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1650s, "of or pertaining to the hair," from Latin capillaris "of hair," from capillus "hair" (of the head); perhaps related to caput "head" (but de Vaan finds this "difficult on the formal side" and "far from compelling, since capillus is a diminutive, and would mean 'little head', which hardly amounts to 'hair'"). Borrowed earlier as capillar (14c.). Meaning "taking place in capillary vessels" is from 1809. Capillary attraction attested from 1813. As a noun, "capillary blood vessel," from 1660s.
capillary cap·il·lary (kāp'ə-lěr'ē)
Of or relating to the capillaries.
Relating to or resembling a hair; fine and slender.
Note: The interaction between the fluid and the vessel walls produces a force that can lift the fluid up into the tube, a phenomenon known as capillary action.