Tangential pinch

Figure 2.2. McCabe-Thiele diagram for (a) ideal and (b) nonideal mixtures. 1, operating line at infinite reflux. 2, operating line at flnite more minimum reflux 3, operating line at minimum reflux 4, equilibrium line 5, composition of liquid and vapor flow that meet on tray 6, composition of liquid and vapor flow that leave from tray Xpi ch, point of tangential pinch.

From Fig. 2.2b it is clear that, in this particular case, the infinite number of steps and, respectively, the area of constant concentrations appear in the point of tangency of the top section operation line to the equilibrium curve (this point is indicated as Xpinch), but not in the feed point. Such an area of constant concentrations is called a tangential pinch. 

Therefore, an infinitesimal amount of heat should be drawn off in each cross-section of the top section and should be brought in in each cross-section of the bottom section. For azeotropic mixtures, the phase equilibrium coefficients field is of complicated character, which leads to nonmonotony of the Liquid and vapor flow rates changing along the sections trajectories (i.e., to the necessity of input or output of heat in various cross-sections of the section). Such character of the flow rates changing at reversible distiUation influences on the conditions of minimum reflux mode in adiabatic columns, which results in a number of cases in the phenomenon of tangential pinch (see Chapter 5). 

The approximate calculation method of minimum reflux mode (Koehler, Aguirre, Blass, 1991) - the method of the smallest angle, which holds good for mixtures with any component numbers and for any sphts, including frequently found at azeotropic mixtures separation cases of tangential pinch, is based on the calculation of reversible distillation trajectories for the given product compositions. 

The appearance of the tangential pinch in the mode of minimum reflux was investigated in the works (Levy Doherty, 1986 Fidkowski, Malone, Doherty, 1991). 

The approximate method of calculation of the minimum reflux mode for three-component mixtures at the absence of tangential pinch was suggested in the work (Stichlmair, Offers, Potthofk 1993). 

Figure 5.18. The tangential pinch in rectifying section for the acetone(l)-benzene(2)- chloroform(3) mixture for the split 1,3 2 (a) sharp separation (the tangential-pinch region Regj g not shaded), (b) quasisharp separation. 1, 2, 3, different values of L/V and different iso-f 2 lines (thin hues) SN, saddle-node point.

Figure 5.19. (L/V)rev as functions X2 on the reversible-distillation trajectories in rectifying section for the split 1,3 2 (for given xo in the tangential-pinch region Regu g) of the acetone(l)-...

If the top product point lies on the edge 1-3, it is the case of tangential pinch, which we are going to consider in the next section (not shown in Fig. 5.28). 

The algorithm of calculation of minimum reflux mode at tangential pinch has some peculiarities. At tangential pinch in top section (L/y) = =... 

At tangential pinch, points x/ i and x/ are located not in minimum reflux bundles but inside rectifying and stripping bundles, as at a reflux bigger than the minimum one (see Chapter 7). In the section where tangential pinch takes place, there is a zone of constant concentrations where the composition at plates corresponds to the composition in the point of pinch, and the second section is flnite. 

The example of tangential pinch for four-component mixture is quasisharp separation of azeotropic mixture acetone (l)-benzene (2)-chloroform (3)-toluol (4) of composition Xf (0,350 0,250 0,150 0,250) at intermediate split 1,3(2) 2,4(3) (admixture components heavy and light key are in brackets correspondingly) at the following composition the products xd (0,699 0,001 0,300,0) and xb (0 0,500 10 0,500). The same top product composition, as in the previous example (Fig. 5.18b) of separation of three-component mixture in the top section, is accepted for convenience of analysis. In this case, the boundary elements of top section trajectory bundle, located in face 1-2-3, completely coincides with top section trajectory bundle at separation of previously mentioned three-component mixture. 

Will tangential pinch arise if the top product contains components 4,5, and 6, tear-off point belongs to region Regl, and in the vicinity of tear-off point component 3 has a phase equilibrium coefficient that is smaller than in tear-off point itself ... 

The Ih symmetry of the 60-atoms molecule allows 2Ag and SH modes to be Raman active and 4T modes to be IR active. The four IR active modes are at 1430, 1185, 580 and 528 cm , respectively. The most important Raman modes are at 1469 (tangential bond alternation or pinch mode, Ag), 495 (radial breathing mode, T ) and 271 (squashing mode, Hg) cm , respectively. In the low temperatur phase degenerate modes split from a crystal field and Davidov interaction. Good reviews on the group theoretical analysis and on the line positions are given in (Dresselhaus et al., 1992 Matus and Kuzmany, 1993). 

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