Parameters reduced

High-Performance liquid Chromatography. Typical performances for various experimental conditions are given in Table 11.15. The data assume these reduced parameters h = 3, V = 4.5. The reduced plate height is... 

Assumed reduced parameters h -linear velocity of the mobile phase. 

The reduced velocity compares the mobile phase velocity with the velocity of the solute diffusion through the pores of the particle. In fact, the mobile phase velocity is measured in units of the intraparticle diffusion velocity. As the reduced velocity is a ratio of velocities then, like the reduced plate height, it also is dimensionless. Employing the reduced parameters, the equation of Knox takes the following form... 

X is the scalar distance between the solute molecule and the center of the imaginary membrane, with the LJ parameters of the solute used as reducing parameters. The residual chemical potential for a pure fluid (which would correspond to component 2 in its pure state at the state conditions of cell A) can then, for example, be found using the expression... 

The terms p, T, and v are characteristic reducing parameters which may be obtained by fitting pressure-volume-temperature data (density, thermal expansion coefficient, and thermal pressure coefficient) for each pure component in the mixture (3,12). Values of p, v, and T are given in Tables I and II. 

The effluent obtained after solids removal and microbiological disinfection could be reused as cooling water, cleaning water or industrial process water in many industrial uses. A final polishing step may be necessary if higher quality requirements are needed in some specific industrial uses, e.g., cooling and boiler feed-water. Membrane processes such as NF or RO eliminate inorganic ions and reduce parameters like conductivity, alkalinity or salinity, etc. 

Comparative Characteristics Often, the electric and other characteristics of batteries differing in size, design, or electrochemical system need to be compared. The easiest way is by using normalized (reduced) parameters. Thus, current density serves as a measure of the relative reaction rate. Therefore, plots of voltage vs. current density provide a useful characterization of a battery, reflecting its specific properties independent of its size. 

Performance Characterization of Liquid Chromatography Columns Using Reduced Parameters... 

TYPICAL REDUCED PARAMETERS FOR DIFFERENT COLUMN TYPES... 

Golay equation 21, 611 gradient (LC) 490 height equivalent to a theoretical plate 11 longitudinal diffusion 16 mass transfer resistance 17 nonlinear chromatography SOS plate model 14 rate theory IS reduced parameters 78, 361, 611... 

Reduced parameters (section 1.7.10) can -be used to compare the potential of open tubular and packed columns to deliver a certain separation potential in SFC [8,43,53-56]. The Golay equation, equation 6.1, can be rewritten as... 

Upon substitution of the reduced parameters given above the separation time for a packed column and an open tubular column would be Identical if d 1.73 dp given the current limitations of open tubular column technology the column diameter cannot be reduced to the point %diere these columns can compete with packed columns for fast separations. This is illustrated by the practical txanple in Figure 6.3 (57). Ihe separation speed cannot be Increased for an open tubular column by increasing the reduced velocity since the reduced plate height is increased... 

The maximum number of theoretical plates that can be achieved for a particular column depends on the pressure drop per theoretical plate and the maximum pressure drop allowed over the column, (ising the same reduced parameters given earlier, the maximum number of theoretical plates obtained for an open tubular... 

Assumed reduced parameters h = 3, v = 4.5. These are optimum values fromagraphofreducedplateheightversus reduced linear velocity of the mobile phase. 

The measurement of effluent volume is not very reliable because of the effect of the geometry and packing characteristics of any column. It is often more useful to use a reduced parameter, such as V/V0, which is not so dependent upon column characteristics and is comparable with the calculation for RF values in thin-layer chromatography. 

A more vigorous treatment similar to the van Deemter equation but developed specifically for HPLC is the Knox equation, which uses a number of reduced parameters where h is the reduced plate height (h/dp) and vis reduced velocity (V dJD. ... 

The explicit expressions for either the binding constants or the correlation functions are, in general, quite complicated even when the subunits are identical. We present here some selected expressions obtained for special cases. As before, we use the reduced parameters... 

The nonclassical equation of state of Levelt Sengers et al. (1983) for the critical region of H2O may be expressed in terms of reduced parameters (cf. section 9.2) as follows ... 

The use of complementary data from different techniques can be a powerful tool to reduce parameter correlation in least-squares methods and to obtain the best estimates compatible with all available physical information. 

According to the van der Waals equation of state, the value of compressibility at the critical point should be 3/8 = 0.375. When does a real gas depart significantly from an ideal gas We can write equation (4.9) as the reduced equation of state, with the reduced temperatures, pressures, and volumes = TITc, Pi = P/Pc, Vr = V/Vc- Then, all gases would have the same equation of state in the form of reduced parameters ... 

Employing the reduced parameters the equation of Knox takes the following form,... 

In terms of reduced parameters the critical point occurs at Vf =1 and Tr=l. Thus from eq 4.1-2 we can note that at critical point the value of "compressibility factor , also known as the universal constant, is ... 

The velocity profile, Eq. (7.62), can be plotted as a function of position in the gap along the x direction, now given by the reduced parameter, p, of Eq. (7.64). This is done schematically in Figure 7.65. Notice that ai p = X the velocity profiles are flat that is, the flow is plug flow, because the pressure gradient vanishes at these locations. As promised, the pressure profile can also be solved for, for which the result is... 

The usefulness of c tf as an approximate reducing parameter for the zero shear viscosity at moderate concentrations is very well established. Master equations of the form... 

The hat-curved-harmonic oscillator model, unlike other descriptions of the complex permittivity available now for us [17, 55, 56, 64], gives some insight into the mechanisms governing the experimental spectra. Namely, the estimated relaxation time of a nonrigid dipole (xovib 0.2 ps) is close to that determined in the course of very accurate experimental investigations and of their statistical treatment [17, 54-56]. The reduced parameters presented in Tables XIVA and XIVB and the form of the hat-curved potential well (determined by the parameters u, (3, f) do not show marked dependence on the temperature, while the spectra themselves vary with T in greater extent. We shall continue discussion of these results in Section X.A. 

From a macroscopic point of view, yielding of thermoplastic or thermosetting polymers is similar and depends mainly on Tg — T or T/Tg, as a reduced parameter. 

Finally, the parameter describing the dephosphorylation of the internalized receptor is mapped according to a standard lumping reduction [6]. This means that the reduced parameter p D in Adi is equal to the corresponding original parameter pd times the fraction of the total amount of phosphorylated receptors that is made up oflRi- P-ins... 

Some comparisons of the efficiencies of chromatographic separations are facilitated by defining so-called reduced parameters, which correct for... 

Reduced parameters, 66-69 Refractive index (RI) detector, 206-207 Regular solution, 49 Relative retention, 20-21, 22, 77 Repeatability, see Precision Reproducibility, see Precision Resolution, 17-19, 55 Response factors (detector), 104, 125 Response time, 94 Retardation factor, Rf, 71 Retention index of Kovats, 78 Retention ratio, 11, 12, 71 Retention time, 6, 9 Retention volume, 9, 75 adjusted, 10, 75 corrected, 62-63, 75 net, 63, 75 specific, 110 Reverse phase LC, 158 Rohrschneider/McReynolds constants, 137-140... 

The two parameters in the rate equation that have been redefined are the column diffusivity H and the linear velocity u. The reduced parameters, which are dimensionless, are... 

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