When a cork is pulled out of a wine bottle, why does the inner end often expand more than the outer end? When I pull a cork out of a wine bottle, it usually expands slightly in circumference. This makes sense: you want the cork to be slightly compressed relative to its natural diameter when it's inside the bottle in order to make a tight seal.
But I've noticed that the cork usually expands asymmetrically, with the end that was originally toward the inside of the bottle expanding significantly more than the end that was toward the outside of the bottle. After the cork is pulled out, it usually ends up noticeably asymmetrical, with the inner end wider than the outer end. This isn't just true for mushroom-shaped champagne-style corks, but also for corks that (as far as I can tell) are perfectly cylindrical and symmetric when they're initially inside the bottle.
In fact, the asymmetry in the expanded cork is often so pronounced that the end that was initially toward the inside of the bottle has expanded so much that I can't fit it back into the bottle, but I can fit the end that was initially toward the outside into the bottle. That is, I can't fit the cork back into the bottle in its initial orientation, but if I flip it upside-down then I can fit it in.
What causes this asymmetric expansion (for still wine corks)? Do the manufacturers actually make the corks asymmetric for some reason? Or does it have something to do with the fact that the corkscrew is penetrating the outer end of the cork but not the inner end, so the force is applied unevenly? Or maybe something to do with the difference in air pressure on the two ends as the cork is pulled out? Or maybe I'm just making up this whole phenomenon? (Although other people I've spoken to have noticed it as well.)
It seems to me that the asymmetry is much more pronounced for synthetic corks than for natural ones, so I suspect that it may have something to do with corks' material properties.
 A: Not specifically a cork expert, but I do work as an analytical scientist in an Australian commercial wine testing laboratory. (@Barmar, hope that is sufficient expertise!)
To answer @tparker first; Corks are not tapered, as they are cut by coring the peeled bark of the cork oak with spinning/rotating knives or punches (See Riboulet and Alegoet 1994 "Practical aspects of wine corkage" ISBN 2 9054208-07-04)for more on this). Corks are therefore nominally the same diameter along their length when prepared. Cutting a taper on cork might be possible, (perhaps https://woodworking.stackexchange.com/ might help here) but quite difficult and not worth the effort for bottling hundreds or thousands of bottles at a time.
As to the different expansion of cork at each end, I spoke to one colleague who suggested "the reason is that the internal diameter of the bottle increases with increasing distance from the finish of the bottle (the ‘finish’ = the very top of the bottle) – that is, after a short distance of somewhat consistent internal diameter, the diameter starts to increase (the internal diameter is sort of cone-shaped if viewed from side-on, which helps keep the cork in the bottle!).  Consequently, the section of the cork at the bottle finish is more compressed than the opposite end. I suspect that the more a substance is compressed towards its elastic limit, the less likely it is to revert to its original shape – this would explain the observations."
According to the French manufacturing standard CETIE BV4, standardised modern bottle necks are 18.5 mm ± 0.5 mm at 3 or 4 mm down the neck and 20.0 mm ± 1 mm 45mm down the neck (Riboulet and Alegoet 1994). I couldn't access the CETIE documents on the website directly as they seem paywalled (https://www.cetie.org/en/the-ceties-documentary-database_122.html). Even screw-capped bottles (the predominant packaging format here in Australia) have a 5-7degree taper over the 50-60 mm at the top of the neck before the screw fitting. Manufacturing a cylindrical rather than tapered bore would weaken the top or bulk up the lower part of the neck (See Stelzer 2005 "Taming the screw" 978-0958062848 for more details on these).
For those that require evidence, I checked with another colleague who stated that wine bottle necks are indeed tapered internally, even if the outer dimensions appear to be uniform down the neck. He provided some data from some tests we ran on bottle neck consistency last year. The graph below shows neck diameter from top of bottle (0 mm) to 45 mm down. (Graph rotated 90degrees because I couldn't find a quick way to do it vertically).

