Author Topic: Coulometric hourmeters  (Read 1661 times)

Offline klugesmith

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Coulometric hourmeters
« on: May 27, 2024, 08:26:11 AM »
Storage space cleanup revealed a gadget I made about 20 years ago, to demonstrate a "Curtis" type hourmeter.
Full scale in this one is 2500 hours when connected to 12 volts DC.

A glass capillary tube contains a tiny slug of clear electrolyte between two columns of mercury metal.

Last Thursday I replaced the broken 9-volt battery connector, then plugged in a battery to start the clock.
Initial battery voltage is 9.09 V, with 7.48 V across the hourmeter and 1.61 V across the indicator LED.
Current is about 80 microamps.  In a few days we will be able to see how fast the gap is moving, and in which direction.

This gadget was reported at 4hv forum in 2009.
https://4hv.org/e107_plugins/forum/forum_viewtopic.php?p=1&id=77016
« Last Edit: May 28, 2024, 11:06:24 PM by klugesmith »

Offline klugesmith

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Re: Coulometric hourmeters
« Reply #1 on: May 28, 2024, 11:30:50 PM »
When re-commissioning the demonstration, I guessed at the meter polarity.
Now we see it's "wrong".
In 4.75 days, the gap moved from about 518 hours to about 450 hours on the scale.

The indicated change is -68 hours,  actual elapsed time 114 hours, ratio -0.60.
Consistent with applying -7.2 volts to a 12 volt meter.  We have used about 9 mAh of the battery capacity.

Let's run it backwards for a few more days, and see what happens to the irregularities on mercury column between 350 and 400 on the scale.

[edit] p.s. How do you like that LED at 80 microamps?   I bet we could read a book by its light, in spot diameter of 1 or 2 inches.
« Last Edit: May 28, 2024, 11:39:27 PM by klugesmith »

Offline klugesmith

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Re: Coulometric hourmeters
« Reply #2 on: June 04, 2024, 10:31:58 PM »
I came here with a question for some applied physics expert, after looking up the number density of conduction electrons in mercury. Then figured it out while typing the question.  Here presented for review.

The only reference I've found is a table at hyperphysics website: http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/fermi.html#c2.
That cites a venerable solid-state physics textbook by Ashcroft and Mermin. 
The value for copper is familiar from drift velocity presentations all over the place:  8.47e22 free_electrons/cm^3.
The values given for Al, Fe, Cu, Ag, and Hg are 3.00, 2.00, 1.00, 1.00, and 2.13 times the atom number densities I computed for the metals. 

Why the non-integer ratio for Hg?   It's listed in table as Hg**, and the double asterisk refers to a unique note "at 78K".
6.5% seemed like a lot for thermal contraction between room temperature and 78 K, but I think it's the real explanation.
Most of the factor is from liquid to solid transition.  The remainder is from change in specific volume, which is always 3x greater than linear dimension change in a solid.  How do they even measure mobile charge density except by Hall effect?  In metals that's a challenge even with very thin films, because density of mobile charge is high, so its velocities are low. (Hall established that its sign is  usually negative, long before electrons were discovered.)

Here is the hourmeter picture near end of day 12.

We've run about 20 mAh through the instrument, so far. 73 coulombs.  If it all went through the electrolyte, we have transferred 5 cubic millimeters of Hg.  I think the capillary ID is too narrow for that, especially considering the optical magnification from thick glass tube.  Must remember to get it x-rayed at my next visit to dentist.  There might be a current divider inside the black box, but what purpose would that serve, compared to just using a higher value metering resistor for 12 volt service?
« Last Edit: June 05, 2024, 01:49:00 AM by klugesmith »

Offline klugesmith

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Re: Coulometric hourmeters
« Reply #3 on: June 08, 2024, 05:38:14 AM »
After 15 days of this experiment, I made some dimensional measurements.   
Concluded that of the 71 uA in meter, only about 3 uA is going through mercury and electrolyte -- the rest has another path inside the black box.   Turns out I'd reported the same numerical answers in that old 4hv post from 2010!  In which this specimen is called "the Russian meter".

The 2500-hour scale is 40 mm long, so the nominal speed of visible gap (and speed of drifting electrons in liquid Hg) is 0.016 mm per hour.   That's a little more than 1 cm per month.   The day-of-month wheel in a mechanical watch moves faster, but the high digits in a mechanical odometer move slower.

