Dispersion coefficients, apparatus

The dispersion coefiicients can now be foimd from the Ni/q by a nonlinear calculation procedure, such as the Newton-Raphson method, utilizing the expressions for Nt, Eqs. (56) or (57). In the general case, values of Pli, Psit Pl2, Pr2, and the physical dimensions of the apparatus are substituted into Eq. (56) or (57), and then Pl and Pr can be found from the simultaneous (nonlinear) solution of the expressions for Ni and N2. The variances of the dispersion coefficients could also be found from the variances of the Ki by standard statistical methods. 

Variation with Water Flux of Soil and Apparatus Dispersion Coefficients... 

TThe subscript A indicates the dispersion coefficient used for the layer which describes the dispersion induced by the apparatus. 

Possible optimization of pastes and the according apparatus in process engineering by MRI flow experiments were described. The spatially resolved determination of velocities in suspensions by means of NMR imaging techniques was applied to steady tube flows (with regard to the total flow rate) in different geometries. Three types of suspensions with different solid volumetric concentrations were examined in order to demonstrate the effect of the material-specific flow-behavior and of the geometry of the experimental set-up on the observed flow pattern. The local probability distribution of single velocity components is determined and then both the local mean value and the standard deviation can be derived from the probability distribution. The standard deviation can be interpreted as the local dispersion coefficient of the velocity component. 

On the base of experimental data the equations correlating emulsification effectiveness (percentage content n of disperse phase drops with diameter d 0,8mm) in tubular canals of divergent-convergent design with flows rate w (R - correlation coefficient, apparatus numbers are in Table 2.1) were obtained ... 

The fascinating aspect of this apparatus is the way in which the diffusion coefficient appears. Equation 5.6-8 has the same mathematical form as Eq. 2.4-14, but the dispersion coefficient E replaces the diffusion coefficient. So far, as good. However, E varies inversely with D, as explained in Section 4.4. Consequently, a widely spread pulse means a large E and a small D. A very sharp pulse indicates small dispersion and hence fast diffusion. 

Inlerfacial Contact Area and Approach to Equilibrium. Experimental extraction cells such as the original Lewis stirred cell are often operated with a flat liquid-liquid interface the area of which can easily he measured. In the single-drop apparatus, a regular sequence of drops uf known diameter is released through the continuous phase. These units are useful for the direct calculation of the mass flux N and hence the mass-transfer coefficient for a given system. In industrial equipment, however, it is usually necessary to create a dispersion of drops in order to achieve a large specific inlerfacial area. u. defined as the inlerfacial conlael area per unit volume of two-phase dispersion. Thus the mass-lransler rale obtainable per unit volume... 

Due to fine-disperse emulsions reception at high dispersion medium movement s rates w and under apparatus No.8 use (Table 2.1) microscopic method was used in this work in spite of photograph analysis of disperse inclusions. Microscopic method was realized with the help of LOMO-MIKMED-1 microscope with screw ocular micrometer EFM-16X-E (twenty-fold increase). Microscope method is described in [108]. In the work lower limit of disperse phase diameters for photographic method was about 0,2 mm, and the high level under microscopic analysis was 0,5 mm. Results of two methods of obtained emulsions analysis correlated with coefficient not less than 0,95 (Fig. 2.5), that allowed investigation of received emulsions in interval of disperse inclusions sizes broad enough (diameter from 0,01 to 3 mm). 

Polydispersity coefficient ko (1.22) is one more important magnitude characterizing resulted emulsions. For monodisperse systems - kn = 1 and for polydisperse kn < 1, and the lesser the ko parameter value, the bigger the dispersal of particles by their sizes. The ratio Ls/dd practically doesn t influence on resulted emulsions polydispersity as in the case of dispersions formation with surface-volumetric diameter d32 (Fig. 3.33). Particles dispersal is increased when dd/dc ratio is raised and sufficiently homogeneous emulsions are formed in divergent-convergent canal of tubular apparatus with dd / d = 1,6. In particular for Ls / dd = 2-3 the value of ko at dd / dc = 1,6 is 0,72-0,75, where as at da / d = 2 and 3 kn is decreased down to 0,63 and 0,41 accordingly. 

There are two possibilities fisr determinatirm of the axial mbdng coefllcients, respectively the Pellet numbers. The first is to obtain them fiom mass transfer experiments and the dispersion mass transfer model using optimization procedure. The second is to determine them separate using tracer methods. By the first method the Bodenstein, respectively Peclet, numbers for both phases are calculated together with the volumetric mass transfer coefficients for the gas and the Uquid phas. This leads to enormously grt influence of the primary eiqperimental error on the obtained results. The error is especially great for the cases when the influence of the respective obtained values on the mass transfer in the packing is comparatively slight. That is why the so determined values are reliable only for fee oases they ate obtained in, for mcample for automation purpose. They are not fee best solution for calculation of new apparatuses and new processes. That is why in this book only fee tracer method is considered. 

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