Bundle of parallel tubes

Figure 1. The BPT (bundle of parallel tubes) model. The flow-rate in a tube with residence time between t and t +dt is dQ = E(t )dt. The fluid flows in the tubes at constant velocity. All particles on a vertical have the same age. The height of the pile is Q. The locus of tube extremities is a picture of F-curve...

To demonstrate the viability of these multi-scale solutions, the multi-scale reactor is first considered as a bundle of parallel tubes or channels, corresponding to the subflows, with a channel diameter D, a length L and a total number of channels N. The heat-transfer characteristic time, the reactor volume and the specific mechanical energy can be expressed as a function of these independent geometric parameters. Moreover, the ratio of the specific energy of a reactor after intensification (subscript 2) and before intensification (subscript 1) can be related to the features of interest as follows ... 

In this work, the dependency of the resistance coefficient on the Reynolds number Rev of the gas phase, which characterises the flow, is presented on the basis of the channel model, which describes the packing as a bundle of parallel tubes with equal diameters, see Fig. 3-1 and [1-12, 19-29]. 

Diffraction patterns of well isolated SWCNT are difficult to obtain due to the small quantity of diffracting material present, and also due to the fact that such tubes almost exclusively occur as bundles (or ropes) of parallel tubes, kept together by van der Waals forces. 

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. 

SWNTs (1.4 nm diameter) have been purified similarly, however, since these tubes are very long and occur in ropes (i.e. thick bundles of parallel SWNTs) they are first chemically cut into smaller pieces (100-300 nm). The final stable suspensions then permit manipulations such as sorting by length [121]. 

These simulation results were obtained using a simpHfication of the geometry the surface was assumed to be an infinite, periodic array of parallel tubes lying on a flat surfrce. If a more realistic description of a nanotube bundle were used, the abrupt transitions appearing above would all become rounded. This can be seen in Fig. 9.18 for the case of CH4. 

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... 

NAFION systems have also been used to construct devices for 1) separating monofunctlonal carboxylic acids like propionic, butyric or valeric acid from other acids (75), 2) nitrating and sulfonatlng aromatics In an annular tubular flow reactor where the Inner tube Is NAFION and the outer tube Is TEFLON fluorocarbon resin (76), 3) sulfonatlng aromatics In a two-compartment cell separated by a membrane sheet (77), and 4) alkylating aromatics with a tightly-packed bundle of parallel tubular NAFION In a stainless steel tube (78). 

Assume that the porous medium is composed of a series of parallel tubes (bundle of tubes model) each of diameter 2a (Fig. 2c). The unit cell is now formed by the region 0 < r < a, 0 < r < L, where L is an arbitrary length. The external field E and the pressure gradient VP are applied parallel to the tube axis. The capillary axis is z, and the distance to this axis is r. 

Streaming potential When liquid flows along a narrow tube or capillary, or through a porous plug (a bundle of narrow tubes in parallel or channels in BLMs and... 

Considering the flow of clean liquid through a packed bed, Kozeny assumed that the pore space of a packed bed of powder could be regarded as equivalent to a bundle of parallel capillaries with a common equivalent radius, and with a cross-sectional shape representative of the average shape of the pore cross-section. Using Poiseuille s law for the flow of fluids through capillary tubes, Kozeny and later Carman were able to relate the permeability to the porosity, the specific surface and the density of the powder in the bed. 

Geankoplis [54] fabricated a porous medium for which the values of K, and are known a priori. This was accomplished by sealing a bundle of identical parallel cylindrical capillary tubes between the two chambers of a Wlcke-Kallenbach apparatus. Then the relevant flux relations are those which apply to a single cylindrical capillary, rather than a porous medium, and these are obtained by setting... 

Fig. 4. Schematic of a hemodialyzer. The design of a dialyzer is close to that of a sheU and tube heat exchanger. Blood enters through an inlet manifold, is distributed to a parallel bundle of fibers, and exits into a coUection manifold. Dialysate flows countercurrent in an external chamber the blood and dialysate are separated from the fibers by a polyurethane potting material. Housings are typically prepared from acrylate or polycarbonate. Production volume is...

Hollow fiber modules, or permeators, are precisely machined units containing bundles of fine hollow fibers, positioned parallel to and around a perforated center FW tube, with only one or two bundles per pressure vessel. They are widely used for brackish and seawater supply applications. Hollow fiber modules exhibit a low flux rate (permeate flow per unit membrane per unit time) and foul easily, but... 

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