How the capillarity and ink-air flow govern the performance of a fountain pen

As kids, the authors enjoyed learning how to write by dipping nib pens into ink, and then later, using flex nib pens for calligraphy. They remember, less fondly, the troubles with ink leaks and spills over the paper's surface. Despite advances in fountain pen design, the performance of fountain pens is still not perfect. A robust fountain pen has to provide a sustainable ink flow-no leaks-for smooth and precise writing on paper. In the long history of the design and development of fountain pens, more attention has been focused on the ink flow than on the ink/air capillary flow balance. It is found that as ink flows out of the cartridge, the holding pressure in the ink cartridge builds up and the pressure drop across the capillary valve increases. Consequently, the air is sucked toward the ink cartridge. An air-ink meniscus is formed at the capillary valve and finally breaks into air bubbles due to Rayleigh instability. The air bubbles float into the ink cartridge under buoyancy force to reduce the holding pressure so that the ink can continuous flow out to the nib to keep the fountain pen in function. The unbalance between the air holding pressure in the ink cartridge and the pressure drop across the capillary valve is the key for the functionality of the fountain pen. A poor design of the feed/cartridge connection with a small orifice of the capillary valve leads to the malfunction of the fountain pen.