Going Green, Shaken But Not Stirred

It is not chlorophyll but the reduced quinone or palstoquinol molecule that plays the role of $OH$.  Reactions at both the cathode and the anode collector are two different redox reactions.  The electrolyte at the anode collector is oxidized, at the same time $OH$ is being reduced producing $H_2O^{+}$.  At the cathode $H_2O^{+}$ is being reduced and $MH$ is being oxidized producing $OH$.

The problem is to move $OH$ back to the anode so that the cycle repeats perpetually.

$H_2O^{+}$ redistributes by heat diffusion and by its charge.

$OH$ redistributes by heat diffusion only.

When $H_2O^{+}$ is replaced with $LiH^{+}$, $Li$ being lighter improved efficiency, but $LiOH$ formed in the presence of $H_2O$ or $OH$ precipitate under heat and localized high concentration at the cathode kills the battery.  The accumulation of contact hydride, $MH$ at the anode will also kill the battery, but this can be solved by a suitable choice of metal.

Hydrogen fluoride is poisonous!

The battery can be shaken but not stirred!  Shaking a battery to redistribute $OH$ inside prolongs its life.

It may not be possible to have both positive and negative charge carriers in the same cauldron.   Opposite charges will tend to bond ionically and neutralize.  A battery actually works because $OH$ is not charged.

If a negatively charged $OH$ equivalent can be created, it must also be separated from the positive $H_2O^{+}$ reductive carrier using a suitable membrane.  Which leads us to an oscillatory battery,

The battery oscillates chemically; a pair of redox reactions at the two electrodes working in opposite directions, producing charged redox carriers separated by a membrane moving in opposite directions.   The carriers produced by oxidization at one site are transport to the second site and are reduced there.  The reduction reaction creates another type of carriers and is transported in the opposite direction to the first reaction site.  It is oxidized there.

Electricity is tap off at the electrodes to drive a load.

Now, we look for a pair of redox reactions that produces charged redox carriers with PH change across the membrane.