An alternative look at ink wetness

[LizEF]

It appears, @dipper, you beveled the edge for easier entry.  And the ink thanked you by flowing gloriously wet.

[InesF]

16 hours ago, dipper said:

 

 

Well done!

 

Your nice drawing and the photos before initiated some more thoughts about fountain pen (or nib+feed) wetness. The outcome is: more questions than before!

- can it be, if the ink channel in the feed has a more narrow part (like the compressed part in your drawing) than the slit between the nib tines, the flow will be poor (or hesitant) because capillary pressure is higher in the compressed zone than at the nib point?

- will widening the ink channel (to a certain maximum!) increase the pens wetness - and the opposite, if narrowing it? With the follow-up questions: As long as the slit between nib tines is the most narrow part of the whole ink channeling system, spreading the tines will make the nib more wet - does that always work, until the nib slit size exceeds the feeds minimum ink channel width? And if this doesn't work: the most narrow part of the feed is already the limit?

- will widening the air channel (to a certain maximum!) decrease the pens wetness - and the opposite if narrowing it?

- will widening (or narrowing) both channels in the relation: r_Ink / r_Air = constant, keep the wetness constant?

- is the proportion between the channels linear or by square or logarithmic?

- widening one of the channels to much will cause the ink to run out - but don't worry, the pen will create nice droplets on the paper, with more or less nice sheen! 

 

The plan for finding the causes behind fountain pen wetness is starting to grow. Thank you, @dipper, my initial thinking was way too complicated.

[dipper]

Another interesting ink feed:

 

This pen was sold in 1980's by UK shops of WHSMITH stationers with "WHS" on the nib. Original manufacturer unknown.

 

Air enters under the feed, and then spirals around the outside of the feed in a helical path.

... to the back of the feed where it passes through a flat gap at the side of the feed...

In the photo above, the slot at the centre of the back face of the feed is where ink enters the feed capillary.

 

The feed is an assembly of two parts. The ink channel takes the central route, inside the air helix, and then passes up to a more conventional position under the nib.

 

This pen is a cartridge/converter type, so it has to have a small projecting part inside the pen section to pierce the ink cartridge (international small standard).

Ink/air exchange needs paths continuing through the narrow neck of the cartridge. But this feed has a flat back end......?

 

In some other pens the feed has a narrow tail that fits inside the section small projecting part, linking ink and air paths all the way up into the ink chamber.

In this pen that linkage is made by capillary slots moulded into the pen section itself.

 

The ink has a strange journey between ink cartridge and paper: From the body of ink held in the cartridge it flows directly into any one of the three capillary slots in the sides of the part that projects into the cartridge. Then it has to bridge some small space to reach the flat back of the feed, where it enters one larger capillary slot and passes down the central axis of the feed.

Then that slot takes a dogleg path, stepping up to contact the underside of the nib. And onwards to the nib slit, down the slit, out onto the paper... .... "My dearest young son, I was so glad to read that you remain well and have grown another foot since leaving us to join the army last year. For your comfort I enclose one extra sock."

[LizEF]

4 hours ago, InesF said:

- will widening the air channel (to a certain maximum!) decrease the pens wetness - and the opposite if narrowing it?

Wouldn't widening the air channel allow air in faster, thus allowing (or forcing) ink out faster, thus making the pen wetter?  Why would a wider air channel decrease wetness?  My physics-deprived mind is confuzzled.

[InesF]

21 hours ago, LizEF said:

Wouldn't widening the air channel allow air in faster, thus allowing (or forcing) ink out faster, thus making the pen wetter?  Why would a wider air channel decrease wetness?  My physics-deprived mind is confuzzled.

Me too, @LizEF, me too!

During writing these bullet points, I may have messed up. Sorry to all reader for the confusion! 🤭 

 

The hypothesis, which remains to be experimentally tested, is:

the bigger the difference in channel diameters (air - ink, at their thinnest parts, respectively), the dryer the pen.

