# Atmospheric pressure changes on plastic bottle containing a liquid

We have a problem at work and I need some help on a theory.

We ship a liquid in plastic bottles using a pump closure. Recently some of the bottles have been arriving to customers having leaked. The pumps are still in the closed position and the boxes are not damaged.

We heat the liquid slightly before filling the bottles (120∘F) but it has mostly cooled when filling takes place (70∘F - 90∘F). Filling is done near sea level. The pumps that we use are a screw on type with a dip tube that reaches the bottom of the bottle. There is a small amount of air in the bottles after filling. Sometimes during filling air bubbles are incorporated briefly into the liquid but float to the surface after 15-30 seconds. This liquid will solidify at around 55∘F.

The liquid, when it does leak, is exiting from the spout of the pump. The vast majority do not leak.

If you squeeze a bottle you can see the liquid flowing up the dip tube.

I had several bottles leak when I drove from our filling facility to Asheville, NC (~2300 ft.)

My theory: When we fill a bottle and then screw on the cap, we are increasing the pressure of the air trapped inside the bottle. The pressure of the air could also be affected by the heat of the liquid when bottled and amount of air still incorporated into the liquid when the cap is applied. When the product is then shipping to or over higher elevations, the air pressure decreases which allows the air inside the bootle to expand which causes pressure on the liquid. The liquid is then pushed up through the dip tube and out the spout of the bottle. This may be exaggerated by the solidification of re-liquification of the liquid as it does contract slightly when it becomes a solid.

Am I completely off my rocker or is this tracking with anyone else? Let me know if photos would help or more explanation is needed.

EDIT: Additional thought. When the leaking occurred for me on the trip to NC, the bottles were stored in the car which was reaching 30∘F at night and probably 90∘F during the day. I know that heat will make the liquid expand as is proven when we overheat a drum and have to clean up the mess. So it could be a combination of lower ambient pressure (altitude) and expansion of the liquid (heat) that is causing the internal pressure to rise. Therefore the pump is acting like a pressure release value.

• When the bottles are shipped, do they have a temporary increase in altitude? – Jiminion Apr 19 '16 at 15:18
• regardless of any pressure differential that might be happening either from initial pressure at fill time, or from temperature changes, it sounds to me the root cause of your issue is an improperly designed pump. I would expect such a pump to have an internal check valve that would prevent outward flow unless the pump mechanism is purposely operated. – docscience Apr 19 '16 at 15:45
• @Jiminion - It depends on where they are shipped to. We are packaging at near sea level in New England. If the product is going to the West Coast, it inevitably crosses the Rockies. If it is shipped via a priority method, than it is partially transported via air. – Brian Morris Apr 19 '16 at 16:06
• @docscience I would tend to agree BUT we are buying the best quality pumps on the market which are manufactured in the USA (which used to mean more). I will be contacting the manufacture soon. The anomaly is that it is not happening to all the bottles/pumps. I would assume that a defect would affect a batch rather than random individual pumps. – Brian Morris Apr 19 '16 at 16:08
• @Brian Morris Not necessarily so. The design might have a marginal feature that leads to random occurrence of failures. – docscience Apr 19 '16 at 19:13

As I understand it, you have two theories.

1. the leak is caused by the drop in temperature of the liquid
2. the leak is caused by the increase in pressure when screwing on the top

I think we can probably rule out both of these, and here's why:

## Temperature drop

As we know from the ideal gas law, $$\displaystyle \frac{P_i V_i}{T_i} = \frac{P_f V_f}{T_f}$$ Where $P$ is pressure, $V$ is volume and $T$ is temperature. Subscripts are $i$ for initial and $f$ for final. This suggests that as the liquid cools (assuming constant volume) the pressure would also go down. So that would seem to eliminate the possibility of the temperature change causing a pressure increase and therefore a leak.

## Placement of cap

If we suppose that the volume of the cap is $A \text{cm}^3$ and that the cap effectively seals completely when the threads first engage (which is unlikely, practically speaking), and the volume of air within the bottle is originally $B \text{cm}^3$, then the increase in pressure would be $(A+B)/B$. So if the volume of the cap is significant compared to the volume of air within the filled bottle and if the cap seals immediately, then it could be a factor. However, it seems unlikely to me that the screw top seals immediately on engagement of the threads. This is easily checked -- screw on the top half-way and squeeze the bottle. If gas escapes, it's not that tightly sealed and we can probably eliminate this theory.

## Reduction in ambient pressure

An altitude change, especially if the product is shipped by air, would have the effect of reducing the external (ambient) pressure outside the bottles which could indeed cause a leak.

• To clarify, my theory is really based on the reduction of ambient pressure with the other factors I mentioned contributing to the relative pressure inside the bottle that is being affected. ~~ You were correct that the cap seals when it is close to being seated. Maybe a quarter turn after sealing. – Brian Morris Apr 19 '16 at 16:21

The bottles are filled at sea level. There is a small bit of air in them, so the inside pressure is also at sea level, along with quite a bit of (presumably) incompressible fluid. Bottles are plastic and thus flexible.

Assuming leaks occur when travelling to 2300 feet, outside pressure drops from 760 mm Hg to 702 mm Hg. This would flex the bottle and since the air is all at the top (away from the dip tube) only fluid would come out if something comes out.

I'd say the bottle flexing reduces its volume somewhat which puts a positive pressure on the fluid to go out of the bottle. (You could test and verify this with a bell-jar, if you have one around.)

• Are you saying that at lower pressure the bottle would flex inward? I would think it would do the opposite. – Brian Morris Apr 19 '16 at 17:07
• No, it would flex outward (on the major axis) but overall, the volume might still be reduced. – Jiminion Apr 19 '16 at 17:08
• Even if the volume increased, it still might push out fluid, as the space would be filled the gas topping. and the incompressible fluid might be pushed out. (Hard to figure this out for sure...) – Jiminion Apr 19 '16 at 17:10
• I don't know if you say my edit above. The car that the bottles were being transported in did get up to about 90F during the day and the liquid in question does expand when heated. I am going to bring a heat lamp into the office tomorrow to see if we can get it to expand some. This will not have the decrease in ambient pressure from altitude changes but it will give us part of the equation. – Brian Morris Apr 19 '16 at 17:44

There are three possible contributors to the leaking:

1) a reduction in ambient pressure as you drive to a higher altitude;
2) a possible expansion of the liquid if it heats up during transport, which makes the liquid expand and decreases the vapor space (hence increasing the air pressure inside the container);
3) If the liquid has a moderate vapor pressure, that will add to the pressure inside the container when it heats up.

RECOMMENDATIONS:
1) Take some containers to a lab and heat them slightly while pulling a moderate vacuum on them. This experiment may let you see exactly what is going on.

2) Leave a bit more vapor space in the container before it ships to a higher altitude, and don't pressure the container up before it ships if you are sending it to a higher altitude.

3) Make sure that there is only vapor in the dip tube when the bottles ship.

Good luck. This seemingly simple problem could be a bit tricky to diagnose.

Is it possible that the AIR expands with the heat and puts downward pressure of the liquid, which has nowhere else to go but back up the tube in the bottle, forcing the liquid up to tube where it leaks out of the nozzle? Same thing happened to me with a spray bottle (which was glass, the liquid was alcohol) when I left the bottle in a locked vehicle in the hot sun.