Characteristic dimensionless

Consequently, the characteristic dimensionless rate group for the second-order reaction and initial conditions is given by... 

Another approach is to regroup the characteristic dimensionless variables in the problem so that the unknown (D. ) appears in only one group. After rearranging Eq. (7-25) for /, we see that the following group will be independent of Dcc ... 

In a series of studies, summarized in Ref 18, Merzhanov and co-workers examined conditions under which thermal explns may be quenched. This theoretical analysis provided two characteristic dimensionless parameters which determine the conditions for quenching. These are Kcr obtained from inflection points of 0M vs k plots (0M is the max value of 6), and a quantity e = [(6m/k) (deM/dK)] =Kcr,whichisa measure of the uncertainty in the determination of the critical conditions. Both CI and are functions of 0 and 7, which (as well as k and 0) are defined as follows ... 

Using characteristic values is a widespread and helpful means. An example for material characteristics is the specific energy input based measured in kWh/kg (see Section 6.5.1), while the available torque/axis distance measured in Nm/m3 is a machine characteristic. Dimensionless parameters (with the unit 1) play an important role for scale down/scale up considerations. The Reynolds number is a known dimensionless parameter, determining whether flow is laminar or turbulent. However, it is of little importance for extruder scale downs/scale ups. 

On a RDE, in the absence of a surface layer, the EHD impedance is a function of a single dimensionless frequency, pSc1/3. This means that if the viscosity of the medium directly above the surface of the electrode and the diffusion coefficient of the species of interest are independent of position away from the electrode, then the EHD impedance measured at different rotation frequencies reduces to a common curve when plotted as a function of p. In other words, there is a characteristic dimensionless diffusional relaxation time for the system, pD, strictly (pSc1/3)D, which is independent of the disc rotation frequency. However, if v or D vary with position (for example, as a consequence of the formation of a viscous boundary layer or the presence of a surface film), then, except under particular circumstances described below, reduction of the measured parameters to a common curve is not possible. Under these conditions pD is dependent upon the disc rotation frequency. The variation of the EHD impedance with as a function of p is therefore the diagnostic for... 

In Eqs. (202)-(203), tjH is the characteristic dimensionless local thermal mixing time, which is given by... 

As in the analysis of catalytic reactions we make the modelling equations dimensionless and establish the characteristic dimensionless parameter combinations associated with the LPCVD process. By defining ... 

The transition between both globular structures and the coil state turns out to be the first order phase transition. The relation between the free energies of structures A and B depends on the temperature and on the characteristic dimensionless parameter /7a. The latter dependence is manifested already at the temperatures which are much lower than the coil-globule transition temperature, i.e. formally at A > l13. In this region, the following simple result can be obtained ... 

By examining these characteristic dimensionless numbers, it is possible to appreciate possible interactions of different processes (convection, diffusion, reaction and so on) and to simplify the governing equations accordingly. A typical dimensionless form of the governing equation can be written (for a general variable, (p) ... 

Rhodamine B was added to the tank inflow, and the resulting effluent concentration was recorded as a function of time in a double-beam (Zeiss) spectral photometer. These measurements were evaluated statistically in order to describe the hydraulic characteristics of the tanks. Effluent concentrations of the tracer, dosed as a delta impulse, observed for different (hydraulic) surface loading (q = 0.28, 0.58, and 1.0 m/h) were evaluated in terms of a characteristic (dimensionless) number, the dispersion number (4), and shown in Figure 3. 

In the model [57], the coumarin coverage is defined by a Langmuir isotherm (Equation 2.2) with electrochemical reduction of the adsorbed coumarin (Equation 2.9) being balanced by diffusion of coumarin to the interface (Equation 2.3). Incorporation of the coumarin in the solid was considered to be negligible. The results of the model have been summarized by three characteristic dimensionless groups, X, y and p ... 

In order to enable the prediction of the purification effect of the rinsing step, Wangnick (1994) introduces a characteristic dimensionless number won from a dimension analysis of all influencing parameters... 

The foundation of similitude theory is that there is no law of nature depending on the dioke of units used for describing the corresponding phenooKnon. Consequently, these laws can be expressed by relations between dimenaonless quantities termed similitude param rs (see Table 1). a) Characteristic dimensionless group... 

Calculate the characteristic dimensionless velocity at the surface for bubble flow Wg b for bubble flow Wg must be larger than Wgb, where... 

Calculation of the characteristic dimensionless velocity at the liquid surface for chum turbulent flow Wg a according to Eq. (10.13) gives... 

A characteristic dimensionless number that Synonyms determines the nature of fluid flow in a given setup. 

This liquid flow trapping affects the quality of distribution. Hoftyzer (196 ) analyzed the dispersion from a variety of distributors e.g., a central stream, disc, ring, annular disc and an eccentric stream. This study showed that the characteristic dimensionless group for all geometries is given by... 

Hence, the semidilute solutions with a high value of the characteristic dimensionless parameter cS have the tricritical properties if and only if the other dimensionless parameter c. So turns out to be. small to satisfy inequality 190. 

The characteristic dimensionless numbers such as Reynolds number (Re) and Peclet number (Pe) are very suitable for discussing the operating conditions for micromixers. From the definitions in Equations (7.1) and (7.2), the relation... 

Table 27.8. Characteristic dimensionless numbers for Newnans Lake. ...

In the qualitative sense one can arrive at a similar conclusion as above regarding the bed by examining the magnitudes of characteristic dimensionless parameters (Table 27.8). Observe that Sw/h = 0.0005 from water. The Mach number Mao is about 0.14, which means that wave speed in water would be about seven times that in mud, a manifestation of the significant role of mud as an energy dissipater. The very low value (0.002) of r]"/rim, the ratio of loss due to mud elasticity to mud viscosity, corroborates the inference that the muck was more like a fluid than a solid. 

One such study by Hoftyzer [29] proposed a characteristic dimensionless parameter Iz/y to characterize this dispersion. 1 is the lateral dispersion coefficient, z is the axial distance down the bed required to achieve the equilibrated condition, and y is the radial distance for which this equilibrated uniform flow is found. The dispersion coefficient can be quantified by using the data from several workers [24], [52], [72], [89] as shown by Koros [35]. Thus, a value can be obtained v ich gives the com-... 

The above expression is formed by combining Eqs. (3.1), (3.2), (3.3) and (3.5). The expression is dimensionless and independent of the natme of the system, temperature, heating rate or any other factors that influence the rate. Therefore, it is evident that every possible reaction mechanism will exhibit dimensionless characteristic values at particular temperatures for the heating rates Pi and p under consideration. Hence, it is quite possible that the actual mechanism of a solid state reaction under non-isothermal condition can be identified by matching the characteristic dimensionless theoretical values of g ( /) (7/) for different... 

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