Each cubic mm of mercury represents 13.03 coulombs of what Faraday called "electricity" 200 years ago.   
So for nominal speed we need 57.9 amperes per square meter, 57.9 microamps per square millimeter.
Apparent diameter of capillary bore is 0.35 mm, for area of 0.096 mm^2, so it needs only 5.6 microamps, about 5% of what the instrument draws at 12 volts. (Measured resistance between terminals is 102.5 kΩ.)

Of course our view of capillary ID is magnified by the cylindrical glass OD.   Has anyone here ever run the optics numbers (lens formula) to get a factor for that?

[edit] Battery voltage is down to 8.79, meter voltage 7.18, after 15 days and 26 mAh.   Zinc anode metal in each battery cell is being depleted much faster than the mercury on left side of gap.
« Last Edit: June 08, 2024, 05:44:58 AM by klugesmith »

Offline klugesmith

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Re: Coulometric hourmeters
« Reply #4 on: June 19, 2024, 04:54:15 AM »
It's time to pause the experiment, at the end of 26 days (624 h), with an indicated travel of -364 hours on the scale.
The mercury column on Start end has shortened by 5.8 mm, and the sea of conduction electrons has drifted that far toward Start.
From apparent diameter, the volume change is 0.56 mm^3, with charge transfer of 7.3 c (2.03 mAh).
But the external terminals have carried 43.9 mAh at average of 70 uA, draining battery down to 8.69 V, with 7.07 V at meter terminals.
How much will the battery voltage rebound now that the load has been removed?


Tomorrow I'll ask my dentist if we can try some x-rays, to learn about tube dimensions and terminations.
I discovered that unit can be opened without much trouble, so let the teardown presentation begin!

I think the nominal voltage isn't 12 V, it's 12.6 V.  (Вольт in Russian)
From negative to positive terminal we see R1 (100K) in series with R2 (2.7K). The latter is shunted by R3 (not readable) + R4 (15K) + meter tube from Start to End.  Those last 4 elements form a loop, making R measurement tricky, so we'll save that for another day.

Any guesses about why R4 is smaller & styled differently?   Selected to match a tube lot?  It's hard to believe the intended accuracy is enough for temperature coefficients to matter.

Now we know it'll be easy to run this much faster than nominal, without bringing in high voltage.   Does anyone think it would be abusive to run it at double speed?  10x speed?  Is anyone familiar with the current densities or thickness rates in commercial electroplating processes?
« Last Edit: June 19, 2024, 05:06:28 AM by klugesmith »

Offline klugesmith

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Re: Coulometric hourmeters
« Reply #5 on: June 20, 2024, 04:43:05 PM »
Couldn't hold back from showing x-ray taken yesterday. The exposure normally used for human teeth seems to have been appropriate for these materials and thicknesses.  It wasn't planned that R3 and R4 would overlap as seen. :)
Image resolution (and geometric blurring?) make it hard to get a good reading of Hg column diameter; I think we can do better by figuring the actual tube current.

We will be able to determine the R values accurately without unsoldering anything.  Just make careful voltage map of energized circuit, and experimentally bypass sections of the loop using an alligator clip lead.
Final post in the old 4hv thread is by "Wolfram" (Anders M.), who gives R values for a specimen that's obviously different from mine.
« Last Edit: June 20, 2024, 04:49:55 PM by klugesmith »

Offline klugesmith

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Re: Coulometric hourmeters
« Reply #6 on: June 25, 2024, 01:50:57 AM »
Now we can wrap this up and put a bow on it.
Here's a resistance model that matches observed voltage map within 1%, including a case where mercury tube R5 is bypassed, and where R4 and R5 are bypassed. (R3 is soldered in a way that makes it impossible to see its resistance label.)


That means that when 12.6 V is applied, the tube current is 2.80 microamps.   
Full scale deflection (2500h) requires only 7.00 mAh = 25.2 coulombs, moving 1.93 mm^3 of mercury.  26 mg, as much as a few CFL's.
We know the electroplating current density should be 57.9 uA/mm^2.  So area = 0.048 mm^2, diameter = 0.25 mm.

