Curved channels

Knapp, R. T., Design of Channel Curves for Supercritical Flow, cited in R. L. Daugherty and A. C. Ingersoll, Fluid Mechanics, McGraw-Hill, New York, 1954. 

Fig. 6 Axial temperature and methane conversion distributions in a catalytic combustor with alternate channels coated. One-half of the total gas flow passes through catalytic channels. Curves are calculated solving Eqs. (1), (2), and (5) for the conditions presented in Table 1, after substituting Eq. (7) in the heat balance Eq. (5). Temperatures are much lower than in the fully coated monolith of Eig. (4). (View this art in color at www.dekker.com.)...

FIGURE 5. Chemi-ionization excitation functions for endoergic channels, curves represent data fits by phase space theory [14]. 

Fig. 22. Calculations of the double photoionization cross section a for helium by Carter and Kelly, ref. 107. Curves labelled LOL(LOV) are lowest order length (velocity) results for the kskp channel. Curves labelled L(V) are length (velocity) results containing higher-order corrections for both kskp and kpkd channels. Curve labelled BJ is dipole-velocity result from Byron and Joachain, ref. 106.

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]. 

The flow distribution in a manifold is highly dependent on the Reynolds number. Figure 14b shows the flow distribution curves for different Reynolds number cases in a manifold. When the Reynolds number is increased, the flow rates in the channels near the entrance, ie, channel no. 1—4, decrease. Those near the end of the dividing header, ie, channel no. 6—8, increase. This is because high inlet velocity tends to drive fluid toward the end of the dividing header, ie, inertia effect. 

Separate sample blanking requires an additional analytical channel, and is therefore wasteflil of both reagents and hardware. An alternative approach that is used on several automated systems, eg, Du Pont ACA, BM-Hitachi 704, Technicon RA-1000, is that of bichromatic analysis (5) where absorbance measurements are taken at two, rather than one, wavelength. When the spectral curves for the interference material and the chromogen of the species measured differ sufficiently, this can be an effective technique for reducing blank contributions to assay error. Bichromatic analysis is effective for blanks of both the first and second type. 

For friction loss in laminar flow through semicircular ducts, see Masliyah and Nandakumar AlChE J., 25, 478-487 [1979]) for curved channels of square cross section, see Cheng, Lin, and On ]. Fluids Eng., 98, 41-48 [1976]). 

As a result of the electric field around the conductors the frequency of the system has a very significant bearing on the skin effect. The various curves as established through experiments and, as reproduced in Figures 28.13 (a), (b) and (c) respectively for rectangular, tubular and channel conductors, are thus drawn on the basis. 

A continuous lipidic cubic phase is obtained by mixing a long-chain lipid such as monoolein with a small amount of water. The result is a highly viscous state where the lipids are packed in curved continuous bilayers extending in three dimensions and which are interpenetrated by communicating aqueous channels. Crystallization of incorporated proteins starts inside the lipid phase and growth is achieved by lateral diffusion of the protein molecules to the nucleation sites. This system has recently been used to obtain three-dimensional crystals 20 x 20 x 8 pm in size of the membrane protein bacteriorhodopsin, which diffracted to 2 A resolution using a microfocus beam at the European Synchrotron Radiation Facility. 

The exit region of a die used to extrude a plastic section is 10 mm long and has the cross-sectional dimensions shown below. If the channel is being extruded at the rate of 3 m/min calculate the power absorbed in the die exit and the melt temperature rise in the die. Flow curves for the polymer melt are given in Fig. 5.3. The product pCp for the melt is 3.3 x 10. ... 

A polyethylene moulding material at I70°C passes along the channel shown at a rate of 4 X 10 m /s. Using the flow curves given and assuming n = 0.33 calculate the pressure drop along the chatmel. 

Simulations of water in synthetic and biological membranes are often performed by modeling the pore as an approximately cylindrical tube of infinite length (thus employing periodic boundary conditions in one direction only). Such a system contains one (curved) interface between the aqueous phase and the pore surface. If the entrance region of the channel is important, or if the pore is to be simulated in equilibrium with a bulk-like phase, a scheme like the one in Fig. 2 can be used. In such a system there are two planar interfaces (with a hole representing the channel entrance) in addition to the curved interface of interest. Periodic boundary conditions can be applied again in all three directions of space. 

The exponent Up in Eq. (9.2) was found to be 0.65 for our samples [31 ]. With this value we attempted to model the experimental curve in Figure 9-17 by Eq. (9.8). We obtained 0.12 and 0.37 eV for the energies W, and W2, respectively. These numbers mean that the 0.12 eV process reaches the magnitude of the temperature-independent decay rale, E, at 170 K, while the 0.37 eV process reaches this level at 200 K and becomes the dominant decay channel above 220 K (see Fig. 9-17). 

Because there is no depletion layer between the substrate and the conducting channel, the equations of the current-voltage curves are in fact simpler in the TFT than in the MISFET, provided the mobility can still be assumed constant (which is not actually the case in most devices, as will be seen below). Under such circumstances, the charge induced in the channel is given, in the case of an /l-channel, by Eq. (14.23). In the accumulation regime, the surface potential Vs(x) is the sum of two contributions (i) the ohmic drop in the accumulation layer, and (ii) a term V(x) that accounts for the drain bias. The first term can be estimated from Eqs. (14.15), (14.16) and (14.19). In the accumulation regime, and provided Vx>kT/q, the exponential term prevails in Eq. (14.16), so that Eq. (14.15) reduces to... 

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