Channels diameter

Stmcture Cation Typical formula of unit cell or pseudoceU Window Effective channel diameter, nm Apphcations... 

Selenourea [630-10-4] ]5k.e urea and thiomea can form channel inclusion compounds (87) with a variety of hydrocarbons. Though the difference in channel diameter between thiourea and selenourea is small, selenourea seems to be much more selective for the inclusion of certain guest molecules (eg, cis/trans isomers). 

However, for flow in micro-channels, the wall thickness can be of the same order of channel diameter and will affect the heat transfer significantly. For example, Choi et al. (1991) reported that the average Nusselt numbers in micro-channels were much lower than for standard channels and increased with the Reynolds number. 

Bubbly/slug flow. Bubbles both longer and shorter than the channel diameter (Fig. 2.30b). The bubble frequencies increase rapidly with the heat flux in the evaporator, reached a peak 900 Hz and then decreased due to coalescence. 

Slug flow. Vapor bubbles longer than the channel diameter, which is slightly smaller than that of the tube. The bubbles were separated from the inner channel... 

Chung PM-Y, Kawaji M (2004) The effect of channel diameter on adiabatic two-phase flow characteristics in micro-channels. Int J Multiphase Flow 30 735-761 Colgan E (2005) A practical implementation of silicon microchannel coolers for high power chips. 

The frictional pressure drop for liquid flows through micro-channels with diameter ranging from 15 to 150 pm was explored by Judy et al. (2002). Micro-channels fabricated from fused silica and stainless steel were used in these experiments. The measurements were performed with a wide variety of micro-channel diameters, lengths, and types of working fluid (distilled water, methanol, isopropanol), and showed that there were no deviations between the predictions of conventional theory and the experiment. Sharp and Adrian (2004) studied the fluid flow through micro-channels with the diameter ranging from 50 to 247 pm and Reynolds number from 20 to 2,300. Their measurements agree fairly well with theoretical data. 

The ratio of t/t, which is characteristic of the possibility of vortices, does not depend on the micro-channel diameter and is fully determined by the Reynolds number and L/d. The lower value of Re at which f/fh > 1 can be treated as a threshold. As was shown by Darbyshire and Mullin (1995), under conditions of an artificial disturbance of pipe flow, a transition from laminar to turbulent flow is not possible for Re < 1,700, even with a very large amplitude of disturbances. 

Adams et al. (1998) investigated turbulent, single-phase forced convection of water in circular micro-channels with diameters of 0.76 and 1.09 mm. The Nusselt numbers determined experimentally were higher than those predicted by traditional Nusselt number correlations such as the Gnielinski correlation (1976). The data suggest that the extent of enhancement (deviation) increases as the channel diameter decreases. Owhaib and Palm (2004) investigated the heat transfer characteristics... 

The flow regimes in the test sections were identified visually with the aid of a strobe and a digital camera. The camera was always targeted at the test section center. No systematic attempt was made to assess and eliminate the test section entrance effects on the flow regimes. However, the distance between the point pictured by the camera and the test section inlet was well over 100 channel diameters everywhere. Thus, although the possibility exists that the reported flow regimes are influenced by the test section entrance conditions, this influence may not be significant. 

For all flow conditions tested in that study, a bubbly flow pattern with bubbles much smaller than the channel diameter (100 pm) was never observed. While liquid-only flows (or liquid slugs) containing small spherical bubbles were not observed, small droplets were observed inside gas core flows. Furthermore, no stratified flow occurred in the micro-channel as reported in previous studies of two-phase flow patterns in channels with a diameter close to 1 mm (Damianides and Westwater 1988 Fukano and Kariyasaki 1993 Triplett et al. 1999a Zhao and Bi 2001a). 

The existence of two stable states (at given values of the operating parameters) is due to the dominant role of the gravity or friction forces at the various meniscus positions. A decrease in the gravity leads to the displacement of the meniscus toward the outlet and to a decrease in the heat losses and an increase in the liquid and vapor velocities. A decrease in the micro-channel diameter leads to a monotonic increase in the liquid and vapor velocities, whereas the dependence of the meniscus position versus d has an extremum. 

At given values of the parameters, there are optimal values of the micro-channel diameter and length, which correspond to a maximum efficiency coefficient. 

The last category is the pressure-driven gas flows, which are typical in micro gas fluidic and micro heat transfer systems. Because the channel diameter or width in micro gas fluidic systems is in the scale of sub-micrometer or less, ultra-thin gas lubrication theory plays an important role in... 

