The sink is too small for most people's heads.
Because the sink has a rim, water that falls outside the sink forms large pools outside the sink that remain until someone cleans them up.
You cannot avoid the fact that your face will be at an an angle to the sink.
Your hands, if they are under the faucet, will be fairly far away from your face. The result is that, in order to wash your face, your hands will collect water and then will throw the water onto your face. By the time the water reaches your face, it will have a decent amount of velocity. When it makes contact with the face, water can go everywhere!
The sink is small because the bathroom counter in which it is embedded is narrow. Our bathrooms are fairly spacious for an apartment, but they are not as wide as bathrooms I have seen in some houses.
The small size of the sink saves space and cost. With an apartment, both attributes are important.
The rim is there to keep water inside the sink. Because of the sink shape, however, water inside the sink tends to go down the drain quickly, so I don't know if the rim is really serving a good purpose.
I believe the faucet is placed where it is in order to support hand-washing. When one washes hands, the hands end up directly under the faucet, which in turn is right at the deepest portion of the sink. This gives a lot of space for your hands.
I would make sink rim very slight, and use that space to expand the sink slightly in size. I would not increase the sink size by more than that, though, because that involves additional materials, and also I don't know how feasible it is for every apartment with a small sink to just get a bigger one.
The rim keeps water out of the sink much more often than it keeps water in. As a comparison, the sink in our kitchen has a very thin rim. It is easy to move liquids and crumbs from the outside of the sink to the inside of the sink. Keeping water in the sink is also not really an issue of concern since any water in the sink goes down the drain very quickly anyway. So I would make the rim very thin. This will ease clean-up.
It is actually much more difficult to change the sink design and faucet position than I had previously envisioned. For example, a showerhead-like faucet will not work, because when face-washing, one only wants water to reach the face, not the rest of the body. As another example, you can't lift the sink up so that it is closer to the face, because that will make hand-washing cumbersome. I can think of no major changes to sink design or faucet position that will not affect a common use of the sink.
I propose a change to
the counter design that may help reduce cleanup time. I also suggest a
new product that may help keep water inside the sink. These are explained
below.
To further encourage water to move into the drain, I propose a sloping counter. Water that falls outside the sink will then move towards the sink. This will remove some counter space, which for my bathroom is not an issue, but could be an issue in other bathrooms.
Another option is to put up a vertical plastic shield around the sink that catches water that is in the air and headed out of the sink. This guard can be placed onto the sink when washing one's face and then removed afterwards.
I like this approach because it would be low cost. If it was stretchy, one size could probably fit most sinks. Perhaps suction could be used to adhere the guard to the counter outlining the sink.
I need to work on noticing interfaces that others find awkward, because I rarely notice awkward interfaces myself. I only notice work that I have to do that is related to a bad interface. For example, I will only notice awkward pothandles if the awkward pothandles cause me to drop the pot and then I have to clean up food that fell onto the floor. Otherwise, I don't pay any attention to them. If I were more alert, I think I would be a better designer.