Grease from caster wheels stain my floor?

Couple of years ago I my office chair's original caster wheels broke, and I ordered some new ones online, just like pictured below.

The wheels (notice the bearings out in the open under the dark base of the shaft)

They've been working great, however I started to notice after a bit of time that they drop some kind of soot on my floor, that's incredibly difficult to clean(dry methods don't "pick it up" when it's stuck, water just spreads it around making it worse). I first started noticing it when I found those stains on the floor, and realized I had some stuck on my feet as well.

Upon further inspection and replacing them with new similar wheels, I'm just now realizing that it's probably the grease from those open bearings you can see in the picture, mixed with dirt. While replacing these dirty wheels I actually stuck a screwdriver into the bearings, and wiped it off with a paper just to confirm that the bearings was where that soot was coming from. You couldn't touch most of the parts of those wheels without dirtying your hands in it(like those black metal struts were quite stained in it).

I tried googling about it, but I didn't see anyone really having similar problems...

So my question mostly is, has anyone else had similar problems? Any remedies? Any better and easier ways to clean it off? If I've hypothetically also used this chair on a dark mat where the soot cannot be seen with naked eyes, how to clean it? Any ways to just prevent this from happening?