Most of the bottles are narrowest (about 18.9 mm diameter) at the top of the bottle  then the diameter increases from (~19.4 mm up to almost 21 mm) between 25 mm to 50 mm down the bottle.
@njzk2, there is pressure in a bottle of wine, even if it is "atmospheric" pressure (STP in my old physics textbook). Although, wine can be packaged under positive or negative pressure if the wine has been heated or chilled at bottling. I have measured both + and - pressure in "still" wines in the order of -10 to +40 kPa with a pressure gauge mounted to a wide bore needle pushed through the cork. Sparkling wines can reach 400 kPa which is "exciting" when opened at STP.
I haven't seen what happens to a cork removed after being inserted into an empty, dry bottle, but I imagine it will still expand at the lower end due to the slightly lesser compression it experiences, compared to that at the top of the neck. Moisture in the cork probably increases expansion due to rehydration of the cork cells, but it is probably a smaller contribution than the de-compression following removal.
A: Just to add another random guess (tho' at least for natural cork I agree it's largely moistoure):
If the cork is long enough that the bottom extends past the narrow portion of the neck, then that section is not compressed.  When you remove the cork, the compressed (upper) section demonstrates hysteresis and may never expand back to its original manufactured diameter.
A: It could simply be that the end of the cork that was in the bottle has greater moisture content, so it has a tendency to expand. Wood typically expands when it absorbs water. If you waited long enough for the cork to dry would it still show a difference in circumference?
A: Wine corks are cylindrical before they go into the bottle. When you remove the cork then they may have different shapes.

Not all corks have the tapered shape. Only some.
Champagne corks
The tapered shape is especially present with champagne wine corks. Below you see the before and after image of a Champagne cork. The top is wider because the cork does not fully enter the bottle. But the bottom is tapered. The reason for this is that the bottom is made out of two dense cork disks rather than agglomerated material. The material is different.
The degree to which the bottom part expands depends on the age and the shape is given names juponne (strongly tapered like a petticoat) for young corks that expand a lot, and cheville (little tapered almost straight like a wall plug) for old corks that expand less.

Regular wine corks
The tapered shape can still be present with other corks that do not have these disks on the bottom.
Plasticiser
A reason for this can be that the water activity of the cork is different on the inside than on the outside and this changes the properties of the cork material.
One the one hand water works as a plasticiser and the Young's modulus decreases when corks are more humid (this is possibly why people sometimes soak wine corks in water before bottling). So you would expect that the wet bottom side of the cork is expanding less extremely but possibly the hysteresis is stronger for the dryer top side (although I can't find any sources about this).
Also an aging effect like with the champagne corks might play a role. The wine cork will not return fully to it's original shape after having been compressed for such a long time and the dryer side might be more rigid and rearrange less fast or structures could have been broken which did not happen as much on the wet side.
Swelling
Another effect is that cork expands when it is more humid. This effect is described in this article:
Rosa, M. Emília, and M. A. Fortes. "Water absorption by cork." Wood and fiber science (1993): 339-348.

"Water absorption in the cell walls causes the expansion of cork"

Bottleshape
These images from https://winemakersacademy.com/cork-closures-oxygenation/ show that it appears that the bottle neck does not cause the shape.
In this image the neck is straight and the cork still comes out tapered. It is also visible untill what point the wine entered into the pores of the cork and it is that line where the difference between the diameter is more pronounced.

