Dimensionless moderator

The metal in solution (dissolved phase) may be picked up by the phytoplankton (regulated by pelagic uptake rate). The pelagic uptake rate may be influenced by pH, total-P and color and by the specific lake characteristics (water retention time, area, mean depth, etc.). In traditional mass-balance models, one would multiply an amount (kg) by a rate (1/year) to get a flux. Here, we multiply kg (l/year) mod, where mod is a dimensionless moderator which describes empirical knowledge how environmental variables (like pH) influence the given flux. 

B. Definition of dimensionless moderator (Dim. less) for radiocesium in lakes. Empirical data from 41 Swedish lakes (data from H anson 1991). Cspi = Cs in pike in Bq/kg ww, Cssoil = fallout in Bw/m p//J5=mean lake pH from 36 months. Regression lines for data for 1988 and 1989... 

In the following simulations, the other sensitivity factors (color, total-P and morphometry) were kept constant and pH varied to simulate effects of limings on the biouptake of the two test substances, Hg and Cs. It is possible to apply a given dimensionless moderator on many rates and model variables. This is schematically illustrated in Fig. 9.6 by the dotted arrow from YpH to the partition coefficient, since the water chemical conditions (pH, alkalinity, etc.) could influence the way metals are bound to carrier particles. 

Only those components which are gases contribute to powers of RT. More fundamentally, the equiUbrium constant should be defined only after standard states are specified, the factors in the equiUbrium constant should be ratios of concentrations or pressures to those of the standard states, the equiUbrium constant should be dimensionless, and all references to pressures or concentrations should really be references to fugacities or activities. Eor reactions involving moderately concentrated ionic species (>1 mM) or moderately large molecules at high pressures (- 1—10 MPa), the activity and fugacity corrections become important in those instances, kineticists do use the proper relations. In some other situations, eg, reactions on a surface, measures of chemical activity must be introduced. Such cases may often be treated by straightforward modifications of the basic approach covered herein. 

For typical experimental parameter values (a =0.5, NM-1019 atom/m2, P,=l D=3.3-10 30 C-m, T=673) the dimensionless parameter IT equals 32 which implies, in view of equation (11.12), dramatic rate enhancement ratio p values (e.g. p =120) even for moderate (-15%) changes in the coverage 0j of the promoting backspillover species, as experimentally observed. 

The large heated wall temperature fluctuations are associated with the critical heat flux (CHE). The CHE phenomenon is different from that observed in a single channel of conventional size. A key difference between micro-channel heat sink and a single conventional channel is the amplification of the parallel channel instability prior to CHE. As the heat flux approached CHE, the parallel channel instability, which was moderate over a wide range of heat fluxes, became quite intense and should be associated with a maximum temperature fluctuation of the heated surface. The dimensionless experimental values of the heat transfer coefficient may be correlated using the Eotvos number and boiling number. 

As a result, many correlations are available for heat and mass transfer at moderate pressures that have been developed over time. Perry and Green [6] give a fairly complete amount of data with regards to correlations for different arrangements [7], On the other hand, very few data and correlations are available in the field of high pressure heat and mass transfer, as will be reviewed later. Correlations are in terms of the individual coefficients, ki and h, included in dimensionless groups such as those given before in Eqns. (3.4-10). 

Several studies have shown that a pAa match provides only moderate energy (-5 kcal/mol) in solution.(8,12-15) Ab initio calculations also confirmed this conclusion.(16) A linear correlation between AGHB and Ap a was proposed in both experimental and computational studies where the dimensionless Br0nsted slope j3 is... 

We have considered here the influence of dispersion asymmetry and Zee-man splitting on the Josephson current through a superconductor/quantum wire/superconductor junction. We showed that the violation of chiral symmetry in a quantum wire results in qualitatively new effects in a weak superconductivity. In particularly, the interplay of Zeeman and Rashba interactions induces a Josephson current through the hybrid ID structure even in the absence of any phase difference between the superconductors. At low temperatures (T critical Josephson current. For a transparent junction with small or moderate dispersion asymmetry (characterized by the dimensionless parameter Aa = (vif — v2f)/(vif + V2f)) it appears, as a function of the Zeeman splitting Az, abruptly at Az hvp/L. In a low transparency (D Josephson current at special (resonance) conditions is of the order of yfD. In zero magnetic field the anomalous supercurrent disappears (as it should) since the spin-orbit interaction itself respects T-symmetry. However, the influence of the spin-orbit interaction on the critical Josephson current through a quasi-ID structure is still anomalous. Contrary to what holds... 

The characteristics of the experimental aquifer were independently determined from appropriate flowthrough column experiments or obtained directly from the literature. The dry bulk density of the sand ph= 1.61 kg/1, and the aquifer porosity 0=0.415 were evaluated by gravimetric procedures. The dimensionless retardation factor, R= 1.31, of the aqueous-phase TCE was determined from a column flowthrough experiment. The tortuosity coefficient for the aquifer sand was considered to be x =1.43 [75]. The molecular diffusion coefficient for the aqueous-phase TCE is D=0.0303 cm2/h [76]. The pool radius is r=3.8 cm. Bromide ion in the form of the moderately soluble potassium bromide salt was the tracer of choice [77 ] for the tracer experiment conducted in order to determine the longitudinal and transverse aquifer dispersivities a =0.259 cm and a-,— 0.019 cm, respectively. The experimental pool contained approximately 12 ml of certified ACS grade (Fisher Scientific) TCE with solubility of Cs=1100 mg/1 [78]. 

