13) in Figure 7. The partition model predicts the magnitude of the separation factor better than the parallel capillary model (see Figure 1), however the parallel capillary model predicts the shape of the curves better. This suggests that neither model alone is sufficient to account for the separation. 

If many parallel capillaries of equal length and diameters are used to carry the fluid, the ratio of Fto /I remains constant and equation (7.16) becomes... 

Capillary rise is the elevation of liquid in a capillary tube above the general level. Capillary separation is the separation of gases by flow through a porous medium, in a theory of this process based on the concept of momentum transfer, the actual porous medium is treated as equivalent to a bundle of parallel capillary lubes. 

The simplest capillaric model is the one representing a porous medium by a bundle of straight parallel capillaries of average diameter <5, as shown in Fig. 5.14. The equivalent voidage a can be related to the averaged diameter by... 

Figure 4.4. Capillaric model of a packed column. The flow space is assumed to consist of a bundle of parallel capillaries.

A liquid chromatographic column packed with 5.00 fim diameter solid support particles and having a porosity e = 0.400 is found to have a flow resistance parameter 750. Calculate the specific permeability K0. Assume that the flowrate/pressure drop relationship is identical to that of a bundle of identical parallel capillaries whose axes are spaced (in a square cross-sectional array) a distance of 5.00 /im from one another. What is the single capillary diameter of the hypothetical bundle ... 

The as-synthesized amine intercalated VO, nanolubes could be aligned on glass substrates by using micromolding in capillaries (MIMIC).86 An elastomeric polydimethylsiloxane (PDMS) stamp where parallel capillaries of 5 pm were patterned was used as the mould.86 The capillaries were filled with a VO, nanotube suspension in octanol. After evaporation of the solvent and removal of the mould, long lines of assemblies of well aligned nanotubes were obtained. 

There is now one commercial system available (MCE2000, Combisep) which uses parallel capillary synthesis. It is reported (Strasburg) that up... 

The analysis of the flow of fluids through a permeable bed of solids is widely applied in filtration, leaching, and several other processes. A first approach may be made by assuming that the interstices of the bed correspond to a large number of discrete, parallel capillaries. If the flow is streamline, the volumetric flow rate Q is given for a single capillary by Eq. (14) ... 

Figure 10-5 Design of a complex microfluidic device for parallel capillary electrophoresis. Figure shows the mask pattern for a 96-channel radial capillary electrophoresis micropiate in glass.The separation channels with 200pm twin-T injectors were masked to 10pm width and then etched to form 110pm wide by approximately 50 pm deep channels.The diameter of the reservoir holes is 1.2 mm.The distance from the injector to the detection point is 33 mm.The glass substrate is 10 cm in diameter. (From Shi Y, Simpson PC, Scherer JR, et al. Radial capillary array electrophoresis microplate and scanner for high-performance nucleic add analysis. Anal Chem 1999 71 5354-61.)...

Plastic microcapillary flow disk (MFD) reactors have been constructed from a flexible, plastic microcapillary film (MCF), comprising parallel capillary channels with diameters in the range of 80-250 jxm. MCFs are wound into spirals and heat treated to form solid disks. These reactors are capable of carrying out continuous flow reactions at elevated temperatures and pressures with a controlled residence time. ... 

There are many other approaches to industrial applications of flash chemistry, although available information is limited. Let us briefly touch on some examples. The Kolbe-Schmitt synthesis serves as a useful standard method to introduce a carboxyl group into phenols (Scheme 10.6). The Kolbe-Schmitt synthesis has been widely used in industry, and there are many variants of this transformation. Microflow systems can be used for conducting the Kolbe-Schmitt synthesis under aqueous high-pressure conditions.A decrease in reaction times by an order of magnitude (a few tens of seconds instead of minutes) and increase in space-time yields by orders of magnitude can be attained using a microflow system. For example, a microflow system composed of five parallel capillaries (inner volume 9 ml) has a productivity of 555 g/h, whereas the productivity of a macrobatch reactor (IL flask) is 28 g/h. 

Description of Model. Our model describes the diffusion of oxygen across a section of uniform tissue separating two parallel capillaries. The... 

