Does English “sludge” relate to “slough” (swamp)?

In a comment, John Lawler wrote:

Slough is quite common in places with a lot of water. Note that the aquatic noun is pronounced /slu/ while the verb of disposal is pronounced /sləf/. Beyond etymology, most English simplex words beginning with sl- refer in one way or another to a two-dimensional interface, with one side liquid and slippery. See the link for examples. Such an interface is a natural for pejorative terms and they also abound.

There can be no definitive answer to the question Does English “sludge” relate to “slough” (swamp)? They are both of uncertain origin. If they are of uncertain origin, we cannot say whether that origin is the same for both.