I originally thought this was pashut, but as I discovered over shabbos that it is still a chiddush to many people, I am posting this leto'eles harabbim.
Floating wicks are a wick pushed through a doughnut-shaped base of cork covered by thin foil. The premise is that the cork base floats the wick on top of the oil, ensuring a clean burn all the way through. The cups stay clean, the oil gets burnt, and shoin.
The problem is that eventually, the cork starts absorbing the oil and gets heavy and heavier, eventually sinking into the oil and smothering the wick.
The solution- leave the old wick in! the tip of it will push the new wick up long enough to burn a significant time.
As for the first night, they usually give you an extra few wicks and bases. Just pre-soak a wick and base to make it old, and transfer it to the new glass every night.



