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If you take an ordinary sized plastic water bottle full of water and pour a packet of powdered (or liquid) drink mix into it, Will shaking the bottle with the cap screwed on to dissolve the mix into the water work better if there is a small amount of air inside the bottle? Or does it not make a difference at all and will shaking work just as well with no air bubbles at all in the bottle?

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up vote 6 down vote accepted

Within reasonable limits, the more air in the bottle the better the mixing.

This isn't to do with air bubbles. To get good mixing you need turbulent flow, and for that you need high flow velocities. If the bottle is completely full it's hard to get a high flow velocity started because for water to move it has to push other water out of the way. If the bottle is only half full the moving water only has to push air out of the way, and air is both much more compressible and much less viscous than water. For any given amount of shaking effort you'll get higher flow velocities and therefore better mixing if there is a substantial amount of air in the bottle.

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After a certain level of bubble fraction, bubbles' surface tension would start stopping the process.

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