# Would oil flow through a one-way valve into water by itself?

I read about heron's fountain recently and it got me thinking about liquid and air pressure and things like that.
And it led me to the following idea:

Basically what is happening here is that there is a container with water and oil.
Oil will float to the top as it is less dense than water.
At the bottom left there is some more oil and the gray circle is a one-way valve.

So my question is:

What will happen if I add a bit more oil at point A?

Would the oil go through the valve at the bottom and then flow up through the water and eventually overflow at the top and do this continuously forever once there is enough oil in the system, without more oil being added at A?
Or do I need some kind of external interference for the one-way valve to work ?

I suspect the valve might require pressure on one side to be more than the other side or something like that.
If that is the case, would it make a difference if I made the area on the left larger than the area on the right and kept adding oil at point A until the pressure from the oil on the left is large enough to force oil through the valve?

Update 1:
I understand that volume or amount of liquid is not important and it's all related to the height, thanks to Azzinoth for pointing that out.

Would it then make a difference at all if the height on the right is divided into different sections so the height on the left is more than the height of any of the sections on the right, or would it add up?
I am thinking the pressure from the oil on the left will push the oil into the first container on the bottom right through a one-way valve. And with enough pressure, into the second container, and the third and so on.
Or would the pressure of all three containers on the right add up and equal or exceed to pressure of the oil on the left?
Below is a diagram of what I mean: