Return to the Bubble Bottle
How do surface tension and capillary forces work in a fountain pen feed? In sketch 1 from the chapter Bubbles and Bottles, the problem was to get air inside the bottle/reservoir. The water outlet and air inlet are determined by the same component, the bottleneck.
Sketch 1 – separating functions: feeding ink, air inlet
I always found it to be good ingeneering practice to have a component or an element of it carry out one function, only. This permits to adjust this function without affecting any other, or at least minimise the interference. I show this in sketch 1.
The first function is “feeding the ink”. For this, I chose a narrow capillary, d1 (two, actually, about that, later). The second function controls the entering of air (air inlet). The surface tension will prevent the ink from flowing out through the air inlet because the diameter d2 is smaller than the maximum diameter the surface tension can bridge. The diameter needs to be smaller because it not only has to hold the ink column resting above it but also resist the possible increase of air pressure inside the reservoir. Note: d1 is much smaller than d2.
Like in sketch 2 in the chapter about Bubbles and Bottles, in our current example the ink is drawn out of the reservoir by the suction of the paper (could be any other method), hence, the vacuum Pin increases. When the resulting forces between the vacuum and the atmospheric pressure Patm are stronger than the surface tension of the membrane at d2, the membrane ruptures and lets in a bubble of air. You know why. This reduces the vacuum Pin, the resulting force drops and the surface tension closes the air inlet.
This design permits subtle adjustments of the d1/ d2 ratio until small changes in the pressure difference between Pin and Patm regulate the ink supply within such narrow variations so that no noticeable effect on the ink supply will be noticed by the writer.
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Sketch 2– pendant drop test
A hint for the capillary designer: An easy way of finding out whether a diameter is within the range of capillary action is testing the meniscus at the air inlet. If it curves concavely, towards the fluid, yes, then the design is within the range of capillarity, and the surface tension can hold the column of liquid. If it forms a semi-drop, when it curves convexly, away from the fluid, the situation is unstable and the design needs to be corrected.
To examine the effect of alterations, I used a measuring microscope to observe and measure the curvature of the meniscus at the lower end of a capillary. By now, you will certainly appreciate that the standardisation of the ink was absolutely crucial.
For calibration of the ink, I modified the standard pendant-drop-test, sketch 2, to suit my purpose, where I measured the drop size pd (length of pendant drop) at a constant capillary height h. In one go, I could test the characteristics of the ink with regard to capillary action and surface tension.
Applying to Fountain Pen
Sketch 3
Sketch 3 shows the progress towards the application of the above to the design of a fountain pen feed. The feed is in blue/grey and the nib depicted in gold. I have chosen a schematic display to explain the feed’s function without the distraction of individual design features of the feeds of various manufacturers. I may come to this later on.
Now I will address the various functions of the feed and how they are carried out. Since we have focused on the air inlet, let’s stay with that.
The air inlet needs access to the ambience, hence needs a vent which usually passes through the feed. There are reasons for the location of the air inlet near the reservoir; one is the height of the column of ink. You can see the abrupt crossover from d1 to d2 where the diameter of the air-hole d1 which is suitable to hold the membrane, to a larger diameter d2, which is still within the capillary range of ink. However, the meniscus forming at this cross-section is not stable enough to suit the standard function of the fountain pen. Through this significant change of cross-section, I can accurately determine the position of the meniscus.
Let me repeat this core principle of controlling the direction and amount of ink and airflow in the feed: Significant, abrupt crossovers in cross-section. It applies for all functions where the direction of the ink or airflow needs to be switched, for example: directing the ink to the nib under normal circumstances or guiding the ink into the overflow chambers.
As I said, the primary purpose of the air canal d2 is to provide air access into the reservoir through the feed. The increase of diameter from d1 to d2 prevents the air canal to be filled with ink under ordinary conditions. When ink is pushed out of the reservoir the surplus is taken up by the overflow chambers; only after they are filled, ink can enter into the air canal and as long as the fountain pen is not agitated, the ink will stay in there.
In my construction, the overflow chambers open into the air canal which not only achieves that they are completely filled but also assured the draining of the air canal in case ink has entered. As long as there is ink in the air canal no air can enter the reservoir.
