TITLE: Why can't CO$_2$ mix back with the liquid after a soda bottle has been shaken?
QUESTION [16 upvotes]: If you shake a soda bottle before opening it, and then open it, you get the fizz.
That is the compressed CO2 releasing to the atmosphere which is at comparatively low pressure value.
Two questions (related)

Why does shaking a bottle make the compresses gases un-dissolve?
Why can't the gases dissolve back into the liquid?

REPLY [8 votes]: I cannot see, above, the correct answer to the first part of the question. They all have the second part right. 
The first part: Why does shaking the bottle make it fizz when you open it? 
The gas is in solution in the closed, unshaken bottle. The solubility of that gas in that liquid at that temperature and that pressure dictates the saturation level of the gas in the liquid. Any more gas than that and it bubbles out, increasing the pressure inside the closed bottle and forcing more gas in solution thus reducing the pressure. An equilibrium is reached.
But why does shaking cause a problem?
Because when you shake it, you slosh the contents around. The liquid flows quickly from one end of the container to the other. As it does so, it flows fast enough to become turbulent. In the turbulence, the curlicues, the intricacies, the eddies and the complex flow there are many locations in the liquid where the local pressure is forced lower than the saturation pressure. This is because any packet of liquid that is accelerating in any direction will leave a low pressure zone in its wake.
When the pressure is forced below the equilibrium level, the gas (given sufficient nucleating seeds) will come of of solution instantly given that the operation is occurring in the bulk and gas bubbles can be created anywhere in 3D.
But when the gas wants to go back into solution it is severely limited by the relatively small surface area of the liquid in the neck of the bottle. There is only a tiny surface available for gas transport through the liquid/air interface. We are severely dissolution rate limited. It can take hours for a shaken can to quiet down. It can be hastened by chilling as more gas can always be dissolved in a cooler liquid.
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