Researchers deconstruct the physics of writing with a fountain pen

Dec 30, 2011 By Peter Gwynne
Credit: János Fehér

Wetting a fountain pen to compose a thank-you note is a grand way to express gratitude for a holiday gift, yet we often don’t give a thought to what happens when ink moves from pen to paper. But for a team of South Korean and American scientists, the medium is more important than the message -- and can even provide new insights into ancient biological systems.

The researchers first developed a theory of ink flow that involves the basic properties of paper and fountain pen. Then they confirmed the theory using rudimentary pens made of tiny glass tubes, glycerin ink, and faux paper etched on the silicon wafers used to produce electronic devices.

The team reports its findings in the journal Physical Review Letters.

"Writing is one of the most important inventions of human beings," said team leader Ho-Young Kim, professor of mechanical engineering at South Korea’s Seoul National University. "But surprisingly there had been little study of the scientific aspects of the process. This motivated our attempt to understand the phenomenon."

"The topic is interesting and the authors are experts," said Howard Stone, a professor of mechanical and aerospace engineering at Princeton University who was not involved in the project. "Their results are impressive."

The team identified multiple related physical properties responsible for the transmission of ink from pen to paper.

Capillary action allows fluids to flow in thin tubes against the pull of other forces such as gravity. For instance, it causes paint to move up the bristles of a paintbrush, and paper towels to absorb liquid spills through their microscopic, wood-based, cylinder-shaped fibers.

Capillary action results from two processes working together. The first is adhesion, or the attachment of a liquid to a solid object, such as water to a glass tube, due to the attraction between the molecules of the liquid and the solid object it contacts. The second is surface tension, the cohesion of liquid molecules on its surface. Surface tension allows liquids to form round drops and insects called water striders to walk across the taut surfaces of ponds.

Another important phenomenon is viscosity, a fluid's resistance to flowing. For example, tomato ketchup is more viscous than water.

One other factor comes into play: the speed at which the writer moves the pen.

Team member Lakshminarayanan Mahadevan, a professor of mathematics, , and biology at Harvard University, explained that the new theory views the process of writing as a competition for the ink between pen and paper.

"The pores [in the paper] draw in the fluid via capillary – surface tension – forces, while the viscosity resists this motion," he said. "The moving pen drags along the fluid, and again viscous forces resist this. Together they shape the blot, if one hesitates, and the line when one's thoughts flow from the mind to the machine that records them – the pen."

To test their theory, the researchers devised "minimal pens," imitation inks, and jury-rigged “paper."

The pens consisted of glass tubes with diameters between half a millimeter and one millimeter. Solutions of glycerin in various concentrations provided the "ink" that filled them. And to mimic paper, the researchers etched tiny pillars, of various heights and separated by distances much less than the pen's diameter, on the surfaces of silicon wafers.

Careful observation showed the glycerin ink from the minimal pen flowing into the valleys between the pillars in the faux paper in just the way the team had predicted. "The agreement was excellent," Kim said.

The shape of the ink front ahead of the moving pen also confirmed the theory.

"Physiologist Douglas Wilkie said that facts and theories are natural enemies," said Mahadevan. "But here they were friends, helping each other along."

The researchers emphasized that their theory does not apply to ballpoint pens. "They use fundamentally different ink from what is used in fountain pens," Kim explained. "It doesn’t spread like usual ink."

However, Mahadevan said, "We are currently thinking of a different theory for this process."

Kim pointed out that, because paper consists of a network of cellulose fibers, the research has implications beyond writing.

"Cellulose is the major constituent of plants' cell walls," he said. "Therefore, understanding liquid flow into a cellulose fiber network has a profound implication for water transport in plants. Our work can be used to enhance our understanding of how water can climb up tall trees without mechanical pumps. And there are functional porous materials [based on cellulose] which are particularly useful in biomedical fields."

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User comments : 20

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FieroGT42
3 / 5 (6) Dec 30, 2011
I don't really see what was learned here that many of us don't already know...
rawa1
1.8 / 5 (19) Dec 30, 2011
We just learned, when allowed free, the physicists manage to spend all money into useless confirmation of existing theories into account of research of phenomena, which seemingly violate them, like the cold fusion and they may be extremely useful. These freaks don't care about destiny of civilization, until their money are going.

