Household appliance with coagulant dosing system

A household appliance configured to perform a cycle of operation, using water, on an article, the household appliance comprising:

• a treatment chamber configured to receive the article for treatment according to the cycle of operation;
• a treating chemistry dispenser coupled to the treatment chamber;
• and
• a water treatment system comprising:
• a sediment tank fluidly coupled to the treatment chamber and having a sediment outlet and a clarified water outlet, which is located above the sediment outlet and fluidly coupled to the treatment chamber;
• an impermeable separation layer extending substantially across the sediment tank and moveable within the sediment tank to separate any sediment from any clarified water;
• a coagulant dosing system fluidly coupled to the sediment tank;
• and
• a fresh water supply fluidly coupled to at least one of the treatment chamber or the sediment tank;
• wherein fresh water supplied by the fresh water supply is used during the performance of the cycle of operation and then directed as used water to the sediment tank, where coagulant from the coagulant dosing system is supplied to the used water to increase the sediment in the sediment tank, which settles in the tank forming a layer of sediment, which can be removed via the sediment outlet, and a layer of clarified water, above the sediment, which can be removed by the clarified water outlet and reused.