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Fountain pens have to breathe
In older pens with sealed chambers, drawing the ink down creates a bit of a vacuum that can choke the ink flow. The pens have little ways for air to soak in, through the fins at the back of the feed or through the hole at the top of the split.
Writing too fast shows another effect. Some pens put down a dotted line when pushed quickly, and a pen can choke if you go too fast, especially the older ones with vacuum chambers. Rayleigh instability is what happens when a turned-on tap sprays off into little droplets. In a pen, the same thing happens in reverse as air goes back into the main chamber.
What makes a stream break into droplets?
Surface tension pulls a liquid column toward the shape with the least surface area, and a sphere has the least. Any tiny ripple on a thin stream grows because the narrower sections get squeezed harder, until the stream pinches off into drops. Joseph Plateau studied this experimentally in the 1800s, and Lord Rayleigh worked out the math in 1878. The effect is called the Plateau-Rayleigh instability.
Why do pens leak on airplanes?
Air trapped in a pen's chamber expands when the outside pressure drops, as Boyle's law describes, and the expanding air pushes ink out through the feed. Airliner cabins are pressurized to the equivalent of roughly 6,000 to 8,000 feet of altitude, with 8,000 feet as the regulatory ceiling. Pens with more air inside have more room for that expansion to push ink out.
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