NOVELTY - Anaerobically digesting organic material involves providing a reaction chamber (12) comprising first and second cells (20, 22) linked by a passageway (24) for flow of organic waste slurry (S) from a bottom region of one cell to a bottom region of another cell; placing an organic waste slurry in the chamber to fill at least the bottom region of each cell; displacing the slurry through passageway from first cell to second cell to build a head of organic waste slurry in second cell; and discharging head of waste slurry from second cell to agitate waste slurry in the chamber.    USE - For anaerobically digesting organic material (claimed), e.g. food waste.    ADVANTAGE - By discharging the head of organic waste slurry, the method reduces the extent to which organic waste slurries separate into three distinct phases. Particularly at elevated pressure (e.g. to a pressure of 0.3 bar or more over atmospheric pressure, perhaps about 1 bar or even about 2 bar), the method prevents separation of organic waste slurry into at least one of the three phases. At least part of the head of slurry in the second cell is rapidly discharged back to the first cell, such a rapid discharge back-flushes the passageway and agitates the slurry to avoid phase separation.    DETAILED DESCRIPTION - Anaerobically digesting organic material involves providing a reaction chamber (12) comprising first and second cells (20, 22) linked by a passageway (24) for flow of organic waste slurry (S) from a bottom region of one cell to a bottom region of another cell; placing an organic waste slurry in the chamber to fill at least the bottom region of each cell; displacing the slurry through passageway from first cell to second cell to build a head of organic waste slurry in second cell; and discharging head of organic waste slurry from second cell to agitate organic waste slurry in the chamber. The organic waste slurry is actively displaced by pressurizing the first cell relative to the second cell. The first cell is pressurized relative to the second cell by pumping gas into the first cell. The gas comprises at least a component of biogas. The head of organic waste slurry is discharged by rapidly depressurizing the first cell. The displacing and discharging steps are part of a cycle that is repeated during anaerobic digestion of organic material. An INDEPENDENT CLAIM is included for apparatus for anaerobic digestion of organic waste, comprising: the reaction chamber for receiving an organic waste slurry; device for displacing organic waste slurry through the passageway from the first cell to build a head of organic waste slurry in the second cell; and device for discharging the head of organic waste slurry from the second cell to agitate organic waste slurry in the reaction chamber.    DESCRIPTION OF DRAWING(S) - The figure shows key stages in anaerobic digestion of organic waste.    Reaction chamber (12)    First cell (20)    Second cell (22)    Passageway (24)    Valve-controlled slurry inlet duct (40)    Valve-controlled links (50)    Organic waste slurry (S)