How do bubbles on water surface merge?

Question

When we open a tap over a water surface, we get to see a lot of bubbles ("half merged in the water") coming out on the surface.

Now what I saw was that two such nearby half bubbles merge to form a bigger one. But I couldn't really think of what goes on at the point of contact between them. How exactly does air gets transferred from one to the other? Another point which I wanted to mention was that in such mergers, the bigger bubble gets bigger and the smaller one vanishes which is opposite to what I read in my high school about bubble mergers.

So someone please clarify what goes on at the interface.

Answer 1

I aimed to expand on John Rennie's comment by adding more details to clarify his answer based on my understanding.

Coalescence

Happens fast. When two bubbles merge,the smaller one quickly disappears into the larger one because of the pressure difference. The math behind it involves the pressure differences due to surface tension. The pressure inside a spherical bubble is given by the Young-Laplace equation:

$$ P_{\text{inside}} = \frac{2 \gamma}{R} + P_{\text{outside}} $$

$ \gamma $ is the surface tension of the liquid, $ R $ is the radius of the bubble and $P$ is the pressure outside the bubble (like the air pressure around us).

When you have two bubbles,one smaller and one larger:

• The smaller bubble has a higher internal pressure because its radius is smaller.
• This pressure difference drives the gas from the smaller bubble into the larger one when they touch.

So, if the smaller bubble’s pressure is $ P_1 $ and the larger bubble’s pressure is $ P_2 $, the difference between these pressures is:

$$ \Delta P = P_1 - P_2 = \frac{2 \gamma}{R_1} - \frac{2 \gamma}{R_2} $$

Since $ R_1 $ (the small bubble) is less than $ R_2 $ , $ \frac{2 \gamma}{R_1} $ is bigger than $ \frac{2 \gamma}{R_2} $. That means the smaller bubble’s pressure is higher, pushing its gas into the larger bubble.

Ripening

Happens slowly. It’s the gradual process where gas moves from smaller bubbles to larger ones over time through diffusion. The math here involves how gas spreads out through the liquid film.Gas moves through this film due to diffusion, which is essentially the movement of gas from areas of higher concentration to lower concentration. The rate of gas transfer between bubbles is governed by Fick’s law of diffusion. For a gas diffusing through a thin liquid film of thickness $ \delta $, the rate of change in gas volume $ V $ in a bubble is proportional to the pressure difference and inversely proportional to the film thickness: $$ \frac{dV}{dt} = \frac{D \cdot A \cdot \Delta P}{\delta} $$ $D$ The diffusion coefficient of the gas (how easily it moves), $A$ The area of the film between the bubbles $\delta$ The thickness of this liquid film. Here,$ \Delta P $ is the pressure difference driving the diffusion.

So, if you’re seeing bubbles merging quickly, coalescence is likely the process at play. For gradual size changes, ripening is the mechanism to consider.