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I know that if two air bubbles which are formed inside a liquid are somehow joined using something (say a small tube), then, as the bubble with the larger radius has less pressure and the one with the smaller radius has more air pressure, air will flow to the larger bubble from the smaller bubble as the excess pressure inside the smaller bubble is greater.

But will we be able to quantitatively calculate the time taken for this to happen?

If so then what is the relation connecting time and every other variable?

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It is possible to write a relationship between flow and pressure drop in a tube. If the flow is laminar, this will be given by the Hagen–Poiseuille equation (http://en.wikipedia.org/wiki/Hagen%E2%80%93Poiseuille_equation). For turbulent flow, phenomenological correlations can be used (http://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equation). With this, it is possible to calculate the flowrate between the two bubbles and how it varies with time.

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