 

Another reason for confusion is: as long as the nib slit is the most narrow part of the ink channel, not much will happen if you fiddle around with the feeds ink channel.

 

Hmm. Now I'm so deeply self-confused, almost unable to formulate my thoughts.

 

My consideration is: the more narrow the ink channel, the bigger is the "sucking" capillary force opposing the reduced pressure in the ink tank → more ink is available at the nib.

BUT: if the channel is very narrow, the pressure is so high, that the nib will not let the ink go (holding it back and refusing to deliver to the paper).

BUT: if the wick effect of the paper is stronger than the highest capillary force in the ink channel, ink will flow!

AND: the space between the globular nib tip and the paper surface may always form the most narrow space with the highest capillary pressure as soon as the tip touches the paper.

AND: if this nib-tip-paper-capillary pressure is not much higher than the capillary pressure along the whole ink path, the nib will write dry → in this case: widening the ink path increases the wetness.

 

In the "resting" position, shortly before touching the paper, the nib tip should be the most narrow part of the whole ink path.

Once the nib touches the paper the narrowest area of the entire ink path is either somewhere in the ink channel or it is the small area under the nib tip. In the first case, the nib will write dry (or even stop writing) and in the second case, it will deliver the usual amount of ink. If so, the greater the difference in the diameters of the ink channel and the air channel, the more ink will be delivered.

Remark: Translated with www.DeepL.com/Translator (free version)

 

Ok, so far the freaked-out part of the nerds theory. 👩‍🎓

[LizEF]

3 hours ago, InesF said:

The hypothesis, which remains to be experimentally tested, is:

the bigger the difference in channel diameters (air - ink, at their thinnest parts, respectively), the dryer the pen.

Oh, that's interesting.  My assumption was based on the fact that when there's an air leak - poorly set feed, crack in the pen, it can lead to ink dripping out...

 

3 hours ago, InesF said:

Hmm. Now I'm so deeply self-confused, almost unable to formulate my thoughts.

No worries.  I think I brains formulate some ideas down deep and it can take a while for those ideas to rise up to where we can put words around them.  In the meantime, they're just these things that we can't quite put to words.

 

3 hours ago, InesF said:

Ok, so far the freaked-out part of the nerds theory. 👩‍🎓

That's a very interesting theory!  I'm looking forward to your experiments and observations!

 

I predict lots of questions based on the experience that a nib with a larger gap (to a point) between the tines writes wetter than a nib where the tines are touching at the tip.  If your theory is correct, that gap at the tip, however large, still needs to be narrower than the ink channel in the feed.  Hmm.  I'm glad I read this before trying microscopic pictures of my feeds, because it suggests a need to also take microscopic pictures of my nibs - and of the two together, if that's possible...  (Goodness.  May take me a while - there are so many other things I need to be doing first.)

 

Thanks, @InesF, for always challenging my brain to think more and in new ways!

[dipper]

Shock Newsflash !!!!!!!!

There are no "capillary forces" in any narrow channels filled with ink. 

 

Has Dipper gone crazy?

Possibly.

But consider the points below:

 

Imagine zooming-in to view one part of a narrow glass capillary tube containing ink. Zoom-in so close that all you can see is a small part of the tube entirely filled with ink. Is there any "capillary force" acting on the ink, directed along the axis of the tube? If there is a force, does it act to the left or to the right?

There seems to be no reason why any such force should favour pointing to the left or to the right. After all, the small part of the tube we are zoomed into is symmetrical. Left and right we see just more tube, and ink, disappearing out of sight on each side of our viewing window.

 

The resolution of any confusion here is the fact that there is no capillary force acting in either direction. All we have is ink at some local value of hydrostatic pressure. And that pressure acts equally in ALL directions.

