In airlift systems, there'is a mixture of air and liquid water whuch in an upward flow in a pipe called riser, we wish know the effect of pubble size on the liquid flow rate.
Depending on the size of the duct and the characteristics of the flow, the influence of the bubble on the flow can be from very small to very large like stopping the flow.
for air lift system there bubble diameter is correlated, but for the influence of bubble diameter on the liquid flow rate that is related by flow regime, for void fraction is less then 0.3 its the bubbly regime where gas have a bubble form. for void fraction between 0.3 and 0.55 bubbles are a slug form its diameter is near of tube diameter, in this regime liquid and gas have the same velocity (m/s). for other regime churn and annular liquid velocity is less then gas velocity
What you're describing is the subject of two-phase flows. Hence, the flow rate of this two-phase flow system is a function of how the bubbles are distributed in the pipe. There are several two-phase flow types as follows:
1) Mist flow where the bubbles are small and well-distributed in the liquid phase.
2) Slug flow where the bubbles form slugs that fills all the cross-section of the pipe and separated liquid slugs.
3) Film flow where the liquid forms a film near the wall of the pipe and the bubbles for the core of the two-phase flow system.
In summary, the flow rate will depend on the void fraction (alpha) occupied by the bubbles.
Hope this helps answer your question.
Professor Yehia Khalil, Yale University, USA
Fellow of the University of Oxford, UK
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