The Influence of Orifice Orientation on Bubble Formation

The Influence of Orifice Orientation on Bubble Formation A. Introduction 

Almost all the results reported in literature pertain to studies with horizontally oriented orifices, and the discussions in the preceding sections are applicable only to such orifices. In industrial applications, however, the orifices are usually oriented at various angles, the most common (as in the case of the bubble plates) being n/2 from the horizontal. 

The first quantitative attempt (K12) in this direction was made with vertical orifices, under constant flow conditions. Here, the bubble formation is considered to be occurring in two distinct steps. In the first stage, the bubble is assumed to expand at the tip, moving vertically at the same time. As the bubble is formed at an angle to the vertical, a vertical component of the surface tension force will be operative during this stage. The first stage is 

In the second stage, at any particular instant, the bubble is assumed to be moving with a Stokes terminal velocity corresponding to its size at that instant. Thus, 

The second stage is assumed to end when the base of the bubble has covered a distance equal to the orifice diameter. Thus, 

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