One-Dimensional Pore Structure Models and Pore Size. Experimental data invariably have been characterized in terms of an arbitrary model of pore structure. The most common method consists of a bundle of parallel capillary tubes of equal length and a distributed size. The pore size would be unique only if the pores were tubes of uniform size and cross-section or spherical bodies. As neither is the... 

The apparent mass factor m = a -pflcj) (a > 1) in Equation 2.16b considers that not all of the pore fluid moves along the maximum pressure gradient in case of tortuous, curvilinear capillaries. As a result the pore fluid seems to be more dense, with higher inertia, (a ) is called structure factor and is equal to 1 in case of uniform parallel capillaries. 

The apparent permeability, a function of the proportion of pores penetrated by the mud filtrate, can be determined from the pore size distribution curve, absolute permeability and porosity of the rock material (Tan et al., 1996a). The methodology is based on a simple capillaric model which represents a porous medium by a bundle of parallel capillaries (Scheideggar, 1974). From the law of Hagen-Poiseuille, the absolute permeability of such a model is given by ... 

As CE continues to evolve, it is not surprising to see a concomitant development of optical detection methods. Detector innovations have been required to keep up with smaller diameter capillaries, faster separations, parallel capillary systems, and microfluidic-based electrophoretic formats. In parallel to these changes, more flexible and higher performance imaging detectors, UV light sources, and clever applications of these advances continue to push the envelope in terms of light-based detection forCE. 

Problems with resolution in hydrodynamic chromatography have been shown to result from radial dispersion. In ordCT to minimize this, Dos Ramos [40] has developed a column based on parallel capillaries. The technique, called capillary hydrodynamic fractionation eliminates the possibility of radial dispersion, and produces chromatograms of much higher resolution. An instrument based on this technology is being marketed by Matec Applied Sciences of Hopkinton, Massachusetts. An on-line version is currently under development at Lehigh UnivCTsity. 

Array of 96 sealed glass tubes 120 pi, 110°G Parallel capillary electrophoresis Several catalyst systems identified 2000 70... 

The wetting process of a porous material (for instance, a powder bed) can be described by the Washburn equation (23). This equation relates the capillary force and the flow resistance, approximating the powder as parallel capillaries with a certain radius r, as follows ... 

Coupling Other Modes of CE with MS Because of practical difficulties, the coupling of other modes of CE with MS is not very common. However, some attempts have been made to couple CIEE with ESI-MS [80,91], CEC-MS [92], CGE-MS [93], and MEKC-MS [83,94,95]. A simple MEKC-MS interface is described (Figure 5.15). This interface comprises two parallel capillaries, one for separation and the other for makeup liquid. Both have the dimensions 50 p,m i.d. X 155 p,m o.d. and have tapered ends. The capillaries are housed in a larger capillary (530 p,m i.d. x 690 tim o.d.) with a beveled edge. The larger capillary serves as a nano-ESI sprayer. A makeup liquid allows control of the composition of the spray solution. 

The tortuosity factor q is the square of the tortuosity. Thus the Knudsen flux equation for a porous medium obtained from the parallel capillaries model is given by ... 

The last model assumes that porous media can be idealised as parallel capillaries along the direction of flow. Porous media such as adsorbents and catalysts are usually formed by compressing small grains into pellet, and for such particles the model for unconsolidated media will be particularly useful. There are a number of equations available in the literature to describe the Knudsen flow through a unconsolidated medium. They are identical in form and differ only in the numerical proportionality coefficient. 

We have obtained equations for the viscous flow in a capillary. For a porous medium, the viscous flow parameter Bq can be treated as a fitting structural parameter or it can be calculated from the assumption of a model for the solid structure as it is a function of only solid properties. Like before, if we assume that the solid can be idealised as a bundle of parallel capillaries of equal diameter and length Lc running through the medium in the direction of flow, the average velocity in the capillary is (from eq. 7.5-2) ... 

For particles having shape different from sphere, dp is the equivalent diameter of sphere having the same specific area as the particle. Empirically, the constant k was found to be about 5 to 5.6 (Carman, 1956 Dullien, 1979). Comparing the flux equation for unconsolidated media (eq. 7.5-28a) and that for the bundle of parallel capillaries model (eq. 7.5-20), we get the following relationship between the equivalent capillary diameter d and the primary particle diameter... 

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