The results would have to depend on how much CO2 is in the beverage to begin with. This unofficial page says the initial volume of CO2 (at 1 atm) is about four times the liquid volume, and the pressure required to keep it in solution is about 2 atmospheres. I dunno how standard or accurate that is, but it seems like a reasonable place to start.
The amount of CO2 in solution is linearly proportional to partial pressure (I believe), so (for example) a drop in partial pressure from 2 atm to 1 atm would cut the “fizzyness” in half.
If you had a 50% empty bottle where the pop started with a nominal amount of CO2, the capped it, the system would regain equilibrium when 1/3 of the CO2 had left the pop, giving a partial pressure of 1-1/3 atm of CO2. If you had scrunched the bottle to minimize head space, it would be pressurized to 1-1/3 atm absolute. If you hadn’t scrunched the bottle, it would be pressurized to 2-1/3 atm absolute. So no difference because of scrunching.
If you started with pop that was already half-flat (the initial volume of CO2 in the pop is about twice the liquid volume), and a bottle that was 50% empty, the two things could happen. If you DON’T scrunch the bottle, 1/3 of the CO2 would come out of solution, and the bottle would wind up pressurized to 1-2/3 atm absolute (one atm of air and 2/3 of CO2). If you DO scrunch the bottle, CO2 would leave solution and fill the head space UNTIL the system reaches equilibrium, with 1 atm (or a bit less) of CO2 partial pressure above the pop. That would mean less CO2 leaves the pop than in the non-scrunched case, and your delicious beverage is more fizzy than it otherwise would have been.
(I believe the above is approximately correct, but would welcome additions and corrections from chemists and beverage scientists.)
In terms of the original question, what I’m getting from the folks who posted with very well reasoned explanations (and who also know much, much more than I do regarding the physics in play here) is that the real answer is “it depends on any number of things”. Nobody has mentioned refrigerated vs. room temperature yet, but I’m willing to guess that plays a part as well. Thus, my prediction for this question is that ultimately, over time, the squishers will receive about the same fizzy benefit as the non-squishers.
And, as an aside…
My mom went through this phase where she would leave a bottle of cola in the fridge for days, without the top on. She did this specifically to get rid of as much carbonation as possible. Mom, you know I love you… but sometimes you are gross
Eh, it seems to me that how much of the gas is CO[sub]2[/sub] wouldn’t really matter. Sure, you’ll only get carbonization with carbon dioxide, but we don’t really care about carbonization; we care about little bubbles in the drink. If some of those little bubbles are nitrogen and oxygen instead of CO[sub]2[/sub], what’s the difference?
Because carbonation isn’t just about little bubbles in your beverage, it’s about the distinct flavor imparted by the carbonic acid produced which results from dissolved CO[sub]2[/sub]. You’ve never tasted flat soda? It’s nasty on a level much different than the mere lack of bubbliness.