fill, wear (a smile), clear, pure, dense, deep
湛 centers on a state of being filled to the brim: a container filled with clear liquid, a face filled with a smile, or a quality that is dense and deep. The meanings of purity and clarity extend from the image of still, deep water.
湛 combines 氵 (water) with 甚, which likely contributes the sound and the idea of deep or excessive. The character originally referred to deep, clear water, and later extended to filling and density.
Water 氵 plus 甚 (excessive) suggests water that is excessively deep and clear, filling a container completely. Imagine a deep, pure lake that fills the landscape.
For タン, picture a tan-colored liquid filling a deep tank: tan -> タン, and the tank is filled to the brim with clear, dense liquid.