Steady-state enhancement factor

Let us now And out how the system works. Assume that it starts at a large reduced flow-rate (point A) and reduce the input slowly. Up to the point C, any deviation from the equilibrium curve will die out rapidly. At C, concentration fluctuations become unstable and the system evolves quite rapidly towards D (p is fixed) where it finds a stable steady-state. The system has become unstable because reducing the flow-rate enhances crystallization which through the kinetic factor enhances the rate of precipitation and thereby depletes the residual liquid. The system quenches. Upon reducing the flow-rate further, the stable evolution continues towards point E. 

The terms pc and py correspond to 1/Tic and 1/Tih, respectively, and CTCH is the cross-relaxation rate. It should be stressed that the simplicity of the above equation is a consequence of the rareness of the I spins and of the dominant strength of the dipolar interaction between directly bonded nuclei. The situation for homonuclear proton spin systems is often more complicated, since the protons usually constitute a much larger spin system, and a separation into distinct two-spin systems may be not valid in this case. The broadband irradiation of the protons yields, in a steady state, Mhz = 0 and M z = Mj (1 rj). The factor 1 + 77 is called, as introduced above, the nuclear Overhauser enhancement factor. The NOE factor is related in a simple way to the equilibrium magnetizations of the I- and S-spins (which are proportional to the magnetogyric ratios 71 and 7s), the cross-relaxation rate and the relaxation rate of the I-spin ... 

An iron-promoted cobalt molybdate catalyst (Fe0 03Co0.9 7MoO4) was studied by Maksimov et al. [195,196] with respect to the role of iron in the transfer of charge. Iron strongly enhances the catalytic activity and at the same time increases the conductivity by a factor of 100. Mossbauer spectroscopy reveals that 4% of the iron ions are present as Fe2+ impurity . This fraction is doubled at steady state reaction conditions, and indicates participation of iron in the charge transfer process. 

This model has been used to predict flux, flux enhancement, and the reduction in the lag time when a voltage is applied [55,56]. An enhancement factor (EF) has been defined as the ratio of the steady-state flux with an applied voltage (/ion) to the corresponding passive flux (7pas) ... 

The inhomogeneity of the micellar aggregate also affords assisted spin trapping and the exploitation of magnetic field effects on the charge separated ion pairs [48]. Optical modulation spectroscopy can be used, for example, to follow the decay of radicals formed in homogeneous solution and in SDS micelles. Enhancements of a factor of about 50 in the lifetimes and the steady state concentrations of the radical were observed in the micelle, and a kinetic analysis led to a value of 2 x 103 s 1 for the exit rate constant from the micelle [49]. 

Wagner enhancement factor — describes usually the relationships between the classical - diffusion coefficient (- self-diffusion coefficient) of charged species i and the ambipolar - diffusion coefficient. The latter quantity is the proportionality coefficient between the - concentration gradient and the - steady-state flux of these species under zero-current conditions, when the - charge transfer is compensated by the fluxes of other species (- electrons or other sort(s) of -> ions). The enhancement factors show an increasing diffusion rate with respect to that expected from a mechanistic use of -> Ficks laws, due to an internal -> electrical field accelerating transfer of less mobile species [i, ii]. 

Let us now examine the two minor disadvantages of the laser time-resolved experiments which we mentioned briefly. The low radical concentration normally encountered in such experiments makes evaluation of E-A-type polarization difficult. In fact, even when the radical concentration is not a problem, as in pulse radiolysis study, the time profile has to be fitted to obtain the enhancement factor (124). Another aspect in the time-resolved study is that the experiments have to be repeated at different microwave power levels, as the true intrinsic P or V can only be obtained by extrapolation to zero power. Ironically, these two problems can be overcome readily in semi-steady-state experiments using a conventional slow-response spectrometer. 

The greatest disadvantage of this mode of CIDEP experiment is that the enhancement factor measured is for the "steady-state" spectrum. To calculate the true enhancement factor of the process, both the radical Tj and the radical half-life t /2 have to be taken into account ... 

Deactivation of large-pore slab catalysts where intraparticle convection, diffusion and first order reaction are competing mechanisms was analyzed by uniform and shelLprogressive models. For each situation, analytical solutions for concentration profiles, effectiveness factor and enhancement factor due to convection were developed thus providing a sound basis for steady-state reactor design. 

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