Not only the elementary sense of practicality is missing here, but even the basic principle of scientific curiousness, which forces people to study the unknown phenomena first - just because they're unknown. The contemporary generation of physicists is decadent, scholastic and degenerated from this perspective: they're not interested about something new, but about strengthening of their inter-subjective religion, everything can be computed. So they're avoiding the research of phenomena, which cannot compute and predict so easily instinctively. But the actual research is, if you don't know, what you're doing - everything else is stamp collecting.
sigfpe
4.2 / 5 (5) Dec 30, 2011
FieroGT42,

If you know this already could you please write down a formula the predicts the flow of ink for given paper porosity, ink viscosity and pen geometry?

Thanks
rawa1
1.8 / 5 (20) Dec 30, 2011
If you know this already could you please write down a formula the predicts the flow of ink for given paper porosity, ink viscosity and pen geometry?
For example, when the pop is separating from your ass, it undergoes the stress and viskoso-elastic flow, onto which the Young modulus and Navier-Stokes equation for laminar flow can be applied (albeit we can imagine the turbulent regime easily too). You could solve it with using of supercomputers and to determine the path of falling body for all possible geometries, pressures a viscosities of elastic body. I'm pretty sure, you could spend whole your life with thorough construction of parameter space of this process to reveal all its bifurcations, singularities and hidden fractal nature.

The only question is WHY? Just because it's possible and you could handle it? Why not, but you should research it for your own money like master of free arts, who is constructing some artefacts and just after then it looks for its occasional buyer.
davarm
3 / 5 (5) Dec 30, 2011
It seems this research encourages the flow of writing a tad quickly. Too little thought, no grammar and a superfluity of large words rather than insight and not an iota of physics. The engineers and mathematicians here used their background to expound on the complexity of capillarity. Those who fail to see any significance need to study the paper again I guess. I see enthusiasm, expertise across a number of fields and applications. Why don't you?
rawa1
1.4 / 5 (12) Dec 30, 2011
Many people believe, the basic research will always find its application in less or more distant perspective, but the reality is different. 40% of research time is consumed with collections of money, from the rest 60% of results are redundant and another 60% from the rest becomes obsolete faster, than it can be ever used. The people with better equipment and formal models in distant future would probably solve the same problem in much more effective and cheaper way just at the moment, when they would really have some practical usage for it. Now we are spending too much effort and money for research of curiosities, whereas the research with really useful applications like the cold fusion stagnates for years, while the devastation of life environment continues. This is what really bothers me, not the fact, some theorists will get his money for production of nonsense. The theory of scientific research prioritization is in its very early stage by now, not to say about its praxis.
Isaacsname
4.5 / 5 (2) Dec 30, 2011
So how exactly does their simulation of paper have any realistic relation to real-world scenarios ?

Even someone like myself can see that there are many extremes in printing, from the 1-2 tons of pressure required to print polymer inks on currency( which supposedly never really drys completely ) to the subtle requirements of hand printing with single-frame silkscreen setups.

I would think that the density of the cellulose matrix is not the only thing to consider here, there's all sorts of additives in various papers that I would think would have different electrostatic attraction gradients.

Maybe I'm confused ( not the first time ) but they are saying that Van Der Waals forces at the inter-facial boundary in the fluid affect the flow, than would a gradient dependent on the materials additives also induce an effect ?

I do have some experience with printing, so feel free to get technical.

@ Rawa , wouldn't that be the " turdulent regime " ?

Hahahaha...no, I'm sorry, I'm sorry....
NamVet666
1.7 / 5 (12) Dec 30, 2011
""Kim pointed out that, because paper consists of a network of cellulose fibers, the research has implications beyond writing.
"Cellulose is the major constituent of plants' cell walls," he said. "Therefore, understanding liquid flow into a cellulose fiber network has a profound implication for water transport in plants. Our work can be used to enhance our understanding of how water can climb up tall trees without mechanical pumps.""

The effects and process of pen and ink on paper is being understood more clearly by this study, but it is not as important as the related process of the uptake of water in plant life and this study has the possibility of revealing the secrets of the attraction of fluids to cellulose, both in trees and in writing paper. Sometimes, research on one phenomena presents resolution of another phenomena that was equally not understood. I gave the article a five because it mentions more than just one phenomena, but also a related one that may be solved.
Isaacsname
3 / 5 (2) Dec 30, 2011
I don't understand how this would answer questions of transport in plants, kraft pulping and other alkaline methods of making paper change the crystalline properties of cellulose by removal of the lignin and hemicelluloses.
axemaster
4.1 / 5 (12) Dec 30, 2011
We just learned, when allowed free, the physicists manage to spend all money into useless confirmation of existing theories into account of research of phenomena, which seemingly violate them, like the cold fusion and they may be extremely useful. These freaks don't care about destiny of civilization, until their money are going.

