The most considerable challenges presented to a feed are the variations caused by
■ emptying of the reservoir through writing and the consequential change in air pressure and the increase of the air-volume inside the reservoir
… which exacerbates the effects of the …
■ change of ambient temperature, which will vary the temperature of the air-volume inside the reservoir thus its volume
■ change of ambient barometric pressure, therefore, a variation of the air-volume inside the reservoir
and overall:
■ nasty treatment by frustrated writers. BTW, writer’s block can be alleviated through busying yourself with caring for your fountain pen. Your anxiety moves momentarily into your subconscious where it will dissolve, most likely.
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Reduction of the ink volume alone is no problem because the capillarity of feed and nib is generally capable of holding the column of ink resting on them. Drawing ink out of the reservoir creates a slight vacuum, which initially helps to carry the column. As writing continues and ink is drawn from the reservoir, the vacuum builds up gradually, until the pressure difference is sufficient to rapture the meniscus at the air-inlet. The feed should compensate for variations in ink flow.
In case the air-inlet is inadequately tuned, meaning, it does not rapture at the correct pressure difference, the ink flow will slow down and pulsate noticeably or stop, eventually.
The challenge arises, when the air-volume in the reservoir increases due to ambient variations, which is the case when temperature increases or air-pressure drops. Now ink is pushed out of the reservoir without the need for writing.
Due to tuning its capillarity, the liquid-membrane at the air-inlet will withstand the pressure increase. Now the surplus ink needs to be absorbed and stored in the capillary slits in the feed.
I constructed the feed in a way that the slits also open towards the air-canal. This prevents air to be trapped in the slits and permits them to fill more readily. Just in case some ink does escape from the air hole of the reservoir, it will be absorbed by the slits from the side of the air canal, opposite of the ink canal. Since this would happen at the upper end, near the reservoir of the feed, the ink would be absorbed by the slits near this end. Any surplus of ink in the ink canal would be filled into the lower slits, hence, there will be no competition of demand.
§
In order to test the feed, one must understand the principles of physics and then build an environmental chamber to simulate the two changes of ambient conditions, independently, accurately and repeatably. This permits research on the impact of parameters individually and in combination.
In case researchers are confronted with two (or more) variable parameters, they allow one parameter to remain variable but must keep all others constant. This permits a systematic approach to solution-finding.
I began with:
Keeping the Temperature constant …
… and varying the ambient air pressure. In relation to gaseous substances, Robert Boyle (1662) discovered through experimentation:
P1 × V1 = P2 × V2
and leading from this: P × V = constant
Meaning: at a constant temperature, the product of pressure and volume of one condition C1 equals the product of another pressure and volume of another condition C2.
Said in an applied way: if you have a volume V1 of gas in an enclosed, elastic container (a balloon) surrounded by a pressure P1 and you decrease the surrounding pressure to P2 then, the volume inside the balloon will increase to V2 proportionally
P1 × V1 = P2 ↓ × V2 ↑ … if one goes down the other has to go up in order to keep the product constant.
Diagram 1
In diagram 1 I show the above applied to fountain pen conditions. Here the volume is enclosed in a solid container (cartridge or tank). For the ambient pressure variation to have an effect on the enclosed volume the enclosure needs an opening, which, in the test also serves as an overflow.
Now we have the volumes Vbefore and Vafter – after the ambient pressure reduction – and the volume, which must be absorbed by the capillary slits in the feed, VFeed which is not drawn proportionally!
Vafter – Vbefore = VFeed
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I wanted to find out if it mattered to the fountain pen whether the air volume change in the reservoir had been caused by a change in temperature or ambient air pressure. I did this by:
Keeping the Pressure constant …
… and varying the temperature. Jacques Charles (1787) found for gaseous substances the ratios
P1 ÷ T1 = P2 ÷ T2
And from this it follows that P ÷ T = constant
Meaning: at constant volume (when the volume is firmly enclosed), the ratio between pressure and temperature of one condition C1 equals the ratio of another pressure and temperature of another condition C2.
Said in an applied way: if you have an enclosed volume of gas at a temperature T1 and a pressure P1 and you increase the temperature up to T2 then, the pressure P2 increases proportionally.
Monsieur Charles also discovered, when one keeps the mass of a gas constant (like in a gas-filled balloon, where the number of gas molecules remains constant), then
V ÷ T = constant
Meaning: an enclosed, but expandable gas volume Vbefore changes up or down to volume Vafter proportionally with the temperature changes, which causes hot air balloons to rise up into the air and the colder the climate the easier and higher they rise.
Applied to fountain pen:
■ When the temperature of the gas volume in the reservoir increases, the ink will be pushed out. This ink needs to be captured by the slits in the feed.
