I'm not sure about female's washrooms, but some of the male's washrooms in malls have urinals that do not require flushing. (not an excuse for faulty auto-flush sensors) I suspect they have applied a layer of non-wetting surface treatment to the urinal walls, so that the urine won't stick. But personal experience tells me, the urine stink does stay. X_x
Non-wetting, or hydrophobicity (can be hydrophilicity though), or lotus effect, seems to be the popular thing nowadays. Even one of the final year projects in NUS is on non-wettable surfaces, which a friend of mine is doing. Peter Forbes used one chapter to talk about the lotus effect in his book Gecko's Foot
Let's start with the lotus. A little experiment, next time you go to the lotus pond, pull down your pants and pee onto the leaf. You will observe that the liquid moves around or slip off like pebbles. You may think cos it's a smooth surface, that's why the water slips off so easily. Nope, in the nano scale, the lotus leaf is super rough, with tiny structure that makes dust stick better to water than to the leaf itself, thus the self-cleaning effect. If not why are lotus leaves so spotless in the muddy pond?
This effect has inspired scientists and engineers into developing new technology for our use based on the lotus effect. Things like water-repelling glass, self-cleaning paint, have been commercialised. If only my home's windows are self-cleaning, that would save me so much cleaning time, especially when a cocky bird drop its shitload there.
Come to think of it, toilet bowl can be flushless too. Anybody wants to try?