Almost all empires I've seen that existed north of Sahara, did not expand to the south. And the empires south of the Sahara did not expand to the north (except for post 15th century European colonialists, and the Kushites). Why is this?
I understand supply lines may have been difficult to establish through Sahara interior due to lack of water, but I also know that there were several trans-Sahara trade routes going through the interior. And the corridors along the Red Sea and west Africa had sufficient water availability.