A caliper says the tube OD is 2.5 mm, and X-ray view is roughly consistent with OD/ID = about 10.
Visual ID of 0.35 mm can be explained by optical magnification, here sketched without guessing at refractive index or applying Snell's law.


I guess there is more work to be done.  By connecting directly to the meter tube, we can run it fast without requiring double-digit voltage.  Battery power would be nice, so we don't tie up a wall plug.  Voltage or current regulation would be nice, so we don't have to monitor battery depletion.  Looks like there are three terminal LDO's with quiescent current of 10 uA or less, which will be less of a burden on 9V battery than the unmodified hourmeter. Any suggestions?
« Last Edit: June 25, 2024, 04:15:17 AM by klugesmith »

Offline Mads Barnkob

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Re: Coulometric hourmeters
« Reply #7 on: June 25, 2024, 08:57:57 PM »
I don't have much to add, but I wanted to say that I have been following and reading. This is such a wholesome science experiment that it's just beautiful in itself :) Thank you for sharing.
https://kaizerpowerelectronics.dk - Tesla coils, high voltage, pulse power, audio and general electronics
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Offline TizianoBll

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Re: Coulometric hourmeters
« Reply #8 on: June 28, 2024, 12:47:25 AM »
I'm reading with interest too. (and understanding something  :o)
Regarding low quiescent current LDO: is SMD ok? is 5V fine? *edit, yes it is, they can go down to 1.8V*
I bought the 3.3V variant (TCR1HF33B) of this regulator ->  https://www.mouser.it/datasheet/2/408/TCR1HF33B_datasheet_en_20230120-3159043.pdf and I really liked it. It can work up to 40V, 1uA quiescent current and super cheap but it is a bit difficult to solder.

You can buy knockoffs from china but they are usually much worse.
« Last Edit: June 28, 2024, 12:52:01 AM by TizianoBll »

Offline davekni

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Re: Coulometric hourmeters
« Reply #9 on: June 30, 2024, 12:46:04 AM »
Quote
I came here with a question for some applied physics expert, after looking up the number density of conduction electrons in mercury. Then figured it out while typing the question.  Here presented for review.
Quote
The values given for Al, Fe, Cu, Ag, and Hg are 3.00, 2.00, 1.00, 1.00, and 2.13 times the atom number densities I computed for the metals.
Using a value of 2.00 electrons per atom of mercury is likely accurate for this hour meter, but it has nothing directly to do with density of electrons in liquid mercury.  The value that matters is the oxidation state of mercury in the solution between mercury columns.  Most ionic mercury compounds are Hg2+ such as HgCl2.

Quote
Any guesses about why R4 is smaller & styled differently?   Selected to match a tube lot?  It's hard to believe the intended accuracy is enough for temperature coefficients to matter.
I'd guess it is for calibration.  ~50 years ago I'd purchased two mercury hour meters from a surplus store.  They had just the tube and scale, no internal resistors.  They were labeled with a specified current.  If I recall correctly, labeled currents for the two meters were not quite identical.  Unfortunately I didn't find them today in the box that has a couple similarly-old mechanical hour meters.
I also wonder why the more complex resistor network.  Perhaps designed to work in a humid environment where 4.5M resistors wouldn't be stable enough?  Or it was difficult to manufacture precision 4.5M resistors

Quote
Now we know it'll be easy to run this much faster than nominal, without bringing in high voltage.   Does anyone think it would be abusive to run it at double speed?  10x speed?  Is anyone familiar with the current densities or thickness rates in commercial electroplating processes?
10uA through tube would be 207 amps/m^2, in the typical range for electroplating.  However, I'd guess you could go quite a bit higher.  Normal electroplating is limited by at least two issues.  First is formation of dendrites on plating surface and required solution additives to minimize that.  No dendrite issue with liquid mercury.  Other issue is electrolysis of solution.  As long as voltage across tube is well under 1V, electrolysis shouldn't be an issue.
Another reason to guess that these can be ran fast:  Presuming calibration was done, wouldn't want to take 5k hours to calibrate.  Of course, it's possible that calibration was needed on only a couple tubes from each production batch of capillary tubes.  That would make speed less critical.
« Last Edit: June 30, 2024, 12:47:44 AM by davekni »
David Knierim

