I'm not aware of any and AV didn't provide any.
If you asked AV, he would probably say something along the following lines:
If we are unhealthy and are surrounded by toxins and pollution, then our nutrient requirements exceed our nutrient intakes. So the body has to compromise and prioritize, which tissues get which nutrients. Most of the nutrients end up going to the essential tissues, while the non-essential tissues (such as skin and eyes) get deprived. One way to get more nutrients in, is to feed some of these tissues "from the outside".
It is well understood that the skin can absorb many different substances. (And that's why it's a bad idea to use toxic non-food soaps and creams and lotions). Aajonus is basically saying that the eye can absorb things in a similar manner. If you want scientific validation of this, you should look into books about biology of the eye, and see what they say about the eye membrane, and mechanisms for transporting various substances across it.
Or, if you just want to know that it's plausible, and aren't interested in the details, consider this:
If you go to a drug store, you'll see aisles full of various patented eye drops, eye sprays, and eye washes. Obviously, lots of studies have been done on these products, both clinical and theoretical. Some of these products can affect the working of the eye in a rather sophisticated manner. So it's quite plausible that some substances in the egg white can also affect the eye in a sophisticated manner, and heal it. But nobody's going to study egg white specifically, because you can't patent it.
