There are a number of questions about washing clothes on the ISS, the short answer is that they do NOT wash them.
- Nudism in space: Why wear clothes anyway?
- Washing clothes in space: are there any technical challenges?
- Laundry on the ISS
Answers that go into detail about the challenges talk about the different methods of washing clothes on Earth and how the are problematic in space. When I read them, I realized that washing clothes on Earth is much like what is going to happen to Elon Musk's Tesla, just from being in space
So the question becomes; If I hang my dirty clothes out on a clothesline, from the ISS, how long will it take for them to be freshed?
Maybe the space exposure damages the cloth to fast to make this practical, I don't know.
Obviously I am oversimplifying the solution, as you can't just open a window run the dirty clothes out on a line, but say you had a small air lock with a retractable clothes line...