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When I boil water in the kettle, many tiny bobbles appear after a short time, long before boiling (See video here). They don't seem to come from the bottom of the kettle, like in boiling, but from inside the water.

The strange thing that I don't understand is, why are those bubbles not moving up?

It seems like there are many streams created inside the kettle, and the bubbles are carried in a random direction.

This only happens when I take the hot tap water. I don't see such bubbles with the cold water.

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the "early" bubbles which form before the kettle begins to boil are bubbles of air which come out of solution because air is less soluble in hot water than in cold water.

Those bubbles are very small in comparison to the viscosity of the water, which means they are easily moved about by convection currents in the water, and they rise slowly.

Now, note that the top-most part of the kettle is cooler than the bottom-most part, where the heat is being added. So air comes out of solution in the hottest part of the kettle, is carried around by the currents, and rises slowly. In so doing those bubbles encounter cooler water and redissolve before they reach the water surface.

Hot water under pressure in pipes can hold more dissolved air than at atmospheric pressure. Once the hot water exits the faucet valve, its pressure drops to atmospheric and the dissolved air tends to come out of solution and produce a milky/cloudy suspension of very small bubbles in the water. This process depends on how much air was in the water to begin with and how much time the water spent in the water heater, getting degassed.

Cold water can contain significant amounts of dissolved air and does not become supersaturated when dropped to atmospheric pressure upon exiting the faucet.

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