 

But now examine each of the two ends of the ink thread inside the tube. At each end of the ink thread there is a curved meniscus. Each meniscus is a curved interface between ink and air, and the curve meets the glass wall of the tube at some acute angle. This is where surface tension acts. Each meniscus creates a force acting along the tube, acting in the direction from the ink towards the air. But the two ends of the ink thread are pointing in opposite directions. So the two menisci are both pulling on the thread of ink at the centre of the tube. Pulling with equal but opposite forces. The result is a drop in hydrostatic pressure inside the ink thread, but no movement.

 

The reason ink is drawn into a capillary tube when one end of the tube is dipped into a bottle of ink is that there is only one meniscus in the tube. So that one meniscus pulls and pulls and pulls ink up up up into the tube...... until something stops it. With the tube pointing upwards it is gravity that stops it at some height. The mechanism is that the weight of ink below the meniscus reduces hydrostatic pressure in the ink at the meniscus to a value below atmospheric pressure, and all the forces on the meniscus balance-out to zero.

For more details see the Wikipedia article "Jurin's Law".

 

Fountain pens are more complicated shapes than plain glass capillary tubes. But that does not change the physics principles of ink and air and surface tension. The weird shapes and angles do make analysis confusing. Despite that, it remains true that in any narrow gap filled with ink there are no surface tension forces acting. And also, at all the edges of such gaps where ink meets air there will be a lot of surface tension effects in play. The meniscus forces are communicated through the connected ink body as pressures.

 

Two examples of menisci in fountain pens:

 

1) At nib/paper/air edge.

The ink in the nib slit and under the nib is at some value of hydrostatic pressure. Around the edges of the contact area between nib and paper is an ink meniscus. That meniscus is a "saddle surface", concave viewed sideways-on, convex viewed top-down. The meniscus moves in or out, and its size and curvature changes until all pressures are balanced. If the nib is an EF then the meniscus top view shows a tight convex curvature, acting inwards. Result predicted is that the side-view concave meniscus must have tight curvature, acting outwards to balance. So meniscus must be small. ....... So EF nibs write relatively dry, all other things being equal.

 

2) At top of breather vent, where air enters the main ink chamber.

During use, as ink is drawn out of the ink chamber, the pressure inside the ink chamber will reduce. (That hydrostatic pressure is communicated to all parts of the continuous connected ink body, including ink feed capillary, and nib slit, and nib tip, as mentioned in example 1 above.)

Atmospheric pressure therefore forces air into the ink chamber.... but that air does not get very far.

The air entering the breather paths forms a small shallow curved bubble at the outlet vent in the ink chamber. That shallow curved bubble meniscus balances out the pressure difference, and the air is prevented from entering.

But more ink is used, pressure drops further inside the ink chamber, the pressure difference makes the bubble curve more, and again pressures are balanced.

When will this end?

The tightest curvature the bubble can achieve is when it is a perfect hemisphere sitting on top of the vent outlet. If the bubble grows beyond that size then its curvature is no longer increasing, but is now decreasing as it grows larger.

Result is a catastrophic explosion of air, bursting into the ink chamber. (A very very small catastrophy, but still a dramatic event if you happen to be a tiny air bubble.)

What if the air entry vent is made smaller?    A smaller hemisphere has a greater curvature. So a smaller vent forms a smaller hemisphere bubble before collapsing, and hydrostatic pressure in the ink chamber must drop lower before that occurs.

We can therefore expect pressure cycling in the ink chamber to be of greater pressure variation if breather vent is smaller.

What effect that difference will have on pen wetness is impossible to predict, as many other fountain pen design factors come into play further down the ink delivery path.

 

 

[LizEF]

Some person: "Liz, why in the world do you use fountain pens?"

 

Liz (adjusts glasses, looks thoughtfully at pen): "Well, you know, I just like watching Jurin's law in action - all those catastrophic explosions of air, you see.  Can't get that from a gel pen."

 

 

Thanks @dipper!  Am loving these physics lessons.