In earlier studies on solutions of synthetic polymers (Ferry, 1980), the zero-shear viscosity was found to be related to the molecular weight of the polymers. Plots of log r] versus log M often resulted in two straight lines with the lower M section having a slope of about one and the upper M section having a slope of about 3.4. Because the apparent viscosity also increases with concentration of a specific polymer, the roles of both molecular size and concentration of polymer need to be understood. In polymer dispersions of moderate concentration, the viscosity is controlled primarily by the extent to which the polymer chains interpenetrate that is characterized by the coil overlap parameter c[r] (Graessley, 1980). Determination of intrinsic viscosity [r]] and its relation to molecular weight were discussed in Chapter 1. The product c[jj] is dimensionless and indicates the volume occupied by the polymer molecule in the solution. 

Fig. 7.23. Computed propagation of fuel concentration, velocity, pressure and temperature waves. M is the dimensionless mass fraction of the fuel, normalized by the original value. Moderate temperature gradient of 12.5 K/mm, developing detonation mode. Curves are for different times (1) 0 /as, (2) 12 /as, (3) 24 /as, (4) 36 /as, (5) 48 /as. From [168].

Figure 5 Minimized variance V versus the dimensionless amplitude of the pump field E/Eth = e/eth for both operational regimes, eth is given by Eq. (23). The parameters are (1) x/7 = 0.1 (weak coupling), A/7 = 10 (2) xh = 0-5 (moderate coupling), A/7 = 3 and...

The hard core in Eq. (7.59) has been imposed for numerical convenience. As a consequence, it is mainly the van der Waals-like attractive (rather than the repulsive) part of the LJ (12,6) potential (oc r ) that contributes to the fluid fluid potential. The strength of the dipolar relative to the attractive LJ interactions is conveniently measured by the reduced (i.e., dimensionless) dipole moment m = fi/V a. Depending on this parameter, the Stockmayer fluid may serve as a simple model for polar molecular fluids [258, 259] (small m.) or for ferrofluids [227, 228] (large in). Here wc consider a system with dipole moment m = 2, whicli is a value typical for moderately polar molecular fluids [259] such as chloroform. For this value of m, GCEMC simulations have been presented in Section 6.4.1. 

In Figure 5.2, the dependence of the mean Sherwood number on the dimensionless parameter kv is shown for a first-order volume chemical reaction in the problem of quasi-steady-state mass transfer within a drop for the extreme values Pe = 0 (formula (5.4.2)) and Pe = oo (formula (5.4.9)) of the Peclet number. The dashed line corresponds to the rough upper bound (5.4.8). For moderate Peclet numbers (0 < Pe < oo), the mean Sherwood number gets into the dashed region bounded by the limit curves corresponding to Pe = 0 and Pe = oo. One can see that the variation of the parameter Pe (for fcv = 0(1)) only weakly affects the mean influx of the reactant to the drop surface, i.e., one cannot achieve a substantial increase in the Sherwood number by any increase in the Peclet number. In the special case fcv = 10, the maximum relative increment of the mean Sherwood number caused by the increase in the Peclet number from zero to infinity is only... 

For a given substance over a moderate pressure range the quantity is a function of temperature. Use of Fig. 13.2 is facilitated if this quantity, which can be denoted by j-, is calculated and plotted as a function of temperature for a given substance. Quantity ij/f has the same dimensions as a heat-transfer coefficient, so that both the ordinate and abscissa scales of Fig. 13.2 are dimensionless. Appendix 14 gives the magnitude of for water as a function of temperature. Corresponding tables can be prepared for other substances when desired. 

We plot in Fig. 6.5 the dimensionless front velocity vt/u vs the reaction rate r on a log-log scale. The front velocity increases with r. For the cases / = a and I = 2a, the slope is very similar, but for / = oo it is steeper. In all cases the front velocity increases as a power law of r, straight line in a log-log plot, for small and moderate values of r and saturates to 1 for larger values, the slope in the log-log plot tends to 0. This behavior is due to the fact that an increase of the reaction rate r leads to an increase of the front velocity. However, the front cannot travel faster than the jump velocity of the particles if all of them jump in the backbone direction, i.e., V < ajx. For I = a and / = 2a the transport is diffusive, and the diffusion coefficient is properly defined. If this transport is combined with a KPP reaction, a Fisher velocity is expected, i.e., in both cases v fr. Computing numerically the slope from a linear fit in Fig. 6.5 we obtain and for / = a and I = 2a, respectively. The case / oo is quite different, because the transport is anomalous. Equation (5.36) with y = 1/2 yields v while the linear fit of the numerical results yields Numerical and analytical results are in good agreement. 

For low to moderate mass flux mass transfer studies, therefore, provided that the physical property changes are taken into account, mass transfer coefficients kc or k may be used. The dimensionless mass ratio driving force, A Y, has been used quite successfully in crystallization and dissolution studies (Garside and... 

The data of Mewis et al. (39) and d Haene (40) for poly(methyl methacrylate) spheres stabilized by poly( 12-hydroxy stearic acid) and dispersi in decalin correlate reasonably well with results for hard spheres for low to moderate volume fractions, although the critical stress is somewhat smaller. For highly concentrated dispersions, however, packing constraints cause some interpenetration of the layers at rest and viscous forces at high shear rates drive the particles even closer together. Consequently, the effective layer thickness decreases with increasing 0 and Pe, the dimensionless shear rate. 

In order to understand these results it is necessary to recall that the actual quantity describing the deteriorating effect of BB is not the variance alone but rather the product of the variance and the square of the slope of the calibration curve. This dimensionless efficiency parameter is at least one order of magnitude smaller than the variance and the considerable differences reduced to moderate ones. A correction factor c/can be constructed to describe the shift of the points of inflection due to BB... 

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