#11 corks are all natural corks from Spain. They last indefinitely with the right care. Simply store them outside of your container when not in use so that they can dry out. Cork is mold and mildew resistant. They only need to dry out when your container is empty. Air space, darkness, and moisture can over time discolor the cork.
Use the #11 cork for the 3.5" long body cooler. The opening of this tube is just a bit wider than the 4" tube. The #10 cork will go into the 3.5" tube but will sit a bit low and my become stuck inside the tube.
The #11 cork is too large for most wine bottles.
Any container with an opening that a standard wine bottle cork is a bit too small for should work well with the #11 cork.