Calculation of primary bubble volume in gravitational and centrifugal fields

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\documentclass{article}\pagestyle{empty}\begin{document}$$ \mathop {\rm \gamma }\limits^. = \frac{1}{6}({\rm \Delta \rho }gzd_{\rm B} /{\rm \eta }) $$\end{document}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.