We all have poured liquid from a bottle. Wine, whisky, cognac, milk or maybe even water. When liquid runs out and air can flow back in, all is fine. As we gradually steepen the tilt angle of the bottle, the more the flow-rate increases; still, all is well. However, you will observe, above a certain steepness, the flow begins to fluctuate and bubbles occur, rising speedily from the opening of the bottle, up to the (alas, ever-expanding) air volume above the liquid. The underlying principle, which applies to all liquids running out of containers, including fountain pens: liquid can only escape when air can get in.
Above all, the alert observer will notice, when the liquid level is still high, the bubbles occur frequently (and are smaller) while, as the niveau descends, the rate slows down and the bubbling turns into a glugging (the bubbles gain in size). Very significant for the design of fountain pen parts.
Most of us will have accepted this (the incessant descent of the liquid level) as a fact of life. You may even enjoy the sound of glugging, you may have noticed the change in sound from a higher pitch (many small bubbles) to a lower (a few large bubbles), but that’s irrelevant for fountain pens.
Since you are here and read this, I assume, you are inquisitive enough to want to know why bubbles occur.
Sketch 1 — Birdbath
I drew a stylised bottle (a hermetically sealed container, sketch 1) with its opening sitting on a liquid surface. Some of you may have performed this experiment when you filled a bottle by holding it below a liquid surface. When you pulled the bottle up, holding it at its closed end, hence, with the opening remaining under the liquid surface, to your utter amazement, the liquid didn’t run out. If you have not performed this experiment, it’s about time you do, try it, it’s fascinating, but I suggest you use water, why waste the good stuff. It’s nothing too earth-shattering, but otherwise, it is known as a birdbath.
Let’s observe this a bit closer. After you filled the bottle with water and turned it upside down while keeping the opening closed by the water, a small amount of water will escape and then the flow of water will stop.
Gravity and the volume of water result in its weight, hence, i.e. Fwater, which causes the water to flow out of the bottle. Simultaneously, as the volume of air above the water increases, its pressure Pvacuum falls the below that of the ambient air Pair. This pressure difference causes the force Fvacuum, and as soon as it’s equal to the force Fwater, the water stops flowing out.
Fvacuum = Fwater
This is a stable status, which only changes when circumstances change.
Let’s do this. When lifting the bottle upwards for a small distance, the air-pressure difference sucks in one or several bubbles of air into the bottle. Therefore, the vacuum lessens and so does its resulting force Fvacuum. Subsequently, the force Fwater is larger than Fvacuum and a certain amount of water flows out. Concurrently, the vacuum increases until Fvacuum is again strong enough to counteract the force Fwater created by the (reduced) column of water.
With regard to a birdbath, the above-mentioned change of circumstances can be induced when we ask a chicken to drink some water. The same happens when the writer begins to write and use up some ink stored in the feed. When the ink level has dropped to a predetermined level, air enters into the reservoir and a small amount of ink can escape. The filled feed functions the same as the filled water tub. When the water passes through the tiny, unintentional hole, at a certain niveau, air enters into the bottle and water runs into the tub.
Please note: With every amount of water flown out, the weight of water lessens, therefore the vacuum required to hold it is less. Per repetition, the size of the air bubble increases and more ink runs out. Remember the change of sound when emptying a wine bottle?
I recommend you read this repeatedly until you surely understand it. It is one of the essential principles of the feed’s function and demonstrates the process by which the feed compensates for the variation of parameters.
And please note further: The same principle of physics apply to any other liquid such as the wine mentioned above, including whisky, and cognac. If you want to prove this point, use a drinking glass as the collecting receptacle and try not to spill too much.
And for chicken and other feathered creatures, please note: when you drink water from the little trough and its niveau drops, don’t worry, the same principle applies and the water in the tray gets replenished, as long as there is water in the supply container.
And a final note for fountain pen users: The same applies to ink.
Fountain Pens and Bottles
Sketch 2 — Rudimentary Fountain Pen
Now, I will translate the above into fountain pen physics, with one exception. Since we have not yet handled capillaries and surface tension, I will use a thin pipe for the transport of ink, rather than a capillary. I will talk about the difference in the relevant next chapter.
Sketch 2 is very similar to sketch 1 – the birdbath. The lower water surface is replaced by a piece of paper, saturated enough to withstand the air-pressure difference thus preventing air to enter through the bottleneck, the thin pipe into the reservoir. Hence, the equilibrium of forces can be achieved and sustained. The flow of ink stops.
Technically speaking: If the piece of paper is very absorbent like blotting paper and if it is large enough, and you wait long enough, the container will drain, eventually. Why is that so? Excellent question. Hang in there!
As you move the bottleneck across the paper to a dry area, the pressure difference can push a small amount of air through the paper fibres and a bubble will rise. This allows a small amount of ink to escape from the bottle (the same birdbath process as in sketch 1). The hygroscopic characteristic of the paper and its capillary action contribute to it, but about this, later.
Don’t get too excited; this is not a fountain pen, even though, there are similarities. What I described is only a thinking model. But mind you, it may well have been the function of early fountain pens in pen history. The resulting line of writing would have been rather blotchy. However, having said this, if we can make these burps of ink small enough and more frequent, then the flow would be more continuous, and we have achieved one of the functions of the feed.
Since we are curious, let’s leave behind what we know and explore characteristics of liquids and solids, which help the fountain pen feed to fulfil its function, namely: surface tension and capillarity, in as far as they concern ink and the surface of the feed.
Therefore, the next chapter is on Surface Tension the one after, on Capillaries.
Ω
11 March 2016
Fountain Pen Design 