Shaken, then opened, soda fizzing?

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I am aware that shaking an unopened bottle of soda imparts energy, creating turbulence and forming bubbles. Therefore, if the bottle is then opened the drink 'fizzes' out due to increased effervescence. If the bottle cap is unscrewed slowly then this fizzing appears to be reduced. My question is this: Is that reduction simply due to giving the carbon dioxide more time to redissolve or is there another mechanism at work, for example, due to the increased time over which the pressure in the bottle changes when then cap is unscrewed slowly.

Additionally, what effect does carbonation have on the freezing point of water and what effect might this have on the 'instant freezing' effect observed when a bottle of soda/ beer is super cooled and then tapped/ opened providing nucleation sites?
 
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Welcome to PF;
The rate that CO2 leaves solution depends on how much is in solution, the energy it has, and the pressure of the gas above the liquid surface (and other things too). When you open the bottle quickly, you create a sharp drop in pressure above the gap - making for a more violent reaction.