You do realize that without exactly this kind of research, you could kiss 3/4 or more of all existing technologies goodbye? Penicillin was discovered because a scientist said, hey let's investigate that cool fungus.

With regards to this specific research, it could easily be used to help design better pneumatic systems and ball bearings, which are used in, I dunno, EVERYTHING.

These freaks don't care about destiny of civilization, until their money are going.

Go take a dump and let us know when you've drained out that space between your ears.
NamVet666
1.7 / 5 (12) Dec 30, 2011
Not sure, but I don't think they're considering other types of paper that has had distinctive changes in makeup. The paper they're investigating may have the same consistency of tree pulp, and that would help keep everything in perspective for both phenomena.
The main concern is probably two-fold. In one, the ink is drawn from the pen toward the paper, usually at a lower level than the pen. But in an uptake of fluids and nutrients into the height of a tree, there is probably no "pumping' effect, nor a simple capillary attraction. There may be a different process entirely and that's what they seek. I hope they find it.
bewertow
4 / 5 (4) Dec 30, 2011
rawa is full of himself. He probably flunked out of college. He's just bitter because he's jealous of everyone smarter than him who gets to do research.
Isaacsname
5 / 5 (2) Dec 30, 2011
Interestingly, I did some quick experiments on my desk with various papers and some different ink pens.

I noticed:

A dry erase marker left on a coffee filter, the blot starts normally, but at some distance, which I cannot measure accurately on my desk, transport of the ink happens entirely inside the paper, iow, at some radius, it seems that the fluid is drawn into specific fibers and thrust ahead of the bulk of the fluid, the front of the spreading " blob ", this can be easily seen as small dots appear outside of the blobs radius, but no ink is observed on the paper's surface.

Dang, I just realized how much I'd like a nice digital USB microscope...

Callippo
1.7 / 5 (11) Dec 30, 2011
He's just bitter because he's jealous
I'm smart enough. But I'm upset, when I see, how the people are spending their lives and money of tax payers in development of BS instead of help of civilization and life environment.
snowman95
1 / 5 (1) Dec 30, 2011
Now they tell us, when pen & paper are almost obsolete. How about the aerodynamics of smoke signals, or the physics of impressing cuneiform markings on clay tablets? Inquiring minds want to know.
Humpty
2.5 / 5 (8) Dec 30, 2011
My reasons for calling "bullshit" on this article are:

1. I design and formulate inks for nibbed pens (dipping and fountain).

2. So have an awful lot of other people for centuries - bird feathers / quills, monks in monestaries, scribes, etc.,

3. There are only 5 parts to a good ink - usually.

i) The pigment (i.e. carbon black or dry hot soot - no oily residues in it)

ii) A binder to fix the pigment to the surface.

iii) A solvent or carrier to solute the "pigment and binder" to achieve a consistent darkness and fixative ratio of the pigment and binder to or into the surface of the paper / vellum etc. Usually water.

iiii) Some wetting agent (alcohol) to modify or lower the surface tension and to allow the ink to flow through the channel/s in the nib.

v) Thickeners or viscosity modifiers.

There are preservatives, corrosion inhibitors etc.

All of this is comparatively easy to achieve, almost all of it depends solely upon the ratios of the ingredients to create a good ink.
Anda
3.7 / 5 (6) Dec 30, 2011
I'm smart, I'm right, if you're not me you're an idiot, I'm Rawa1,no wait, now I'm Calippo, and my brain is full of aether.
Callippo
1 / 5 (4) Dec 30, 2011
This is your last ten comments
Reported abuse for the spam (including Oliver)
Well done Robo ;)
Scott, Kevin, u r gods, I'm an ape.
Go to god's sites pls
Aether noise...
You spend it on weapons idiot
Calippo, calippo que tonto es el calippo la madre que lo parió.
Sei proprio cretino.
We all deserve to be banned, mostly Omatumr, theghostofotto1923, Noumenon and of course myself.
That was really funny...
Rawa1 talking about "massive spamming in this forum" :)
Try to imagine the result, if everyone would use this forum, like you...
Argiod
1 / 5 (3) Dec 30, 2011
They still make fountain pens? I thought those were obsolete in today's ballpoint era...
PhotonX
not rated yet Jan 08, 2012
For example, when the pop is separating from your ass, it undergoes the stress and viskoso-elastic flow, onto which the Young modulus and Navier-Stokes equation for laminar flow can be applied (albeit we can imagine the turbulent regime easily too).


Could we please call this Recto-Fluidic Dynamics? Please? Please?