Photo 1 – a piece of paper (internet)
The conical, yellow section in the diagram depicts the nib with its narrowing slit. The capillary forces are so strong that no ink comes off the slit of the nib, under normal circumstances… Unless, it meets paper, which has a higher hygroscopic/capillary force than the capillary force in the nib tip.
Photo 1 shows a magnified piece of paper.
Overflow Slits or Fins
Another significant component of the feed is an array of slits or fins, often called the collector, arranged perpendicular to the axis of the feed. This is shown in sketch 4.
They are capillary slits arranged to absorb any excess supply of ink. (The causes for excessive supply I explain in the chapter on Temperature and Air Pressure). Via a distributor, the slits are connected with the feed capillary and vent into the air canal. Their capillary pull is less than the feed capillary, nib and paper, but higher than the air canal.
Sketch 4 — Simplified Fountain Pen – fill height of overflow slits
There is a decrease of capillarity in the feed, from the feed canal having the highest, a step lower follows the distributor, then the slits and lastly, the air canal.
Under normal circumstances, the ink remains in the ink canal and only wells from it into the marginally wider distributor when an excess of ink is loaded into the feed. After a further increase of ink volume occurs, the ink enters into the slits.
Due to gravitation, the slits fill one after the other, from the lowest upwards. The height of the filling of the slits is determined by the capillarity and the surface tension characteristics of the feed and the ink. I have tested many fountain pens in this regard. The maximum height I have observed occurred in my fountain pen and it amounted to 25mm from the tip of the nib, reliably, see sketch 4. I explained this in chapter Capillaries.
Marginally, this dimension can be influenced by the width of the ink feed capillary of the feed, however, if it is too narrow, the ink supply is reduced and may be insufficient. This is the reason why I put two ink capillaries in my feed design, namely, to create enough capillary pull and at the same time provide sufficient ink.
Now, that’s when the balancing act starts. When a surplus of ink supply occurs, the capillary action of the overflow slits must take the ink away from the feed capillary before a noticeable variation of ink supply at the nib occurs.
Desirably, the capillarity of the nib and feed capillary is high enough so that the slits can fill before the ink drips off the nib. Since the slit closest to the nib experiences the highest hydrostatic pressure, it fills first, then those above it. As I mentioned previously, they don’t fill simultaneously but from the bottom up. Hoping for supernatural participation, I added an extra slit to my feed design, just in case.
Since at the situation of oversupply of ink the function of the air-hole (to the reservoir) and air-canal are not needed, I designed the feed so that, after all the slits are filled, the air-hole membrane breaks before the slits empty into the air-canal. Then the air-canal can absorb surplus ink exiting directly from the reservoir before ink drops from the nib.
As long as the fountain pen is not shaken, the ink will stay in there. When writing commences, the air-canal is emptied first through the lowest slit. Why? Because in the course of the tributary to the nib, it has the highest hydrostatic (inkostatic) pressure and the shortest capillary, hence, the least capillary force to counteract it.
The aim is that the last membrane/meniscus to fracture is the one at the nib. May this be as it is, whatever comes first, any spillage is undesirable.
The magic trick is that all will be emptied through writing or absorption with blotting paper when touching the nib.
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I have seen feeds with slits arranged in excess of the 25 mm limit. They are useless. In some designs, the slits’ widths are reduced as they go up. Doesn’t work, unless they are in the vicinity of the feed capillary, and once they are full, they never empty. Eventually, they clog up and become useless.
The underlying idea for the construction criteria for the slit array is:
During general use, the overflow slits are empty so that their full capacity is available in case of need (oversupply of ink from the reservoir, etc.). If they have been filled, they must be emptied first as soon as the writing starts, before any ink is drawn from the tank. In some fountain pens, those with the air-canal at the nib side, this function is controlled by the airhole.
I would have liked to design a feed with slits increasing in diameter towards the nib, like a small Christmas tree. Pursuant to my understanding, it would have worked. For sure, this would have required a different, unusual shape of the grip section to house it. Since “Form follows function” this new shape would have been an outward expression of a significant inner change.
Management was not prepared to take the risk. They told me that the fountain pen market is very traditional. Finito! … and the world missed out and even more outstanding progress.
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As far as I can see, we have covered now all the functional aspects of the feed. Remind me in case I have forgotten something, which can happen quite easily when one is very engaged in writing. Let us have a look at the design process and design criteria, now.
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The next chapter focuses on the Development of the Feed.
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26 March 2016
Fountain Pen Design 