Sources tubular source

Many of these difficulties can be overcome by choosing an appropriate configuration of the photoreactor system. One such a system is the mechanically agitated cylindrical reactor with parabolic reflector. In this type of reactor, the reaction system is isolated from the radiation source (which could also simplify the solution of the well-known problem of wall deposits, generally more severe at the radiation entrance wall). The reactor system uses a cylindrical reactor irradiated from the bottom by a tubular source located at the focal axis of a cylindrical reflector of parabolic cross-section (Fig. 40). Since the cylindrical reactor may be a perfectly stirred tank reactor, this device is especially required. This type of reactor is applicable for both laboratory-and commercial-scale work and can be used in batch, semibatch, or continuous operations. Problems of corrosion and sealing can be easily handled in this system. 

Alfano O.M., Romero R.L. and Cassano A.E. 1985. A cylindrical photoreactor irradiated from the bottom. I. Radiation flux density generated by a tubular source and a parabolic reflector, Chem. Eng. Sci., 40, 2119-2127. 

Figure 26.1 Examples of basic photochemical reactors (some adapted from Cassano et al., 1995). (a) tubular photoreactor inside a cylindrical reflector of elliptical cross section (b) annular photoreactor (c) film-type photoreactor (d) single-lamp multitube continuous photoreactor (e) perfectly-mixed semibatch cylindrical photoreactor irradiated from the bottom by a tubular source and a parabolic reflector...

The modelling of nonuniform fibers by current sources in the following chapter leads to the tubular current source. This source, which is depicted in Fig. 21-3, consists of a current distribution of density J on the cylindrical surface, or tube, r = Tq defined by [2]... 

When the tubular source of radius Tq in Fig. 21-3 is located within the core or at the core-cladding interface of a step-profile fiber of radius p, the solution of Eq. (21-34) is derived in Section 34-7 and is given by Eq. (34-32) as [2]... 

Fig. 21-6 (a) Plots of the factor C,(0) of Eq. (21-38) as a function of the radiation angle 0q for an axisymmetric source within a step-profile fiber, (b) Normalized power P as a function of the radiation angle 0q for an axisymmetric tubular source coinciding with the interface of a step-profile fiber. The solid curve is calculated from Eq. (21-41b) and the free-space dashed curve from Eq. (21-32). 

We showed in section 21-10 that the radiation from a tubular source with the current distribution of Eq. (21-13) is directed at the angle of EQ- (21-29) relative to the fiber axis. Consequently, the total power P radiated from a tube of length 2L and radius / q < p within a step-profile fiber is given by [2]... 

Consider a weakly guiding, step-profile fiber which contains a sinusoidal line source of length 2L on its axis, directed parallel with the x-axis in the fiber cross-section. The magnitude of the distribution is assumed to be given by the tubular source of Eqs. (21-13) and (21-14) with / = 0 and Tq 0. Hence... 

Example Dipole radiation 25-13 Example Tubular-source radiation... 

Example Dipole within a step-profile fiber 25-15 Example Tubular source within a step-profile fiber 25-16 Effect of a finite cladding... 

Fig. 25-1 (a) A current dipole of strength I and length d is located at the origin of coordinates and is parallel to the x-direction. (b) Cross-section of the tubular source showing the orientation of axes and the current direction parallel to the x-axis. 

Consider a tubular source, as described in Section 21-6, of length 2L and radius Tq, which carries x-directed currents with magnitude... 

We now examine how radiation from the point dipole and the tubular source is modified by the presence of a fiber. In order to relate the results to the correction factor of Section 21-12, the fiber is assumed to be weakly guiding. 

Example Tubular source within a step-profile fiber... 

A tubular source of radius ro is located symmetrically within the core of a weakly guiding, step-profile fiber, i.e. 0 < ro < p, where p is the core radius. To account for the fiber profile, we repeat the analysis of Section 25-13 using the weakly guiding radiation modes of Table 25-4 instead of the free-space modes of Table 25-2. The modal amplitudes of Eq. (25-34a) are replaced by... 

