Most liquid bandages are basically just a kind of superglue. When the bandage is in the bottle, it stays liquid. When it is exposed to the air and your skin, the chemicals in the liquid react to form polymer chains. The polymer binds to the skin, sealing up the wound. The idea is that it holds the wound together temporarily, but eventually breaks down as your body heals. So it does the same job as stitches or sutures, but you don't have to go back and remove the stitches after healing.
Some of the strongest liquid bandages use a type of formula (cyanoacrylates) that is especially strong and very similar to Krazy Glue and other commercial superglue (although they are slightly different from regular superglue, because they have to be nontoxic, of course). Others form somewhat weaker polymers that are more water soluble and don't last as long.
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