delicate hand, mix, blend, adulterate
摻 centers on the action of a hand mixing or blending things together, often with a sense of delicacy or adulteration. The core idea is a hand combining substances, which can extend to the notion of a delicate hand or the negative connotation of adulterating.
摻 combines 扌 (hand) with 參, which likely contributes the sound and the idea of mixing or joining. The exact historical development is uncertain.
The hand radical 扌 beside 參 suggests a hand carefully mixing or blending ingredients. Imagine a delicate hand stirring a pot to combine flavors, or adulterating a substance by mixing in something else.
For サン, picture a hand mixing sand into a blend: sand -> サン, and the hand 扌 is doing the mixing.