Shipping Salty Snacks with Buffer Bags
PROBLEM
Air-tight bags expand at higher altitudes, meaning that when they are packaged for shipment at
lower altitudes, empty space must be left in the shipping cases to allow for the anticipated expansion.
This essentially means that there is unoccupied space in each shipment that has the potential to be
occupied by more bags. This space can only be reclaimed as “useful” if the issue of bag expansion can
be controlled, and the challenge is therefore to design a system in which bags will remain at
(approximately) a constant volume when travelling from lower altitudes to higher altitudes.
BACKGROUND
To solve the problem of the expanding bags, it is first important to understand what is actually
causing the expansion. The clearest way to think of the bags and their expansion is to view the system
as a gas pressure problem in which the elements are always attempting to reach equilibrium. The
simplest way to explain this is that at higher altitudes, the air pressure is lower than at lower altitudes.
When the bags, which essentially contain a small sample of the atmosphere as it exists at this arbitrary
lower altitude, are exposed to this lower ambient pressure, they attempt to equalize with the
surroundings and therefore push out, becoming more voluminous. Another way to think of this is that
the shape of the bag is being influenced by gas molecules from both inside and outside; they are content
to push against each other just enough to reach this stable bag shape. However, when the outside
particles stop pushing as hard (the pressure drops), the inside particles gain the advantage and begin to
push the bag outward to occupy more space in the environment. They will be spread thinner and
thinner, and eventually will only be able to push against the environment as much as the environment is
pushing back: equilibrium will have been reached again.
To think of this same relationship in slightly more scientific terms, it is helpful to understand the
relationships that govern gas pressure. Specifically, the ideal gas law provides us with a means of
directly measuring how much change in pressure will be observed when the volume of a system,
number of gas molecules in a system, or temperature of a system changes. In Equation 1, the
aforementioned ideal gas law, P represents the pressure (typically measured in pascals), V represents
the volume (in square meters), n is the number of gas molecules (in moles), R is the universal gas
constant (m3*Pa*K−1*mol−1), and T is the temperature (typically taken in degrees Kelvin).
PV = nRT
Eq. 1
The most direct way to equalize the pressure in a system (make P1 = P2) is to allow the free
movement of gas between areas of high density to areas of low density (simple diffusion). The high
pressure area will lose gas particles, the low pressure area will gain gas particles, and eventually the
density of particles at all areas will be equal: equilibrium will have been achieved. However, this does
not accurately describe our system in which the bags are sealed in an air-tight manner. When there is a
greater density of particles on one side of the barrier that forms the bag, the gas particles can only
bounce around wildly inside and outside, never crossing over to equalize the pressure gradient.
However, equilibrium hasn’t given up yet: there are still plenty of other variables that can be adjusted.
To simplify the ideal gas law to better represent our system of bags, the terms n and R can be combined
into one arbitrary constant, K. K will be different for every system, as there will be a different number
of molecules of gas in each case, but since there will be no migration of these particles, it can be kept
constant along with the gas constant R. This leads Equation 2 which still demonstrates the same
relationships as Equation 1.
PV = kT
Eq. 2
It can now clearly be seen that there are only 3 more variables to be considered: pressure, volume,
and temperature. By imagining three cases in which each of these terms is held constant, it is possible
to better understand the physical relationship between each of them. For example, if the temperature
of a system is held constant, pressure and volume can be seen to have an inversely proportional
relationship: when one increases, the other must decrease. If pressure is held constant, volume and
temperature are easily identified as varying in a directly proportional fashion: when one increases, the
other must increase, vice versa. Finally, if a constant volume is being maintained, pressure and
temperature must vary in a proportional manner. To sum this all up, an increase in pressure will cause a
decrease in volume and/or an increase in temperature whereas a decrease in pressure will elicit the
opposite effect.
To most effectively maintain a constant volume, it is desirable establish control over the
remaining variable that is simplest to manipulate. That is to say that the environmental pressure and
temperature will be changing constantly, and if you can pick one to be able to control with a dimmer
switch, it will be feasible to create the proper set of conditions to maintain the volume. For example, as
you ascend the rocky mountains with your bags that you desire to maintain at a constant volume, the air
pressure is going to drop (as is the temperature for that matter, for similar reasons as we have been
reviewing). However, if you can measure the change in pressure that will be affecting the bags, you
could find a way of cooling the bags so that their gaseous contents would lose some of their thermal
energy and would not expand in the way that would normally be expected if the temperature were
being held relatively constant. If you were to decrease the temperature too much, the bags might even
begin to shrink, possibly crushing the contents.
If you could directly control the ambient pressure immediately surrounding the bags (i.e. in the
shipping container), then you could monitor the temperature, and adjust the ambient pressure so that
the volume was not altered. On this same train of thought, because the decrease in pressure is
ultimately the reason why the bags expand, if you could simply maintain an environment of known or
controllable pressure, you could easily maintain a constant volume of the contained bags. This would
essentially be a pressure vessel in which the internal conditions would not change, at least not
dramatically, regardless of the external environment. To pressurize an entire shipping container would
be extremely cost-inefficient when compared to the increase in shipping efficiency due to the great
degree of specialization and adaptation that would be required. However, the shipping container is only
one potential barrier between the bags and their immediate environment. This is where the soon-to-be
proposed solution stems from.
