First-order mixing

Figure 1. Jacket water inlet and outlet temperatures in response to a —33°C (Test II) change in the inlet. The response of the jacket outlet temperature typifies a first-order mixing model.

This equation is first order in T with respect to t. A first order mixing pattern has been assumed/ and a first order pattern is exhibited by most "we 11-mixed" vessels that do not have baffles or flow directing nozzles. How closely this first order equation fits the actual process will be determined later. 

Experiments and calculations have shown that the CO exchange process over Ni at 220°C is immeasurably rapid so that the fraction of labeled CO in the surface phase is the same as that in the gas phase (i 7). The response curves can be calculated by using Eq. (4) with j representing one of the isotopes, aU the r/s equal to zero, and t o N/R, where N is the total moles of both kinds of CO in both phases and R is the molar feed rate of the appropriate isotope. Since we know R, tqo, aitd the gas volume, we can calculate the surface coverage of CO from this experiment. The response time Tco is measured for this first-order mixing process, but no... 

Modified Huron-Vidal First-Order Mixing Rule (MHVI)... 

Thus mixes into with the first-order mixing coefficient If we arrange the orbital phases of p% and such that Sj/ is positive, equation 3.24 shows that i//y mixes into in a bonding way (in-phase) if lies higher in energy than ( /.4 0) antibonding way (out-of-phase) if l/f lies lower... 

As shown in Section 3.2A, the first-order mixing coefficient and the first- and second-order energy terms are given by... 

The first-order mixing coefficient rjp and the second-order energy are determined by the term (A/y- This is in general negative if the value of Sij... 

The first-order mixing coefficient tjp and the second-order energy are determined by the term (A// - This is in neral negative if the v ue of S j increases from zero,J)Ut poative if the value of decreases from zero. This stems from the fact that -S(f, and the m ltude of A / is generally greater than that of Therefore, equation 7.1 shows that, If 5//>0, the coefficient is positive for the mixing of an upper level into the lower level < 0)... 

Thus niixes Into with the first-order mixing coefficient tjp. If we arrange the orbital phases of ij/fg such that Sij is positive, equation 3.24 shows tlmt... 

Next, we consider the first order mixed derivatives of the energy with respect to electron and spin number on one hand and the external potentials v and V5 on the other hand. These derivatives are generalizations of the Fukui function, the reactivity index used to probe frontier orbital-controlled reactions. The generalized Fukui function /jvjv can be considered as the spin-resolved extension of the regular Fukui function given in eqn (26)... 

After the perturbation is turned on mixes into with a first-order mixing... 

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