A one-stage model of the formation of primary bubbles is presented in which the bubble volume is deduced from an equilibrium of buoyancy, viscosity, inertia and surface tension forces. In contrast to the two-stage model, presented by Kumar and Kuloor, it was not assumed that the drag coefficient in bubble expansion can be described by the same constants as in the steady-state bubble ascent. The constants were adapted in such a way that the introduction of an additional bubble volume was not necessary. It was demonstrated that this model describes the bubble formation in gravitational and centrifugal fields equally well and, furthermore, is also applicable to structurally viscous liquids, provided that the effective shear gradient is calculated from the equilibrium of shearing and buoyancy forces. The model is based on the assumption of a constant volumetric flow rate during bubble formation and, for this reason, a minimum Froude number is necessary in analogy to the weeping limit for sieve plates. The normalized presentation permits simple operation. The possibility of applying the model to drop formation was confirmed by comparison of experimental values with those, predicted by the model.
In the description of mixing processes influenced by viscosity in pseudoplastic (power-law) fluids, a definition of representative viscosity is normally used which takes into account the variable flow behaviour of the stirred material as a result of different shear stresses. In this context, the Metzner and Otto concept, which postulates that a representative shear rate is proportional to stirring speed, has become widely known, although the power calculation is inaccurate, particularly in the transient regime between the laminar and turbulent flow. A new model of fluid dynamics in the mixing vessel is presented, based on the increase of the mean flow velocity standarized with the stirrer's tip velocity in the transition regime. It provides a physical explanation for the above deviations. A suitable definition of representative viscosity substantially improves the accuracy of calculations of the stirring power in power-law fluids.
In Stoffaustausch-Maschinen wird im Gegensatz zu Stoffaustausch-Apparaten der Phasendurchsatz oder die volumetrische Stoffaustauschrate oder beides durch bewegte (vor allem rotierende und pulsierende) Maschinenteile im oder am Stoffaustauscher erhoht. Die Steigerung dieser GroOen ist eine Funktion der Schleuderziffer z und der spezifischen Leistung E. Die Ausfiihrungen zeigen, wie die volumenbezogene Phasengrenzflache, die gas-und fliissigkeitsseitigen Stoffiibergangskoeffizienten sowie das Volumenverhaltnis von Maschine zu Apparat von den beiden Wirkungsmechanismen z und E abhangen. AuOerdem wird angegeben, wie die spezifische Leistung E verschiedener rotierender Stoffaustauscher mit der Schleuderziffer ansteigt.
Do we need mass transfer machines?In contrast to mass transfer apparatus, the throughput of the phases as well as volumetric mass transfer rates in mass transfer machines are increased by moving machine parts (especially rotating and pulsating). This increase depends on the centrifugal acceleration expressed as the parameter z and the specific power input E. This paper shows the dependence of the volumetric interfacial area, the gas-side and liquid-side mass transfer coefficients, and the volume ratio of machines and apparatus on the parameters z and E. Furthermore, information is given about the increase of the specific power input E of different mass transfer equipment with rising z.
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