 

(Of course, I'm also now imagining our drunken nanites reacting to that catastrophic explosion of air!  I sense a story developing.  A whole world the rest of us know nothing about.  Nanites whose job it is to clean clogged capillaries.  Nanites sneaking into people's pens and wreaking havoc, then laughing at our confusion.  Nanites rearranging ink on the page.  The truth behind nib creep revealed...  The fountain pen world in chaos as nanites invade....   )

[InesF]

My short answer to both of you, @dipper and @LizEF is: 1 + 1 + 1 > 3

I love to create hypothesis, I love to discuss them with the real experts (the physics behind is beyond my expertise - however, I have learned to observe and to draw conclusions) and I love to be pulled back to Earth with a humorous translation of all those "so well thought but totally failed hypothesis".

 

Be assured, I have a great time here in this forum - thank you so much!

 

You know Fantastic Voyage - the movie from 1966? We need to do this in an ink channel!

Thinking: "Would 20th Century Fox still have kept all the equipment?"😋

 

@dipper, again, my writing did not fully reflect my thoughts (deepl did translate what I wrote, not what I thought - haha, it was deepl 😎). When I imagine the inside of the ink (and air) capillary system in the fountain pen, I always have this special image of the shape of the water meniscus between two glass plates in mind. Water climbs up at the narrow space and does this against gravity - I translate this, casually, with capillary pressure.

Similarly, the ink in the capillary system will have a tendency to reach the most narrow part first and stay there, even against other forces (like gravity). Whatever is forcing ink to leave the tip of the nib, it must work against this "staying power".

(this time, no deepl)

You are totally right, that the pressure (in the usual physics meaning) must be the same along the whole ink system, as long as there is no flow! No, Dipper has not gone crazy! 😃

 

OK so far. Now I need to send an urgent eMail to 20th Century Fox ... 😉

[InesF]

On 2/2/2022 at 1:53 PM, dipper said:

The ink has a strange journey between ink cartridge and paper: From the body of ink held in the cartridge it flows directly into any one of the three capillary slots in the sides of the part that projects into the cartridge. Then it has to bridge some small space to reach the flat back of the feed, where it enters one larger capillary slot and passes down the central axis of the feed.

Then that slot takes a dogleg path, stepping up to contact the underside of the nib. And onwards to the nib slit, down the slit, out onto the paper... .... "My dearest young son, I was so glad to read that you remain well and have grown another foot since leaving us to join the army last year. For your comfort I enclose one extra sock."

While it was interesting (if not exciting) to see such exotic feeds, I love how you describe the inks journey.

Wonderful photos and a great read! +1 👍

[InesF]

4 hours ago, LizEF said:

(Of course, I'm also now imagining our drunken nanites reacting to that catastrophic explosion of air!  I sense a story developing.  A whole world the rest of us know nothing about.  Nanites whose job it is to clean clogged capillaries.  Nanites sneaking into people's pens and wreaking havoc, then laughing at our confusion.  Nanites rearranging ink on the page. [...]

... and correcting our spelling and grammar! 😆

 

Waiting for this. Bets are taken, which ink manufacturer will be the first? 😆

[dipper]

4 hours ago, InesF said:

Whatever is forcing ink to leave the tip of the nib, it must work against this "staying power".

Or, from the ink's point of view, are things the other way round?

 

We know that ink pulls itself into narrow spaces. "Capillary action".

 

When nib tip is not touching paper there are no more narrow spaces for the ink to go into.

When nib tip does touch paper there is a narrow space between nib and paper, and more narrow spaces between the fibres of the paper surface. So the ink pulls itself out of the nib slit and into those narrow spaces.

 

Hydrostatic pressure in the nib slit, and in the ink under the nib tip, is slightly lower than atmospheric pressure. That pressure difference is what limits how far the ink can pull itself out onto the paper.

At the edges of the nib/paper contact patch the narrow space between nib and paper curves upwards and widens. (We are looking at small fractions of a millimetre here.) At the edges of the nib the ink meniscus  becomes less tightly curved, and so the ink cannot pull itself any further against atmospheric pressure. (line width measurement.)

