Line coalescence

Geldart (1970) showed a substantial distinction between bubble sizes in two dimensional and three dimensional beds. He used 128 pm river sand in a 30.8 cm round bed and a 68 1.27 cm rectangular cross section bed. The results, shown in Fig. 12, show that the bubbles in the three dimensional bed are larger. There were differences in the visible bubble flow rate at the same superficial velocity. Geldart ascribes the differences in bubble diameter to differences invisible bubble flow rate as well as to out-of-line coalescence in the three dimensional bed. 

Shortening of the life time due to reaction leads to an increase in line width. The increase in line width will not continue indefinitely. As the rate of exchange of protons rises, two protons in two different environments do not behave as independent and, therefore, the lines broaden and finally merge. If average time spent by a given proton is 0 and if two lines are separated by Avab then at the point where the lines coalesce... 

For all systems studied so far it is found that the rates of racemization R and proton exchange E (measured either by DjO exchange (Sec. 3.9.5) or by nmr line coalescence methods (Sec. 3.9.6)) are both first-order in [OH ]. 

A procedure often used to evaluate t is to estimate the temperature at which the lines coalesce . The disadvantage of this method is that the coalescence point is usually not very sharply defined. 

NMR spectra have been observed in this laboratory of samples of heptanol, octanol, and dodecanol saturated with water. With pure specimens of octanol and dodecanol we have obtained a picture at low temperatures similar to that of Weinberg and Zimmerman (30), the alcohol and water OH groups giving separate resonances. As the temperature was increased in these samples, the lines coalesced to give a single very broad peak. When the lines are distinct, the alcohol OH resonance remains at the same value of chemical shift, 8, as in the anhydrous material, whereas for the water line, 8 decreases by approximately 0.4 p.p.m. in each alcohol from the value in pure water. One deduces that the hydrogen bonding... 

Since the expression (13.122) for h holds in the region 0 < (/Z1/Z2) < 1 for drops of finite viscosity, and 0 < /Z2 < 1, //i = 00 for interaction of a drop with rigid particle on the graph, the intermediate area is shown by dashed line. Coalescence frequency becomes smaller as we increase the viscocities of interacting drops. The smaller the size difference between the drops, the more sensitive their coalescence frequency will be to a change in the internal viscosity. 

When J = 0 (sin 20 = 0), the four lines coalesce into two with equal... 

The theory of the relation between the line shape and the lifetimes is rather complicated, and the best results are obtained by a computer fitting of the observed and calculated curves over their whole range. Less accurate velocity constants can be derived by the commoner procedures of measuring the width of a line at half-height, or determining the conditions under which two lines coalesce to form a single broad line. 

Electron spin exchange is a bimolecular reaction in which the unpaired electrons of two free radicals exchange their spin states. At low concentration (ca. I0 mol/L) the usual isotropic spectrum is observed. As the radical concentration is increased the lines gradually broaden until at high concentration (> I0 mol/L) the lines coalesce to a single line. This single line sharpens further as the concentration is increased. 

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