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If I fill glass jar with tap water and let it stay, small bubbles will appear on the side of jar after a while.

I am wondering what processes create those bubbles and what conditions require to meet?

My thoughts:

  1. Water impurities, i.e. dissolved salts, minerals. I.e. distilled water shall not have it.
  2. Water pressure. I.e. if I fill and close jar with the same water under higher pressure, air pressure of dissolved molecules of air will not be sufficient to create bubbles.
  3. Surface tension. If, instead of water I will use another liquid with higher surface tension - bubbles will not be formed. Then how to calculate "threshold" tension number?
  4. Air composition. Molecules of dissolved gas that has higher hydrophobic properties will form gas bubbles faster.

Anything else I did not mention.

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You pretty much summed it up.. but an important factor is the history of the water. For example water that has been subjected to temperatures exceeding $35^oC$, would have lost most of its dissolved oxygen (the main gas dissolved in water). On the other hand water that has been vigorously shaken would have replenished its dissolved oxygen, for example this is why when you fill your jar with tap water with a very fast running water, more bubbles will form on the inside edges of the jar, unlike when you pour the water very gently.

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