The main design criteria of most TPE dies are to ensure that changes in flow channel diameter from the extruder barrel bore to the die exit are equal. Most of the viscoelastic materials exhibit a die swell on exit from a die. TPEs tend to show die swell significantly lower than that of typical thermoplastics. This swell must be taken into consideration in designing dies and adjusting extrusion condition to achieve a perfect profile. The die swell normally increases with increasing hardness and shear rate and decreasing temperature. 

Common name 3-letter code Channels Window or channel diameter (nm) Pore volume (mLg- ) Si/AI... 

Conclusive evidence has been presented that surface-catalyzed coupling of alcohols to ethers proceeds predominantly the S 2 pathway, in which product composition, oxygen retention, and chiral inversion is controlled 1 "competitive double parkir of reactant alcohols or by transition state shape selectivity. These two features afforded by the use of solid add catalysts result in selectivities that are superior to solution reactions. High resolution XPS data demonstrate that Brpnsted add centers activate the alcohols for ether synthesis over sulfonic add resins, and the reaction conditions in zeolites indicate that Brpnsted adds are active centers therein, too. Two different shape-selectivity effects on the alcohol coupling pathway were observed herein transition-state constraint in HZSM-5 and reactant approach constraint in H-mordenite. None of these effects is a molecular sieving of the reactant molecules in the main zeolite channels, as both methanol and isobutanol have dimensions smaller than the main channel diameters in ZSM-S and mordenite. 

In the following, the impact of the micro-channel diameter on the temperature rise due an exothermic gas-phase reaction is investigated. For simplicity, a homogeneous reaction A —> B of order n with kinetic constant k is considered. Inside the micro channel, the time evolution of the radially averaged species concentration c and temperature T is governed by the equations... 

In Table 1.4, the characteristic time-scales for selected operations are listed. The rate constants for surface and volume reactions are denoted by and respectively. Furthermore, the Sherwood number Sh, a dimensionless mass-transfer coefficient and the analogue of the Nusselt number, appears in one of the expressions for the reaction time-scale. The last column highlights the dependence of z p on the channel diameter d. Apparently, the scale dependence of different operations varies from dy f to (d ). Owing to these different dependences, some op-... 

In cases where the operation time-scale is independent of the channel diameter, as for a homogeneous reaction, it is necessary to keep the residence time fixed when downscaling a reactor in order keep the efficiency constant. When the flow-rate Qtot of the process gas is given, this means that a reduction in the channel diameter has to be accompanied by an increase in the channel length L or the number of channels N, according to... 

More favorable for miniaturization are processes with an operation time-scale proportional to or (d f. For a linear dependence on the channel diameter, the product N L df is conserved under the conditions described above. This means that with shrinking df and for fixed efficiency, the reactor volume decreases proportionally with the channel diameter. For a quadratic dependence of the operation time-scale with channel diameter, the product N L is conserved and the reactor volume decreases as the channel diameter squared. 

In some cases, it may not be desirable to reduce the volume of a reactor, and rather a decrease of pressure drop or channel length may be the goal. In Table 1.5, the dependence of several characteristic quantities on channel diameter is given, where the efficiency and at least one specific quantity is kept fixed in each line. 

The comparison given above shows that a reduction in channel dimensions offers some substantial benefits in cases where surface reactions are involved or efficient heat and mass transfer are needed. One important conclusion to be drawn is that a decrease in the channel diameter at fixed efficiency does not necessarily mean an increase in pressure drop. Rather, the pressrue drop can be kept constant... 

Table 1.5 Dependence of the number of micro channels N, their length L, the cross-sectional area of the reactor S and the pressure drop AP on the micro-channel diameter, when the efficiency (i.e. a fixed number of transfer units) and at least one specific characteristic quantity are kept fixed in each line. Three cases with operation time-scales varying as (c/m)°. are considered [114],...

In practice, the process regime will often be less transparent than suggested by Table 1.4. As an example, a process may neither be diffusion nor reaction-rate limited, rather some intermediate regime may prevail. In addition, solid heat transfer, entrance flow or axial dispersion effects, which were neglected in the present study, may be superposed. In the analysis presented here only the leading-order effects were taken into account. As a result, the dependence of the characteristic quantities listed in Table 1.5 on the channel diameter will be more complex. For a detailed study of such more complex scenarios, computational fluid dynamics, to be discussed in Section 2.3, offers powerful tools and methods. However, the present analysis serves the purpose to differentiate the potential inherent in decreasing the characteristic dimensions of process equipment and to identify some cornerstones to be considered when attempting process intensification via size reduction. 

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