NOVELTY - The system (100) has a positive electrode (112) separated from a negative electrode (108) by a separator (110), where the separator is adjacent to the negative electrode. Electrolyte (160) includes 5 molar lithium hydroxide (LiOH) located within the positive electrode. A pump (126) has a pump inlet in fluid communication with an electrode outlet and a pump outlet in fluid communication with an electrode inlet, and is controlled such that the pump receives the electrolyte from the electrode outlet and discharges the electrolyte to the electrode inlet during charge and discharge of the system.    USE - Rechargeable metal/oxygen air flow lithium-ion battery system for portable electronics and electric and hybrid-electric vehicles.    ADVANTAGE - The battery reduces difference between practical capacity and theoretical capacity of the battery. The battery removes lithium during charging within the positive electrode, thus reducing concentration of LiOH within the electrolyte. The battery avoids passivation of a cathode surface by storing a solid product such as monohydrate crystal, in a reservoir, which limits capacity and current density. The battery reduces mechanical stress on a cathode structure caused by precipitation on the cathode surface and in pores of the cathode surface. The battery allows a processor to control an amount of monohydrate crystal, which is pumped into a supply header so as to avoid clogging of pores of the positive electrode. The battery can prevent reaction of solid discharge products with cell components such as the cathode surface and a solid-electrolyte protection layer on top of lithium anode. The battery avoids irreversible reaction of lithium with carbon-di-oxide (CO2) to form lithium carbonate.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is also included for a method for operating a battery system.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic view of a battery system of a lithium-oxygen (Li/oxygen) system with a reservoir to store discharge products outside of a positive electrode after discharging products to be collected in a reservoir.    Rechargeable metal/oxygen air flow lithium-ion battery system (100)    Negative electrode (108)    Separator (110)    Positive electrode (112)    Pumps (126, 140)    Electrolyte (160)