DEFINITIONS
In describing the proposed solution there are a few terms that need to be kept straight.
Pressures:
Atmospheric—outside, environmental air pressure
Ambient – air pressure immediately surrounding object of discussion (relative)
Internal—air/gas pressure on inside of membrane/container
External—sir/gas pressure on outside of membrane/container
Air/Gas—used interchangeably to indicate a gaseous mixture
Container—when a reference is made to the pressure of a container, it is referring to the
pressure of the gas molecules located only directly within that container, not within
enclosed containers.
Containers:
(Shipping) Container—largest unit of shipment (i.e. box car or semi-trailer)
(Shipping) Case—box in which the individual product units are contained
Buffer (Bag)—membranous, gas impermeable barrier completely enclosing product; new design
for solution
Product (Bag)—product unit that is being shipped and must be maintained at constant volume
SOLUTION
Concept
The proposed solution is to use the expansion of a newly designed air-tight bag in low pressure
environments to prevent the expansion of the current air-tight bags. This will be accomplished by
creating a micro-environment in which the pressure in not affected by volume or gas exchange, and
the temperature change is negligible. If the product bags are placed in this environment, and the
same conditions can be maintained at elevation, no expansion will occur. This will mean that the
packaging will be more efficient by a factor equal to the empty space previously necessary. The new
air-tight bag will be known as the “buffer bag” for the rest of this discussion and is the essence of
the solution.
To explain a little more thoroughly, the idea is essentially to create a “one way” pressure vessel.
As can be seen in the attached Figures 1, the shipped bags are currently expanding to fill the entire
shipping case, because of an equalization of pressure. Figure 2 represents the change that would be
effected by the addition of the buffer bag. The buffer bag, being affected by the lowered ambient
pressure, will expand as the natural, expected reaction. However, when it makes contact with the
rigid shipping case, it will no longer be able to expand. Therefore, the pressure will decrease only
slightly within the buffer’s micro-environment, and the product bags inside will experience this same
slight expansion. Assuming that the initial volume of the buffer bag is approximately equal to that
of the shipping case, this increase in pressure/decrease in volume will be virtually unnoticeable, as
will the increase in volume for the product bags. Figure 3 is simply an illustration of the fact that
more bags will be able to be shipped per shipping container, or conversely the shipping containers
could be made smaller (although this will not be an efficient use of material, unless there is *just*
not enough room for one more bag. Figure 4 is a somewhat exaggerated illustration of what change
will be experienced by the buffer bag. The “normal” condition is a little too flaccid and the
“expanded” condition is not pushing out as fully as it likely would, but the general idea is conveyed.
This concept will not prove useful at all when translating from high pressures to low pressures,
as the means of regulating volume is simply to mechanically create a barrier (with the walls of the
shipping case) that stops expansion/volume change at a pre-defined maximum. The important
factor is that the volume remains constant and predictable, and since an expansion is all you have to
worry about when traveling from high pressure to low pressure, this maximum volume control is
sufficient. Without the specific numbers it is impossible to calculate an initial set of conditions
(concerning the exact volume/pressure of the product/buffer bags), but they can easily be
determined so as to maximize the shipping.
Buffer Bag Construction
The “one way pressure vessels” (buffers) will serve their function by being impermeable to
gasses, thin and flexible to conform to the shape and size of the container while not taking up any
“extra space”, and able to conduct heat. I envision them as clear plastic, most likely a polyethylene
of some sort, but the aforementioned properties are the only real relevant criteria. I am not a
materials scientist or engineer, so I am not certain what would be best to use to fit these criteria
while also being simple to incorporate into the manufacturing/packaging process. Polyethylene is
relatively cheap, and can be fused with heat welding, but I am sure there are other options that
might be more suitable to this design. This all being said, the attached Figures 5-6 illustrate possible
structures that I have brainstormed.
The biggest trick is going to be getting the product into the buffer and then sealing the buffer
while ensuring the correct initial pressure/volume. One thought is to leave a flap open in the buffer,
into which the product can be placed. Figure 5 is an attempt at this design, but both sealing the
edged of the top flap as well as packaging the product will be cumbersome, and neither of these are
particularly appealing attributes of this design. Another more feasible design is to simply construct
the bottom and sides of the buffer, place them inside the case, load the product into the bufferlined case, and then seal the top of the buffer shut. This general design is illustrated in Figure 6
where the sides (front, back, left, right) are all constructed of one piece and the top and bottom are
fitted into this shape by folding the edges and corners around to fit inside (or outside if it is possible
from a manufacturing standpoint). Only the sides and bottom will be assembled before loading the
product bags into the buffer bag/case. Then the top will be sealed, completing the buffer bag.