Tubular sources within weakly guiding fibers... 

Having set up the formalism for the calculation of free-space radiation from current sources, we now account for the effect of the fiber on the radiation fields. We could proceed by solving Eq. (34-16) for a given profile, which leads to the fields through Eqs. (34-15) and (34-13). However, rather than superpose the far fields of point sources, we prefer to determine the Green s function for the tubular source introduced in Section 21-6 and illustrated in Fig. 21-3 [7]. The advantage of the tubular source is that it has the same geometrical symmetry as the circular fiber. Furthermore, an arbitrary current source can be described either by a distribution of dipoles or by a complete set of tubular sources. Here we examine the latter approach. 

The radiation fields of the tubular source depend on the solution of Eq. (34-22) for the cartesian components of A,. Nevertheless, we can make a general deduction about these fields regardless of the fiber profile [7]. First consider the free-space solution when n = Mji everywhere. The spatial dependence of A at radius r outside of the tube is proportional to... 

Here we derive the correction factor for a tubular source in the core of a weakly guiding, step-profile fiber. The solution of Eq. (34-25) is expressible as... 

Biphenyl has been produced commercially in the United States since 1926, mainly by The Dow Chemical Co., Monsanto Co., and Sun Oil Co. Currently, Dow, Monsanto, and Koch Chemical Co. are the principal biphenyl producers, with lesser amounts coming from Sybron Corp. and Chemol, Inc. With the exception of Monsanto, the above suppHers recover biphenyl from high boiler fractions that accompany the hydrodealkylation of toluene [108-88-3] to benzene (6). Hydrodealkylation of alkylbenzenes, usually toluene, C Hg, is an important source of benzene, C H, in the United States. Numerous hydrodealkylation (HDA) processes have been developed. Most have the common feature that toluene or other alkylbenzene plus hydrogen is passed under pressure through a tubular reactor at high temperature (34). Methane and benzene are the principal products formed. Dealkylation conditions are sufficiently severe to cause some dehydrocondensation of benzene and toluene molecules. 

Fig. 29-9. Wet-wall ESP with tubular collection electrodes. Source Oglesby, S., Jr, and Nichols, G. B., Electrostatic precipitators, in "Air Pollution," 3rd ed., Vol. IV (A. C. Stern, ed.), p. 238, Academic Press, New York, 1977.

Having established that a finite volume of sample causes peak dispersion and that it is highly desirable to limit that dispersion to a level that does not impair the performance of the column, the maximum sample volume that can be tolerated can be evaluated by employing the principle of the summation of variances. Let a volume (Vi) be injected onto a column. This sample volume (Vi) will be dispersed on the front of the column in the form of a rectangular distribution. The eluted peak will have an overall variance that consists of that produced by the column and other parts of the mobile phase conduit system plus that due to the dispersion from the finite sample volume. For convenience, the dispersion contributed by parts of the mobile phase system, other than the column (except for that from the finite sample volume), will be considered negligible. In most well-designed chromatographic systems, this will be true, particularly for well-packed GC and LC columns. However, for open tubular columns in GC, and possibly microbore columns in LC, where peak volumes can be extremely small, this may not necessarily be true, and other extra-column dispersion sources may need to be taken into account. It is now possible to apply the principle of the summation of variances to the effect of sample volume. 

The Golay equation [9] for open tubular columns has been discussed in the previous chapter. It differs from the other equations by the absence of a multi-path term that can only be present in packed columns. The Golay equation can also be used to examine the dispersion that takes place in connecting tubes, detector cells and other sources of extra-column dispersion. Extra-column dispersion will be considered in another chapter but the use of the Golay equation for this purpose will be briefly considered here. Reiterating the Golay equation from the previous chapter. 

Figure 4-13. Liquid-liquid heterogeneous tubular flow reaotor (e.g., alkylation of olefins and Isobutane). (Source J. M. Smith, Chemloal Engineering KInetlos, 3rd ed., McGraw-Hill, Inc., 1981.)...

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