How do batteries work?

I have read how batteries essentially work, but what I do not understand is how the cations on one end recognize the anions on the other if the only way they are connected is through a wire. From my understanding, the cations on one end want to receive electrons from the anions on the other end, the electrons flow through the wire connecting the two ends of the battery, and this flow of electrons constitutes an electrical current. But how do the cations sense the anions if the only way to transmit and receive electrons is through a wire, wouldn't the wire, even though it is electrically conductive, act as a physical barrier, preventing the cations from recognizing the anions on the other end?