Hydrodynamics of rising bubbles and drops

Abstract

An analysis of the problem concerning the interaction of moving single formations (bubbles and drops) with the surrounding carrying medium shows the possibility of describing real physical processes within the frameworks of the models of ideal and viscous liquids. Generalization of experimental and theoretical data is made by constructing charts of flow modes. A successful selection of the dimensionless numbersRσ andRν as coordinates made it possible to arrange in an ordered fashion in the diagram all of the media by means of the parameter M, with the data for each specific medium being located on a certain straight line whose slope is determined by M. Vast computational data both of the present author and of other investigators for the region of small and intermediate values of dimensionless parameters, converted into theRσ,Rν functions, made it possible to fully display the region inaccessible for investigation when the effect of all the parameters is significant and their number cannot be reduced. The use of these very parameters for correlating the data of the problem of steady rise of a drop made it possible to simply demonstrate the influence both of the presence of the medium itself and its motion on the drop rise. Comparison of the data with the problem of bubble rise can be made by simple superposition of diagrams. The logical clarity of the parametersRσ, which is equal to the ratio of the equivalent radiusa of a bubble (drop) to the capillary constant of the surrounding medium δσ, allowed the determination of a certain critical sizea after which waves appear on the surface at the back side of the bubble (drop) when the value ofa is higher than 2-3δσ. Another form of instability of steady rise is associated with the formation of a stagnant zone and with the separation of flow from the surface of a bubble or drop characteristic for surrounding media with small values of M. The use of the parametersRσ andRν will definitely significantly simplify the analysis of more complex problems, for example, the problems of the motion of bubbles and drops in tubes with liquid and also the change in the external conditions (reduced or increased gravitation).