James Hahn wrote:

"Meindert Sprang" wrote

I start to charge the set in series, so the current through both
batteries is exactly the same.

No. You are failing to understand that the charging process is a chemical
reaction that converts energy into a differnt form.. The current flowing
at the positive and negative terminal of the whole string of cells is the
same, obviously,

Yes, indeed, obviously. And equally obviously the current flowing at the
positive and negative terminal of each individual cell in the string is
also the same. Surely you would not be daft enough to deny that!

but the current that flows 'through' any cell is a
complex result of the conversion processes occurring inside the cells of
which it is a string.

What exactly happens at the microscopic level may well be complex and
diverse, but the current passing through any surface you'd care to cut
through any cell will be the same.

Each cell can be considered an energy sink. The amount of energy
imparted to each cell will differ, either within a single battery or
within a series of batteries.

This is not in dispute.

The current flowing across any cell, or any group of cells, is most
definately not equal, and there is no reason it should be.

There is every reason it should be. It makes no difference whether
the load seen by a charging device is a string of resistors or of
battery cells, the current at every point in the circuit must be
equal at all times.

There is, however, no reason why the amount of energy absorbed by
each cell during charging should be the same.

One battery will reach the full state before the other but is still being
charged with full current because the other battery hasn't reached the
voltage that corresponds with full charge.

One battery wil reach the full state before the other, like one cell will
reach the full state before some others. It's not a problem.

It is a problem, because the fuller battery's internal voltage will
rise sooner than that of the not-so-full one, and so it will continue
to take a higher share of the monitored charging voltage applied to the
string. This not only means the less full one will take longer to
reach full charge but also that it's being charged at a suboptimal
voltage and so may never reach proper full charge, while the fuller
battery is being overcharged leading to a shorter life.

It is not
being charged with full current because the 'load' that the system
presents to the charging process is reduced by the reduced charging
requirements of the cell (or cells) that have reached or are approaching
full charge.