The effect of rotation rate

The effect of variation of the rotation speed on the current response is shown in Fig. 2.26. The results are for a film of the same thickness as those in Fig. 2.24. We therefore fit the data to the equation for the Case 11/IV boundary (equation (2.21) in Table 2.3). Again, the effect of rotation rate on the NADH concentration at the film/solution interface was determined and accounted for by using equation (2.4). The best fits of the theory to experiment are shown by the lines in Fig. 2.26, and the corresponding values of ca,[site]DsKs and KM/Ks are given in Table 2.6 along with results from a separate replicate experiment. 

Comparing the values for cal[site)DsKs and KM/KS obtained from all the different experiments (Tables 2.5 and 2.6), we find that the agreement between the different experiments is good and confirms the validity of the proposed model and demonstrates the excellent reproducibility and stability of these films for NADH oxidation. 

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The effect of rotation rate was studied in the range of 2,000 to 5,000 rpm, which represents a 90% (= 2.5" ) increase in the rate of mass transport to a RCE. The effect of rotation rate on the deposition process is shown in Fig. 10. As the concentration of WO is increased tenfold, from 0.04 to 0.40 M, the current density increases by a factor of only two. The limiting current density, calculated on the basis of the concentration of WO4 in solution, is much higher than the partial current densities for deposition of this metal, so one would not expect a 40% increase of the rate of deposition of W with the increase of the rate of mass transport, as foimd experimentally. The explanation of these unexpected observations lies in the formation of the mixed-metal complex, as shown in Eq. (33). The concentration of this complex is low, and its rate of formation is also expected to be low. From the dependence of the partial current density for W deposition shown in Fig. 10a, the activation-controlled and the mass transport-limited current densities can be estimated, using the Levich equation, as applied to RCE experiments, namely... 

Figure 10. The effect of rotation rate on the partial current density for deposition of tungsten (a) and nickel (b), the W-content in the alloy (c), and the steady-state deposition potential (d). Plating conditions excess of NH4OH, 0,4 M NagCit, pH = 8.0, i = 30 mA cm. (.) 0.4 M u A I),. 0.04 M Ni-SO4 (o) 0.04 M u A I) . 0.4 M NiSO4. Reproduced with permission from Ref, 92, Copyright (2003) The Electrochemical Society.

A model was developed to cope with nonstationary behavior observed in Fig. 6.10 see Fig. 6.11 for an example of the resulting simulations/ which shows the effect of rotation rate on the current. While results from the simulation exhibit curves similarly shaped to those found in practice/ there are quite a number of parameters that are not accurately known. Such unknown effects as the layer homogeneity on the rate of electron exchange and the swollen layer thickness... 

This expression, eq. (7.106) or (7.107), takes into account the effect of fluid motion on the diffusion layer 8, which is an adherent thin film on the electrode surface. Therefore, diffusion coupled with convection contributes to the total mass transfer process to or from the electrode surface and it is known as convective diffusion in which 6 is considered immobile at the electrode surface [66]. Recall that the limiting thickness of the diffusion layer is illustrated in Figure 4.5. Also, Levich equation describes the effect of rotation rate, concentration, kinetic viscosity on the current at a rotating-disk electrode. 

Fig. 13. Effect of rotation rate on the increase in current, between — 500-mV potential and the inflection point, for a slow potential scan (20 mV see"1) during the time interval At indicated. / = initial current at —500-mV potential, /e = current after time At. Solution 14 0.295 Af CuS04, 1.492 M H2S04. Solution 11 0.05 M CuS04. 0.492 M H2S04. [From Sclman (S8).]...

One of the few theoretical papers trying to explain acceleration under the action of microwaves has recently been published by A. Miklavc [18]. He stated that large increases in the rates of chemical reactions occur because of the effects of rotational excitation on collision geometry. This could be cautiously considered when one has knowledge of the quasi-nil energy involved by microwave interaction according to Planck s law [E = hc/X = 0.3 cal/mol]. 

In principle these should be predictable from theory, but in practice there are many grey areas such as the effects of rotation, convective mixing, mass loss, the mechanism of stellar explosions, nuclear reaction rates such as 12C(a, y)160, the evolution of close binaries and the corresponding mass limits between which various things happen for differing initial chemical compositions. Figure 5.14 shows a version of what may happen in single stars with different initial masses and two metallicities, Z Z and Z Z /20. 

The effect of rotation on transfer to a translating sphere has been studied for both screw motion (El, F6, T2) and top spin (N3, T2) with Re > 1500. The effect of rotation on the transfer rate is less than 10% for vJU < 0.5. The ratio of the Sherwood number in screw motion to that in pure translation at the same Ur is correlated within 10% by... 

In a long series of papers on the master equation, Pritchard and his coworkers elucidated for the first time the effects of rotational and vibrational disequilibrium on the dissociation and recombination of a dilute diatomic gas. Ultrasonic dispersion in a diatomic gas was analyzed by similar computational experiments, and the first example of the breakdown of the linear mixture rule in chemical kinetics was demonstrated. A major difficulty in these calculations is that the eigenvalue of the reaction matrix (corresponding to the rate constant) differs from the zero eigenvalue (required by species conservation) by less than... 

