Bubble Formation under Constant Pressure Conditions

Bubble Formation under Constant Pressure Conditions 

The constant pressure condition arises when the chamber volume tends to infinity (in practice, more than about a liter), and the pressure in the gas chamber remains constant. As the pressure in the bubble varies with the extent of its formation, the pressure difference across the forming device also varies, thereby bringing about a condition of changing flow rates. 

These authors have assumed the bubble to be expanding at the orifice, and have used the force balance equation at the time of detachment. The various forces considered by these authors are buoyancy, force due to the addition of mass (P2), excess pressure force, surface tension force, drag force, and force due to the inertia of the liquid. 

Considering all the above forces, and applying Newton s second law of motion, we obtain 

To obtain bubble volume by Eq. (62), the various terms are evaluated at a time just prior to the release of the bubble. Thus, 

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V. Bubble Formation under Constant Pressure Conditions. 304... 

The set of Eqs. (94) and (95) are quite general in nature, and are applicable to bubble formation under constant pressure conditions, in the range of single bubbling. 

These authors have extended the concepts developed by Kumar and Kuloor (K16, K18, K19) for bubble formation under constant flow conditions to the situations of constant pressure conditions. 

Fio. 3. Equipment for bubble formation under constant flow and constant pressure conditions. 

Data on Formation of Air Bubbles in Water under Constant Pressure Conditions... 

Fig. 15. Comparison of the model (S3) with the data collected for bubble formation in inviscid liquids under constant pressure conditions.

For many purposes, approximate predictions suffice, and may be obtained from the results for constant flow formation using some simple guidelines. Bubbles obtained under constant pressure tend to be larger than under constant flow conditions at the same time-mean flow rate, Q, because most of the flow with variable Q occurs during the latter stages of formation. It is convenient to define a ratio of bubble volumes formed under constant pressure and constant flow conditions as... 

The bed depth has no influence on the size of the bubble produced. This indicates that the bubbles are foxmed under either constant flow or constant pressure conditions. In the intermediate region, Padmavathy, Kumar, and Kuloor (PI) have shown that the bubble volume in an air-water system is highly sensitive to the variation in the depth of the liquid column above the bubble forming nozzle. As the bed has no surface tension, no variation of flow is expected during bubble formation, and the conditions of constant flow are approximated. This explanation is due to present authors. 

For bubble formation from a single orifice without a gas chamber, the motion equation of the rising bubble itself is sufficient to predict the initial bubble size. For the case in which the orifice is connected to a gas chamber, the gas flow rate through the orifice is not constant and depends on pressure fluctuations in both the chamber and the bubble. In order to simulate bubble formation under such conditions, the pressure fluctuations in the gas chamber and in the bubble must be considered to account for the time-variant orifice gas flow rate as illustrated below. 

The effect of pressure on the initial bubble size under various bubble formation conditions is shown in Fig. 3. The solid lines in the figures represent the model predictions. Under constant flow conditions (Yc < 1), the pressure effect on the initial bubble size is not significant however, under variable flow conditions Nc > 1), pressure has a significant effect on the... 

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