How to write into water?

Writing is an ancient cultural technique – people were already chiseling characters into stone slabs several thousand years ago. Although the writing system has been perfected since then, one thing has remained the same: both cuneiform writing and today's writing use solid surfaces to record the characters, such as stone tablets or paper. But how, as scientists from the Johannes Gutenberg University Mainz (JGU), the Technical University of Darmstadt and the University of Wuhan in China considered, do you write into water? In a way like aeroplanes do when they cross the sky, leaving white streaks behind – in three dimensions and not just 2D on dry paper?

Dipping a fountain pen into water in an attempt to write a word is likely to have only moderate success: When you drag the large fountain pen through the water, vortices are created and the writing trace is blurred. But as the Reynolds number shows, the number of vortices decreases the smaller the moving object is. However, a tiny pen would again require a large reservoir of ink, which would negate the advantages of the small pen.

A bead of ion-exchange material serves as the pen

The research team therefore chose a completely different way to circumvent this fundamental obstacle: “We put the ink particles directly into the water and use a 20 to 50 micrometre bead of ion exchanger material as a pen,” explains Professor Dr. Thomas Palberg from JGU.

This bead is small enough not to create any eddies. The trick: the bead exchanges the residual salt in the water for protons and thus locally changes the pH value of the water. When the bead is rolled over the bottom of a water bath, it leaves an invisible trail of low pH. This in turn attracts the ink particles – the path travelled by the “writing ball” is marked with ink and a fine line of only a few hundredths of a millimetre in width is obtained in the area of the respective lowest pH value.

To write a letter into water, it is sufficient to tilt the water bath so that the ball rolls the corresponding path. “For the first experiments we moved the water bath by hand, later we constructed a programmable motorized stage,” Palberg explains. “For example, we painted Santa's house in a water bath the size of a one-euro coin – as big as the I-dot of an 18-point font – and looked at it with the microscope,” says Palberg. “But that is only a first step.”

Writing in a continuous line of any shape works well reproducibly, as accompanying simulations also confirm. Interruptions of the writing, as they exist between different letters, can also be realised: For example, by specifically switching the ion exchange process on and off through exposure. Erasing and correcting are also already possible.

General effect that can be optimised in different directions

Professor Dr. Benno Liebchen and Lukas Hecht from the TU Darmstadt developed a theoretical model that explains the mechanism that makes writing into water possible. The associated simulations showed that the mechanism was generic, i.e. generally valid, and could therefore be realised in many different ways in the future, says Liebchen, head of the Theory of Soft Matter group at the Institute of Condensed Matter Physics (IPKM).

“For example, besides ion-exchange balls, particles heated by laser light or even individually controlled microswimmers could be used as 'pens',” he explained. “This could enable highly parallelised writing in water. The mechanism can be used in the future, for example, to create even the most complicated concentration patterns in liquids.” The new writing technique could also eventually be used artistically.

The theoretical calculations show in particular that this new way of writing is by no means bound to the bottom surface of a water glass. Rather, it is a very general effect. All it takes for the lines to remain clearly visible for a few tens of minutes is rapid transport of the ink to a written track and washout based only on diffusion.

Using UV-sensitive, “sticky” ink, even longer fixation of written lines could be achieved. By further exchanging components – such as the pen, the type of track, the ink or the control system – many different variants can be realised in the future. For example, it is conceivable to use fluorescent ink or several very light writing balls that can then be moved through the water in three dimensions with laser tweezers. In this way, not only could self-luminous writing be placed, but liquids could also be structured three-dimensionally. “The approach is very robust and extremely modular,” Palberg confirms, “and can be optimised in a wide variety of directions.”