■ Ink gets also pushed out when the ambient pressure decreases, as it happens significantly during the ascension of an aircraft, but even barometric changes can be significant enough to this effect.
This is why it is recommended to store fountain pens with the nib upwards. Whoever invented desk-stands for fountain pens where the fountain pen is stored nib-down should be cursed. For many reasons they were very useful for nib holders, but sometimes tradition must be discarded.
When travelling in an aircraft, it is best to empty the tank and remove the residue of ink with blotting paper or remove the cartridge. Just to be on the safe side.
If you know your fountain pen well enough and you want to take the risk: Filling it (reducing the air volume in the reservoir) before embarking can prevent leakage. Reason: If the air volume is only small (the reservoir is almost full), the feed can cope with the small amount of ink pushed out of the reservoir due to the variation of the air volume inside, which happens in response to the drop of air pressure in the aircraft cabin.
Rationale
■ Following the above, it is evident that a feed can absorb a definitive amount of ink. I may be stating the obvious but it cannot be said often and clearly enough. Some still argue this fundamental fact.
■ Ambient influences and the correlating change of the air pocket in the reservoir are irrevocably linked by laws of physics.
■ The amount of ink pushed into the feed slits is linked with the total size of the reservoir because the larger the reservoir volume, the larger the air pocket can be. The larger the air pocket, the greater its variation under altering ambient conditions and the more ink can be pushed out, subsequently.
■ An existing feed has a defined capacity. Hence, the range of variation of the ambient scenario, which is demanded by the market (marketing boss) directly determines the maximum size of the reservoir. The subtler the variations of the ambient scenario, the larger the ink reservoir a fountain pen feed can handle.
In consequence, one must accept, that there is a limit to the permissible air-volume change in the reservoir (and its total volume), which a feed can compensate, namely the volume of available, useful overflow slits.
I hope to have demonstrated the correlations between a gaseous volume, temperature and pressure by laws of physics as they have been established centuries ago, and they still apply. No top management’s authoritarian determination can change this, however demanding they may be. A bitter pill, which was (most possibly still is) a bitter pill for them to swallow:
There is an authority, above them.
However, they blamed my “incompetence”.
§
Let’s calm down. After one agrees to the specific combined maximum ambient variations the feed must be able to compensate, one can calculate the resulting size of the reservoir.
And vice versa: With a given reservoir size, one can calculate the maximum air-volume variation in the reservoir a feed can compensate without spillage. This result would be the theoretically best possible, as the practically achievable result is lower due to the unavoidable production tolerances.
I was faced with a stalemate. No one wanted to accept any of the above. Those days I was much younger and didn’t walk away; partially because of my passion for the task and opportunity to ingeneer a fountain pen all by myself. Secondly, my highest respect was towards my users; hence, I wanted to give them the best possible product within the limitation I was presented with. And thirdly, no one else in the company would understand what I was doing and I would only talk about details when asked specifically which hardly ever happened. Does the end justify the means?
Therefore, I took what was given (size of the reservoir and the outer shape of the section) and calculated the theoretically possible value of air-volume variation. This was important because it indicated how far any feed construction had been away from this optimum. It told me when to sensibly stop with my work trying to improve where there is no room for it.
For my research, I had a chamber with a glass door and internal light which permitted to alter temperature and pressure. Through this, I could simulate the ambient changes and test how close the function of my feed had reached this theoretical target.
From the above clearly follows (am I really saying this now for the third time?):
■ The air-volume inside the ink reservoir, which causes the ink to be pushed out, is in proportion to the overall volume of the reservoir. The larger the overall volume is, the larger the air-volume can be. (Sounds obvious)
■ At particular ambient changes, the larger the air-volume in the reservoir is, the larger its air-volume variation is which pushes the ink out.
■ If one keeps the maximum air-volume variation below the absorption capacity of the feed, the fountain pen will not leak.
■ The size and form of the feed, and thus its absorption capacity depends on the envelope given by the shape of a fountain pen’s grip section and the length of the nib.
Below I show the above criteria in a linear sequence of dependence which applies in both directions.
volume of reservoir ↔ air-pocket-volume ↔ air-pocket-volume variation ↔
volume of absorption capacity of feed ↔ shape of the grip section and length of the nib
Unfortunately, even though this is so transparent, those in charge are blind to it. In the business world, the “real” world, the size of the reservoir is determined by competitive marketing games, organised by the same people who want to have the best product on the market. How can they manage a project or even a company if they are so unaware of the facts? Are they open to negotiation?
Anyhow, I hope you enjoyed this chapter and your excitement lures you to continue reading about the Initial Dry Start.
Ω
04 April 2016
Fountain Pen Design 