A digester is provided for aerobically and microbially digesting a batch of bodily waste material, such as an aqueous slurry of pig manure. The digester comprises side-by-side digestion and separation compartments, separated by a partition wall. A first slanted pipe extends through the wall and has its inlet at the lower end of the separation compartment. Pressurized air is injected into the inlet so that slurry from the separation compartment is drawn into the bore of the first pipe, is mixed and aerated therein and is ejected into the slurry in the digestion compartment as a powerful jet. The jet establishes a vertical circulation in the digestion compartment. Slurry, containing undigestible solids, drains through a second pipe from the central core of the circular flow into the separation compartment. Here the aerated non-digestible solids tend to float and can be removed.