Why do the bubbles in the water cooler get larger as the level gets lower?

Question

I have a typical office water cooler that uses a 19 liter bottle as a reservoir. The bottle is inverted on the base of the cooler with its neck below the water level in the cooler's reservoir. Air pressure (or more precisely, the reduced pressure above the water in the bottle) stops the water from flowing out once the level in the cooler's base reaches the bottle's neck.

I have noticed that the size of the bubbles that enter the bottle as water is withdrawn is inversely proportional to the head (height of water in the bottle). For example, when the bottle is full of water (head ~50cm) it takes about 100 bubbles to fill the jug I use to collect the water. When the bottle is almost empty (head ~ 15cm) it takes only 20 bubbles to fill the same jug. The smaller bubbles when the bottle is full also enter faster (i.e. more frequently) but take longer, that is they continue for a longer period after I close the valve when filling my jug.

Data: Bottle full ~50cm head: about 100 air bubbles to withdraw about 2 litres water. Bottle almost empty ~15cm head: about 20 air bubbles to withdraw about 2 litres of water.

I am at a loss to understand the physics behind this phenomenon.

Water will run out of the bottle (and bubbles enter to replace the volume lost) until the water level in the reservoir (basically a bucket with a valve at the base) reaches the neck of the bottle inverted into it which prevents further air from entering. Water is then removed from the reservoir by opening the valve. This lowers the water level in the reservoir below the mouth of the bottle which allows more air to bubble in and water to flow out until the level again reaches the neck of the bottle. As the air is being drawn in at atmospheric pressure I am confused by the changing size and frequency of the bubbles.

Here is a schematic drawing of the apparatus (apologies for the lousy drawing skills).

Answer 1

This is most likely just the ideal gas law at work.

As you move deeper into a fluid, the pressure is given by $$P=\rho gh$$

Where $\rho$ is the fluid density, $g$ is the acceleration due to gravity, and $h$ is the depth into the fluid.

According to the ideal gas law $$V=\frac{nRT}{P}=\frac{nRT}{\rho gh}$$

As you can see, the volume and the water level are inversely related. A lower water level means a larger volume.

Qualitatively, when the water level is lower, there is less pressure to push on the bubbles, so they are able to expand to a larger size.

Therefore, for the same amount of water that leaves the cooler (which means the same amount of air enters the cooler), when the water level is higher, the amount of air that comes in is divided into smaller bubbles, giving a higher frequency of bubbles. At lower water levels, the same amount of air gets divided into fewer, larger bubbles at a smaller frequency. I believe that the water pressure at the bottom of the cooler also contributes to this, as a larger pressure will "cut off" the bubble formation due to larger forces at the base of the bubbles.

I am unsure about the continuation of bubbles after the valve has closed. It could just be the time it takes for air to flow to the water portion of the cooler, and the rate of air flow could depend on the water level as well. Also, perhaps there is some way the cooler operates to purposefully take in air a certain way that I am unaware of. Have you looked into the inner workings of the cooler?