 

This has a neat link with wetness vs surface tension of ink. Pure speculation, but I like this so much I have to share it.

A ) An ink with higher surface tension will create lower pressure in the ink chamber. ("Stronger" air bubble.)

So lower hydrostatic pressure at the nib tip also.

B ) An ink with higher surface tension will generate more "pull" acting out of the nib slit into the gaps between nib and paper. (Roughly speaking, as contact angles are equally significant here, and they may also change with a different ink.)

 

So potentially A ) and B ) above may cancel each other out, giving a pen that writes equally wet with inks of different surface tensions? A pen like that has been mentioned somewhere before in the zillions of old threads stored in FPnetwork. Searching just now I could not find it, but I did find this  ...... and went down a very deep rabbit hole .....

 

Standardizing the Wetness of Pens

A thread by @nkk from 2011.

 

(How do you make a link to another thread? Not a "quote" from one post, but a link to the top of the first page of the whole thead.)

[LizEF]

6 hours ago, InesF said:

You know Fantastic Voyage - the movie from 1966? We need to do this in an ink channel!

Thinking: "Would 20th Century Fox still have kept all the equipment?"😋

Exactly!!

 

(And thank you for quoting @dipper's post - somehow I missed it until just now!)

 

6 hours ago, InesF said:

... and correcting our spelling and grammar! 😆

 

Waiting for this. Bets are taken, which ink manufacturer will be the first? 😆

  Pfff.  It won't be an ink company, it'll be 20th Century Fox!

 

[LizEF]

On 2/2/2022 at 5:53 AM, dipper said:

In this pen that linkage is made by capillary slots moulded into the pen section itself.

That's fascinating!  Every FP user with an ink flow problem should have to come read all these posts - it gives tons of insight into potential sources of flow problems that I've never even imagined before!

 

On 2/2/2022 at 5:53 AM, dipper said:

For your comfort I enclose one extra sock.

[LizEF]

6 hours ago, InesF said:

1 + 1 + 1 > 3

Unless you spilled some while pouring, then it's < 3.

[LizEF]

19 minutes ago, dipper said:

(How do you make a link to another thread? Not a "quote" from one post, but a link to the top of the first page of the whole thead.)

You have to copy the URL (if you've jumped to some specific post, you can either edit the URL to remove the end, or go to page 1 and use the "..." share icon from the very first post of the thread) and paste it into the editor window.  (Let me know if that's not enough, and whether you're on a mobile phone or a computer and I'll write more.)

 

As for the rest, I was with you (and imagining sentient ink pulling itself around ) up to hydrostatic pressure...  Now I need to do some homework, apparently.

[LizEF]

To save others searching:

 

[Karmachanic]

Or like this if you prefer:

 

Standardizing the Wetness of Pens

[LizEF]

20 hours ago, dipper said:

The tightest curvature the bubble can achieve is when it is a perfect hemisphere sitting on top of the vent outlet. If the bubble grows beyond that size then its curvature is no longer increasing, but is now decreasing as it grows larger.

Result is a catastrophic explosion of air, bursting into the ink chamber. (A very very small catastrophy, but still a dramatic event if you happen to be a tiny air bubble.)

Realization: Only in the fountain pen world is it good to burst your bubble!

[InesF]

Thank you @dipper, @Karmachanic and @LizEF for finding a sharing the link to the old thread.

At first: shame on me for not finding @nkk's thread before.

 

The new-to-me thread contains all the things that originally motivated me to start my measurements:

- the concept of ink wetness = ink delivery amount

- the false concept of making viscosity responsible for flow and wetness

- the idea of measuring ink delivery by weight difference before and after writing

- Richard Binders contribution (great!) mentioning in 2010 that it is surface tension, not viscosity

- nobody believing Richard Binder 

- drawing way too complicated hypothesis ... 

 

Finally, it's a good read and a sign for curiosity being a driver for doing crazy things. This is more often a good than a bad sign, btw.