Two things:
1. You know how oil and water don’t mix, but if you combine two water-based liquids (like water and fruit juice or something), they do mix together? Chemists call that “like dissolves like”. Basically, fatty things can mix with each other, and water-based things can mix with each other, but fat-water combos can’t mix.
2. Your cells all have outer membranes (skins) that are mostly made of fat. Including your skin cells. That means your skin presents a fatty surface to the outside world.
The result of those two things is that (like DragonFire said) your skin is somewhat permeable…but especially to fats and oils, and much less permeable to water. That’s on purpose, to prevent your body losing a ton of water to evaporation. That’s also why you don’t inflate when you go swimming, and why you can spill apple juice on your skin and essentially none of it absorbs.
BUT with fats it’s a different story. You’ll notice that all of the topical medicines are in a greasy or creamy suspension. That’s also on purpose, they’re fat-based and water-free so that they can “mix with” and absorb into the fatty membranes of your skin’s outer layers and into the tissue beneath. Polysporin, Vick’s vapo-rub, BenGay, they’re all greasy. Even Vaseline and baby oil absorb into your skin for the same reason.
Related fun fact: An organic solvent called DMSO (dimethyl sulfoxide) is gasoline-like (fat soluble) and smells sulfur-y. If you dip your finger into a beaker of DMSO, you can almost immediately taste garlicky in your mouth because it rapidly absorbs into your blood and is exhaled in your breath.
If it’s pure DMSO this is pretty harmless, but chemists have to be careful working with this solvent. Anything else already dissolved in the DMSO will be rapidly carried into the body along with the DMSO as it rapid- absorbs into the skin.
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