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Some discussion surrounding this answer on Worldbuilding got me curious.

When water is brought towards a boil, bubbles are formed. Anyone who has ever cooked anything whatsoever knows about this.

However, what about the size of those bubbles? Is the size of the bubbles in the water in any way dependent on the amount of water being heated? If yes, then what is the relationship? Why?

As a bonus question, what happens when the amount of water is small enough that the size of the bubble is a significant fraction of the size of the water as a sphere? Can this happen?

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    $\begingroup$ Regarding your bonus question - have you ever see a water drop "dance" on a hot plate? That's your answer... $\endgroup$ – Floris Apr 25 '16 at 18:40
  • $\begingroup$ @Floris Good point, I hadn't considered that one. $\endgroup$ – a CVn Apr 25 '16 at 18:58
  • $\begingroup$ I think the size of a bubble depends upon its depth within the fluid, the type of gas within the bubble, and the type fluid from which the bubble is originating. I do not recall everything involved in this but I do know for all other variables being constant, the size of the bubble increases as it approaches the surface of the fluid. $\endgroup$ – honeste_vivere Apr 25 '16 at 19:57
  • $\begingroup$ What have you done to try to solve this problem yourself? What research have you done on this topic? $\endgroup$ – sammy gerbil Apr 26 '16 at 22:26
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    $\begingroup$ @sammygerbil sigh $\endgroup$ – Josh Gagnon Apr 29 '16 at 20:38
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Bubbles are formed when the pressure in the fluid is less than the saturated vapor pressure of the liquid at that temperature, modified by surface tension effects.

Surface tension actually increases the pressure inside a gas bubble in water; the approximate increase in pressure is $\Delta P = \frac{2\sigma}{r}$ (see for example this earlier answer). The pressure can be lowered by adding impurities in the liquid that can act as nucleation sites.

For a bubble to start growing, the vapor pressure has to overcome the "net" pressure barrier. When you have a larger volume of liquid, and you are heating it from below (like a pan on a gas flame), then the pressure will be higher if the liquid level in the pan is deeper. The pressure increase at a depth $d$ is $\Delta P = \rho g d$.

This means that the liquid at the bottom has to be hotter in order to start boiling; it also means that as the bubble rises in the liquid, it will more easily grow (both because the vapor inside can expand as the pressure is less, and because, if the liquid temperature is uniform, the lower pressure inside the bubble will allow for additional evaporation into the bubble.)

Finally, as I mentioned in my comment, in the limit of very small volumes of liquid it's possible that the production of steam at the surface of the liquid drop is such that a bubble is never formed: instead the vapor escapes along the bottom of the drop, which ends up suspended on a cushion of vapor.

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Water vapor pressure is a function of temperature (and pressure as well). It increases with the temperature. When vapor is produced on the heat surface, bubble forms. The size of the bubble is determined by the buoyancy and the water pressure at the location.

When the size is large enough, the buoyancy force dominant. The bubble will not stay but rise. Due to the pressure decreasing, the bubble size increases and the bubble moves faster. Buoyancy force can be calculated with, $$f_b=\rho_{water}\times V_b$$ and assuming it is ideal gas $$ V_b=\frac{m_{vapor}\times R \times T}{P_{water}}$$ and the bubble gravity is $$m_{vapor}g$$

When the size is not that large, bubble stays at the bottom, collects more vapor and increases its size.

So you can say it depends on amount of heat (how much vapor produced) but it also depends on temperature and pressure. In non-gravity environment, the bubble can keep growing when surface tension is needed to keep the bubble, which may be used to answer your bonus question.

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