Shoup, G. Lipari, and A. Szabo, Diffusion-controlled bimolecular reaction rates- the effect of rotational diffusion and orientation, Biophys. J. 36, 697-714 (1981). 

To take one example, let us consider the effects of rotational relaxation in BrF. The excited 53FI(0+) state in BrF is crossed by another 0+ state which leads to predissociation of the B state in vibrational levels 7 and 6. The initial study of the dynamics of the B state was carried out in a discharge flow system where the minimum operating pressure was 50 m Torr. The gas-kinetic collision rate coefficient at 298 K for He + BrF(B) collisions is 4.4 x 10-10 cm3 molecule-1 s-1. Thus, at the minimum pressure of 50 m Torr, the average time between collisions of excited BrF molecules and helium buffer gas is 1.5/us. This time is short compared with the radiative lifetime of BrF (42—56/ns [43]) and therefore significant redistribution in the excited state can occur before it radiates. 

The alternative view [705], and the one found in mass spectrometry, is to consider that rotation influences the rate by altering the effective critical energy. Equation (1) can be extended, as in eqn. (2), to include the effect of rotation, viz. 

Having shown that poly(aniline) films can mediate NADH oxidation, studies of the effect of altering the applied potential and the rotation rate of the electrode were undertaken. Preliminary results from these studies showed that the maximum current response was obtained when the applied potential was 0.2 V vs. SCE and that the currents were two orders of magnitude higher for poly(aniline) modified electrodes when compared to a bare electrode indicating that poly(aniline) is a good catalytic surface for the oxidation of NADH. However, studies of the effect of rotation speed carried out at pH 5 show a decline in current with time (see Fig. 2.12). 

Figure 4 shows all the experimental Cq data for the short screws and the corresponding values calculated from Figure 2. Molecular diffusivities at the various temperatures were taken from Figure 3, and the equilibrium values from Figure 5. The scatter is not too bad, and indicates that the model fairly well predicts the effect of rotational speed, throughput rate, and molecular diffusivity on devolatilization performance. The data also indicate that the geometry efficiency, p (which were different for the two screws) has some merit, and provides a convenient means for comparing the relative efficiency of different screw designs.

Effect of rotation rate. This is one parameter which does not have an analogous counterpart in batch column operation. Therefore, this parameter provides additional flexibility when optimizing a separation performed in an annular chromatograph. The rotation rate does not influence the solute residence time in the unit nor does it influence the relative time scales for flow, internal diffusion or external mass transfer. However, the rotation rate does influence the angular distance that a solute traverses in a given time. The result of a slower rotation rate is to decrease both the peak variance and the displacement for each solute and therefore again the resolution between proteins changes less than either mi/mo or a. ... 

Using a horizontal rotating cylinder and several different sand-sand systems, Oyama and Ayaki studied rate equations for mixing and the effect of rotational speed and the volume ratio of sand to mixer. Different methods of loading were also tried. 

The effect of rotational constant mismatches on vibrational quantum beats43 is the subject of this subsection. We first review theoretical results that show that the qualitative effect of such mismatches is to increase the apparent damping rate of quantum beat envelopes relative to the decay rate of the unmodulated portion of a decay and that such beat damping rates increase with increasing rotational temperature. We then review results that show that such effects on beat damping are consistent with experiment. 

Marken et al. (110) have given a detailed account of the factors affecting annular pressure losses, including the effects of rotational flow in the annulus. It might be expected that rotational flow in the annulus would decrease the frictional pressure losses as the increased shear rate would lower the viscosity. However, Marken et al. observed an increase in frictional pressure due to the formation of Taylor vortices. McCann et al. (J07) have observed increases in the frictional pressures in slimhole annuli due to annular rotation of the drilling fluid. 

Calculations have shown that the faster diffusion rates might be explained by an increase in the factor A with no change in activation energy. Miklavc [39], by analyzing the rotational dependence of the reaction 0 + HC1 0H- -Cl, concluded that marked acceleration may occur as a result of the effects of rotational excitation on collision geometry. 

The effects of rotational difhision and energy transfer ate easily sqiarated fey juifidous choice of the experimental conditions. For example, Brownian rotations cause negligible depolarization when the rotational rate is much slower than the rate of fluorescence emisaon. In contrast, RET occurs only in concentrated solution where the average distance between the fluorophore molecules is comparable to a characteristic distance Rg, which is typically near 40 A. One may readily calculate that millimolar concentrations are required to obtain this average distance (Chapter 13). Hence, since the usual concentradons requited for fluotesoence measurements ate about l0r U, RET is easily avdded by the use of dilute solutions. 

FIGURE 14.10 (a) The effect of rotational speed on coating variability (CV) at spray rate of 2.316ml/min and (b) the frequency distribution of the residence time of the coated particles for the effect of speed at 32° tilt. Adapted from Ref. [13] with permission. Copyright 2011, Elsevier. 

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