However, the effect that causes this correlation might be reversed (the cork shape causes the wine to go up, instead of the other way around). If the bottleneck is tapered then the bottom part is compressed less and it is that what might cause the wine to move up the cork.
As explained in the answer by FourW bottlenecks are not completely cylindrical and instead slightly conical. Other sources for this are in Prades López, C., and M. Sánchez-González (2019). They refer to European standard EN 12768 which states that the diameter at the top should be 18.5 ± 0.5 mm and 45 mm below the top it can be 20 ± 1 mm. In addition the mean diameter should be at most 1mm less than the diameter at the top.
Prades López, C., and M. Sánchez-González "Behavior of Natural Cork Stoppers when Modifying Standard Corking Parameters: Three Practical Cases." Cork Science and its Applications II 14 (2019): 20. google-books link
A: I'm also not a cork expert, but maybe the answer is more straightforward. It can ofcourse be the case that the cork already was asymmetric from the start. The purpose of the cork is to seal the bottle, which works best if it is tapered and (with some effort) the wide part is stuck in first.
The way you but the cork back in the bottle is obviously easier, but is also a much less secure seal.
In your case, if the cork moves slightly (e.g. due to the bottle shaking and bumping during transport), the seal will be less tight, making it easier for the cork to fall out, which off course results in more waste than the other way around. If the cork moves a little bit during transport, the bottle will remain properly sealed.
A: I have a feeling that the neck of a bottle is not perfectly cylindrical, but rather it is, let's say, "cone-shaped" i.e. tapered towards the mouth of the bottle. Hence, after capping, the cork marries this cone-shape, thus helping it stay in place in case the pressure inside the bottle increases. Pressure can increase, for example, if the temperature of the liquid and the air inside the bottle increases - think during fermentation, or during transportation. The capsule (i.e. the plastic or metal wrapping that is placed over the bottle neck, after capping) is not strong enough to hold high pressures by itself so the cork must do part of the work.
The pressure inside a sparkling wine bottle is so high that, after capping, the cork is in fact held in place by a metal cage.
A: I have uncorked a few hundred wine bottles in my job, noticing this phenomenon often. It is very clear with the synthetic wine closures that I have encountered as these are far less elastic and undergo plastic deformation much easier.
My mental model has always been that the tension in the cork as it is removed is uneven.
Higher tension as you get closer to top causes these sections to be stretched proportionally more than sections closer to the bottom and there is a corresponding decrease in the diameter to accommodate this.
To see why the tension would be higher at the top imagine a small circular cross section of the cork being deformed a small amount upwards, there is a frictional force from it's contact with the neck of the bottle and a tension downwards from all the segments below it.
Here is a wikepedia article about a more general effect:
https://en.wikipedia.org/wiki/Necking_(engineering)

A: As you can guess I'm not a wine cork expert. 
When you pull out the cork the pressure inside the bottle decreases and so the force pulling on the cork builds up, but is mostly acting on the part of the cork inside of the bottle.
This pressure doesn't expand the cork (perpendicular to the bottleneck) since it's only pulling the cork to the inside of the bottle. 
But this force damages the fabric of the cork, so that it can expand more freely once outside of the bottle.

As Rod Bhar wrote in his answer, the moisture could play a role too.
But when you pull out the cork only a tiny bit of it is moist - at least in my experience - which shouldn't account for the cone shape.
A: Besides the moisture explanation, I've also seen synthetic (plastic) corks that are tapered. Since the plastic shouldn't be affected by moisture content the same way as natural cork, I believe that corks are manufactured to be asymmetrical in addition to the effects of moisture. I'm not saying that the moisture in natural cork does not affect its elasticity.
In the image below, I show three different corks that support the hypothesis that some corks are manufactured with a taper/different diameters:
Left: Used natural cork from a commercial bottle of wine.
Center: Used cork for home-brew use.
Right: Unused cork for home-brew use.
The "commercial" cork has an approximately 1 mm change in diameter between the top (~20 mm) and bottom (~21 mm). It's barely noticeable on the picture, but the change in diameter happens almost exclusively in a 5 mm length span about 40% down from the top of the cork. If the change in diameter was purely an effect of moisture in the cork, I would expect the taper to be more gradual, rather than abruptly like here.
Regarding the "home-brew corks". The diameters of both the used and unused corks are fairly constant along the length of the cork. However, the unused cork has a diameter of 24 mm, while the used one only has a diameter of 24 mm. The corks are crushed as they are inserted, and you have to use a corking machine (bottom picture) to insert them into the neck of the bottle which is about 18--20 mm in diameter.
So why would a manufacturer want to make corks that have a narrower diameter in the top?
Firstly, they want the cork to properly seal, so it needs to have an uncompressed diameter larger than the bottle. This leads to a cork that makes a good seal, but it requires a corking machine to insert the cork.
Next, to help the consumers who don't finish the bottle in one sitting resealing the bottle, the manufacturers give the corks a taper. This way you can reinsert the cork with the narrow end down to save some wine for tomorrow.
Why then insert the cork with the thicker end down?
If the cork was inserted with the smaller diameter down, you risk having wine seep up along the side of the cork until the (uncompressed) diameter of the cork is wide enough to make a good seal. The manufacturers therefore insert the cork with the wide end down, to make a good seal immediately. Since the manufacturers have corking machines, which forces the cork into the bottle through a "funnel", the orientation of the cork's taper does not affect the difficulty to insert the cork for the manufacturer.


A: Inside the bottle the cork reaches equilibrium with the water vapour there, whilst outside it reaches an equilibrium with the atmosphere.
