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.