Apparatus geometry

Rojo, V., Guardiola, J., and Vian, A., A capacitor model to interpret the electric behavior of fluidized beds. Influence of apparatus geometry, Chem. Engrg. Sci., 41 2171-2181 (1986)... 

Mechanically stirred gas-liquid reactor performances are affected by the degree of mixing, apparatus geometry, stirring power, flow rate, discharge and feed locations for the gas and liquid. For a correct design, the following requirements must be satisfied ... 

Molecular theories of flow behavior are applied on the assumption that the macroscopic velocity field can be considered to apply without modification right down to the molecular scale. In continuum theories the components of relative velocity in an arbitrarily small neighborhood of any material point are taken to be linear functions of the spatial coordinates measured from that point, i.e., the flow is assumed to be locally homogeneous. The local velocity field is calculated from the macroscopic velocity field. This property of local homogeneity of flow is an obvious prerequisite for any meaningful macroscopic analysis, and perhaps the fact that analyses are at all successful and that flow properties can be determined which are independent of apparatus geometry constitutes a fair test of the assumption. 

The last remaining parameter in the DPM is the individual rising velocity of a dispersed phase droplet in a certain apparatus geometry. The velocities of both phases are related to the two-layer model [65] which is expressed as ... 

Thornton JA (1974) Influence of apparatus geometry and deposition conditions on the structure and topography of thick sputtered coatings. J Vac Sci Technol 11 666-... 

A" is a variable depending on the apparatus geometry (e.g., type and dimension of stirrer)... 

Systematic error, both in experiment and analysis, can only be eliminated by using a wide variety of apparatus geometries and analytical methods. In the present situation, with respect to research support, this can only be done by a cross comparison of the results of a number of laboratories. As a preliminary check we report a number of calculations of macroscopic properties. Any single macroscopic property will not prove the absence of systematic error. 

The reasons behind the specific choice of apparatus geometry can best be shown by a brief review of prior work. The earliest canal type surface viscometer was introduced by Dervician and Joly (8). In this apparatus, an insoluble monolayer is floated on a substrate fluid in a straight channel. The film is forced to flow through the channel by movement of a floating barrier. This motion is resisted principally by surface viscosity. Thus, the small force required to propel the film at a given speed may be measured and used to determine the surface viscosity of the film. A relatively complete theoretical treatment has been provided by Harkins and Kirkwood (5) for insoluble films with Newtonian surface viscosity in deep channels. Actual measurements are typically made in shallow channels, however, which are formed by floating the channel boundaries on the liquid surface. This method is not applicable to soluble surface films, which tend to diffuse through the substrate fluid and pass behind the barrier. Nevertheless, the most accurate values of surface viscosity available have been produced by this approach. 

Figure 3.14. Dependence of liquid flows longimdinal mixing coefficient E on apparatus geometry (I-VIII, see Table 2.2, 3.3) and reaction mixture volumetric rate w.

Figures 6-41 to 6-43, provide information on operating ranges, loading limits, and separation efficiencies of selected agitated columns. Respective data are also given for certain substance systems with a certain mass transfer direction and apparatus geometry. Transformation to full-scale apparatus is only possible based on experimental scale-up knowledge (see, for example, Eq. (6-56)). Optimized dimensions of experimental extractors cannot usually be transferred to technical extractors, though the enlargement in an axial direction is generally smaller than in a radial direction.

Similarly, the expressions for the signals measured with the mass spectrometer can be expressed as functions of the number density, reaction cell and apparatus geometry, G2> the ionization and fragmentation processes in the mass spectrometer, IFP, and the reaction ceU flow conditions. 

Actually in each run one measures the rate of level variation of the water contained in each semicell. Constant rates have always been found within the first 120 minutes of running. Since apparatus geometry is well defined (see Fig.l) from these constant rates, the water flux can be immediately calculated. These fluxes are plotted in the figure against AT for various average temperatures T over the range between + 18°C and + 40°C. Water is always observed to flow from the warm to the cold semicell. Various interesting features are discernible in these plots ... 

Reynolds numbers - as defined by Eq. 4.8 - that correspond to the lower limit of the stable operating regimes of Fig. 4.13 may be denoted by Re n,sf Correlations developed for RCjn.st are summarized in Tab. 4.5. However, it should be noted that Fig. 4.13 and Tab. 4.5 provide only coarse estimates for the stable operation ranges of different types of spouted bed. The reason for this is that even small variations in the apparatus geometry - especially variations in the construction of the gas entrance - can have a significant influence on the fluid dynamics of the spouted... 

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