There will still need to be some means of ensuring the correct pressure and volume right before
the final seal is made, but a machine could fairly simply be made to do this. If a seal were created
around where the heat-welding (or other form of sealing, depending on the material) was
happening, pressure could be maintained at the correct value to fill the buffer bag with the right
amount of air. Depending on the conditions (i.e. product destination, pressure inside the product
bags, etc.), the amount of air in the buffer bag could be adjusted. Assuming that the buffer was
constructed of thin material and to the size/shape of the container, at atmospheric pressure the
buffer should just touch the sides of the case. It will then be ready to ship.
One general consideration that would impact bag design would be the intended lifecycle of the
buffer bags. If shipments were leaving the same area they were being delivered to, the buffer bags
could be reused for the same task, and a more robust, expensive design may be warranted. The
bags could themselves contain some of the rigidity necessary to put a cap on the volume in the form
of cross-layers of “non stretchable” material. This would take some of the stress off of the shipping
case, and the material for that could be less bulky or structurally important. Otherwise they could
simply be air-tight and strong enough not to be punctured by a stray piece of cardboard for one trip,
and be recycled at the destination (assuming a recyclable material, of course, which would be ideal
and quite feasible).
This discussion does bring to light another important factor: the actual shipping case will need to
be examined to see if the buffer bag design will mesh. If the cases are flimsy and thin material, the
buffer bag will simply continue its expansion outward, causing the cases to bulge, deform, and
expand. (The product bags will also expand, but they are basically irrelevant at this point, because
they are contained within the volume of the larger buffer bag.) Even if a little bulging is
experienced, the design is not useless, because the product bags are assumedly being transported
over the Rocky Mountains. If they were being opened at the top of the mountain (or at high
elevation in general), opening the cases would likely be unpleasant as the buffer bag would rapidly
expand upon opening the shipping case, and the product bags would expand upon opening the
buffer bag. However, this is not a solution for that problem and I do not deem this limitation to be
relevant in these circumstances.
Conclusion
This solution is really quite simple at its core. An air-tight container will attempt to expand in
volume when subjected to an ambient pressure that is lower than its internal pressure. And so, the
simplest way to prevent this expansion is to control the ambient pressure. To do this, a microenvironment must be created in which the pressure remains relatively constant, regardless of the
environmental air pressure. This micro-environment will be created using “buffer bags” that are
sealed around the bags of product which need to maintain a constant volume. The volume of the
buffer bag at the time of packaging will be very close to that of the internal volume of the shipping
case. This means that the buffer bag will very quickly fill all of its available space once the external
pressure drops and the amount of possible expansion (and therefore decrease in pressure) will be
minimized. The buffer bag will be the immediate environment of the product bags, and therefore
the pressure difference between the product bags and the new, slightly lower pressure of the buffer
bag will cause a small increase in volume. However, this will be a much smaller volume change than
without the buffer bag, and as a result more bags can be packed per buffer-bag-equipped shipping
case.
POSSIBLE ISSUES
The temperature variable is not being actively controlled here, which appears to go against the
claim that was made earlier about how the ideal gas law is the be-all-end-all for designing a solution. If
pressure is being controlled but temperature is allowed to run rampant, then what good is being done?
This is an interesting scenario in which other contending forces must be considered. Just as pressure is
attempting to equilibrate, so is thermal energy. Heat is constantly flowing from areas of “high density”
(hot things) to areas of “low density” (cold things). The kinetics are not necessary to understand for the
general theme of this concept, but it is important to realize that certain materials are more thermally
conductive, just as some materials are more electrically conductive. If the materials that are used in the
system have high thermal conductivity (that is, they allow heat to flow quite freely), then it is possible
for heat exchange to occur across the membrane where gas exchange is prohibited. Therefore, any
marked increase or decrease in heat energy inside/outside the product bags, buffer bags, shipping
container, etc. will essentially allow the equilibration of the heat. A call for a decrease in pressure might
elicit a cooling response, but this will be largely offset by the ambient temperature attempting to
establish equilibrium with all elements in the system.
INTERESTING NOTES
Using the highest point in the US interstate system (12,182 ft. or 3713 m. on Rt. 34 in Colorado
between Estes Park and Grand Lake) as the assumed maximum for altitude, and Equation 3 which
relates air pressure (P, in pascals) to elevation above sea level (h, in meters), the lowest pressure that
could be experienced by the shipment would be 100,726 Pa.
P = 101325*(1 - 2.25577x10-5*h)5.25588
Eq. 3
Assuming that the lowest altitude (and therein pressure) would be sea level at 101,325 Pa, the percent
increase in volume, assuming constant temperature, would only be .60%. This essentially means that for
every 167 bags that held at constant volume would allow for one extra bag to be shipped. However,
experimentally this value may be larger due to other factors such as temperature or weather patterns
that cause a deviation from the pressure calculated from Equation 3. Also, a solution may be deemed
worthwhile for such a small increase in efficiency.
ATTACHMENTS