I've dehydrated a bunch of potatoes and don't have a problem with them turning black. Here's how I do it:
Since I don't peel mine before drying, I make sure that the skins are very well scrubbed and any blemishes or eyes are taken out.
Slice thin, I slice mine about 1/8 of an inch. After slicing I drop them into a bath of water and powdered vitamin C (ascorbic acid, commonly sold as Fruit Fresh in the grocery store). I have used lemon juice when I was out of the other but I like the end result with the vitamin C powder better. I let the potato slices soak until I have sliced enough for a good batch.
Blanch the slices in boiling water for 2-3 minutes or until the slices become translucent. They won't quite be cooked, but the starch will be coming off of them. Be prepared to change the water at least once, maybe more, depending on how large a batch you're doing. The potato water is excellent if you make bread, btw. When the timer goes off, lift them out and immediately plunge them into an ice water bath; this will stop the 'cooking'. I also add some powdered vitamin C to that water, although that might be overkill. Let them sit until they're easy to handle, but don't let them sit in there a long time or else they'll absorb water.
Place the slices on a towel and pat dry with another towel to remove as much water as you can. They'll still be wet, but not sopping wet.
Arrange the slices on your dehydrator trays. The slices can touch each other but don't overlap them.
Turn on the dehydrator and let 'er rip! I have an Excalibur and the drying time will vary according to the type of potato, the thickness of the slice, etc.
It sounds like a lot of work, but it's not bad at all if you have everything set up and handy ahead of time and know what you're going to do. And, it's like anything else that's worth doing, the rewards are great. I have put up many, MANY jars of potatoes and mine come out perfect, just like the commercially dried ones.
Hope this helps!
