A refuelable electrochemical battery or cell is provided that features three phases of operation that repeat cyclically. In an intake phase, electrochemically active particles that are at least partially magnetic and a suitable electrolyte are admitted or fed into a cell cavity. In a power phase, oxidation and reduction reactions produce electrical energy while an electromagnet and/or permanent magnet attract the particles toward one electrode. A gas-diffusion membrane permeable by oxygen operates in conjunction with another electrode. During the exhaust phase, a piston forces residue of the reaction from the cavity to prepare for the next cycle of operation.