The Black River, or Rio Negro, gets its name from the color of the water. The Solimões River in Manaus is a sandy brownish color. This means you can see exactly where the two rivers come together. Not only that, each river on its own is a different temperature and run at a different speed, so when they come together the water doesn't just mix to create a muddy soup - instead, the rivers essentially run alongside one another.
The river "borders" are constantly moving and changing as the water flows, but a clear delineation between the two rivers is visible well beyond where they actually meet. In fact, you would need to travel for nearly four miles downstream before you saw the Solimões River and Black River finally starting to blend. When the two rivers do actually come together, they form the Amazon River.