penetrate, soak in
沁 centers on liquid seeping deeply into something: penetrating, soaking in, or permeating thoroughly.
沁 combines 氵 (water) with 心 (heart), suggesting water soaking into the heart or core. The exact historical development is uncertain, but the phono-semantic structure is plausible.
Water 氵 seeps into the heart 心, soaking in deeply until it penetrates every part.
For シン, imagine water seeping into a thin fabric: thin -> シン, and the liquid soaks right through.