Battery charging: Minimum voltage differential?

[ErnieGG]

I have a question that I believe requires knowledge on the graduate level, but I can't necessarily express it in terms more complicated than plain English. If this is not so, moderator, please adjust to your taste, and thank you!

If it helps to know this, I'm an audio/video systems designer and installer with electrical and electronic experience including electronic design to the board level (PC Board) of analog circuitry. I've worked with electronics for decades.

If I have it right, when one charges a battery, energy is required from the charger to undo the chemical reaction that discharged the battery. This is accomplished by having, at its simplest, a source of voltage higher than the battery will be when charged, with some kind of current limiting typically set to a value that maintains the best battery life.

But someone posed one of those it-can't-happen questions and I've found an interesting detail.

First, let's say this is a physics problem where everybody promises not to blow up while we discuss things.

If one were to connect two batteries of identical design, one charged and one depleted, positive to positive and negative to negative, the charged battery would charge the discharged battery, and as it did so its charge and ultimately its voltage would lower. This differs from standard battery charging in that here, the "supply" is lowering in voltage and energy as the charging battery charges.

Here's the question: do the two batteries come to equilibrium of voltage? I propose not, since, speaking inexactly, electrons are being pushed around, and in electricity, pushing is voltage. Does the supply battery have to be some particular voltage higher than the charging battery in order to keep charging it? Does the process stop when the supply battery is exactly that voltage higher than the charging battery?

Let me describe a roughly analogous situation: If one were to do this with a silicon diode between the batteries, we know that the supply battery would not go below 0.7 volts above the charging battery, because of the forward voltage drop of the diode. But is there a similar forward voltage drop of the charge process itself?

Why? How?

Thanks.

 

[anorlunda]

It is quite common to connect batteries in parallel. They do come to equilibrium where no more current flows between them. But they are not like capacitors. Their charging cycles are nonlinear.Batteries have an internal resistance that drops their voltage in proportion to the current flowing.

 

[ErnieGG]

Thanks, but this case is not quite parallel enough, pun intended, to answer what I'm asking.

Batteries in parallel are all discharging, and the effect of one battery set up to charge another may result in a more subtle state than two or more batteries that are all discharging. The internal resistance of batteries will tend to make them all output almost the same current as one another (this, at least in a power amplifier with multiple output devices, is called current sharing).

When water overflows the edge of a level surface, it does so until some point is reached where there is no longer enough water flowing into it to push the water over the edge. But at that point, there is usually a meniscus that allows the water to be higher than the edge of the surface. That difference in height is potential energy added to the water above the level of the full container. It takes just a bit more push to get the water to flow.

Is there not such a need for some kind of potential difference between two batteries connected as described? And won't current stop flowing when that potential difference is lower than the voltage difference required to cause the chemical reaction which is charging?

 

[sophiecentaur]

Are you expecting some sort of 'threshold' condition for the voltage difference, for current to flow? The simple model we use, with an Internal Resistance would suggest not.
Slight differences in temperature could possibly cause small currents to flow, which would involve small amounts of energy loss (internal resistance again).

 

[ErnieGG]

"Are you expecting some sort of 'threshold' condition for the voltage difference, for current to flow? The simple model we use, with an Internal Resistance would suggest not."

Exactly. I don't see how there cannot be some kind of threshold voltage difference, below which charging does not occur.

I almost have to laugh that you're saying the simple model you use suggests not. OF COURSE the simple model would not suggest that! IT'S THE SIMPLE MODEL! I'm asking about what really happens beyond the simple model.

Thanks for asking me that particular question!

 

[anorlunda]

Clarify your question please. Are you asking about charging current or the rate of change of state-of-charge?

It is common to leave a trickle current oh a fully charged battery.

 

[sophiecentaur]

Exactly. I don't see how there cannot be some kind of threshold voltage difference, below which charging does not occur.

I think the thermal energy / noise would take care of any threshold for the ions in a solution to change behaviour - at least, near room temperature.
I just checked in this link and found that kT is around 25meV at 295K. Wouldn't that 'blur over' any binding energy that you could be considering? That suggests (to me, at least) that we would be dealing with a continuum of energy transitions; no threshold.