Offline klugesmith

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Re: Coulometric hourmeters
« Reply #10 on: June 30, 2024, 03:19:40 AM »
Thanks for the review, and info about practical electroplating. I had failed to point out that free electron density in metal is just for electron drift velocity. And had glossed over assumption that the carriers in electrolyte are, sort of coincidentally, bivalent cations. Thats my basis for 13.03 coulombs/mm^3. We could see what the patents say. :)
« Last Edit: June 30, 2024, 04:00:00 AM by klugesmith »

Offline davekni

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Re: Coulometric hourmeters
« Reply #11 on: June 30, 2024, 06:49:45 AM »
Wouldn't be too expensive to buy some other models for potentially-destructive over-current testing.  A couple EBay listings:
    https://www.ebay.com/itm/334366585217
    https://www.ebay.com/itm/226021685783

Adding another thought:  If you measured R5 (mercury tube) resistance with a typical DMM, that was likely a brief run at ~100uA.
« Last Edit: June 30, 2024, 07:13:39 PM by davekni »
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Offline klugesmith

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Re: Coulometric hourmeters
« Reply #12 on: July 01, 2024, 08:09:42 AM »
Thanks, Dave.   Good to see those units are still easy to get.   One of your ebay links shows user-shiftable scales and physically reversible mercury tube, like one pictured in 4hv thread.   An Ebay search for Indachron turns up some with very large-ratio current dividers.  The ones hardwired in series with deuterium lamps look like ones reported in 4hv to operate at 300 mA.   Another one has ebay picture with the statement: "use with 50A:100MV shunt". :)


Quote
Adding another thought:  If you measured R5 (mercury tube) resistance with a typical DMM, that was likely a brief run at ~100uA.
I might have done that momentarily in a non-recorded quick check.  The 740 ohm value comes from voltage measurements with 12.685 V between meter terminals. Saw 282.0 mV across R3, 42.42 mV across R4, and 2.095 mV across R5.

You got me wondering about the Hg oxidation state.   Turns out the +1 state (mercurous) tends to be a covalently bonded pair of Hg atoms with net charge of +2, a thing discovered in 19th century!.  https://en.wikipedia.org/wiki/Mercury_polycations  Maybe some bored chemist can explain how the equilibrium between mercurous and mercuric is affected by choice of anions in the electrolyte.   The patents (many by an inventor whose first name is Curtis) seem, at first glance, to mention only Hg++. US3343083A
« Last Edit: July 01, 2024, 09:11:04 PM by klugesmith »

Offline davekni

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Re: Coulometric hourmeters
« Reply #13 on: July 02, 2024, 05:16:30 AM »
Quote
You got me wondering about the Hg oxidation state.   Turns out the +1 state (mercurous) tends to be a covalently bonded pair of Hg atoms with net charge of +2, a thing discovered in 19th century!.
When researching for my previous reply, found that Wikipedia and other sites all say that mercury compounds are mostly Hg++, and that Hg+ (usually Hg2++ as you said) is relatively rare.  I think it was also Wikipedia that mentioned somewhere that coulometric measurements using Hg were Hg++.  Can't find that again at the moment.
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Re: Coulometric hourmeters
« Reply #13 on: July 02, 2024, 05:16:30 AM »

 


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post Re: No change in Phase Lead
[Dual Resonant Solid State Tesla coils (DRSSTC)]
davekni
July 05, 2024, 11:50:37 PM
post Best core material for QCW Buck modulator ?
[Dual Resonant Solid State Tesla coils (DRSSTC)]
Simranjit
July 05, 2024, 10:07:04 PM
post 230v Tesla coil and krypton gas
[Spark Gap Tesla Coils (SGTC)]
gravitysrainbow
July 05, 2024, 07:13:25 PM
post Re: No change in Phase Lead
[Dual Resonant Solid State Tesla coils (DRSSTC)]
Admiral Aaron Ravensdale
July 05, 2024, 06:17:13 PM
post Re: Phase lead inductors
[Dual Resonant Solid State Tesla coils (DRSSTC)]
Benjamin Lockhart
July 04, 2024, 11:40:45 PM
post Re: Sling Psychrometer
[Laboratories, Equipment and Tools]
Twospoons
July 04, 2024, 11:02:32 PM
post Phase lead inductors
[Dual Resonant Solid State Tesla coils (DRSSTC)]
flyingperson23
July 04, 2024, 06:28:08 PM
post Re: Sling Psychrometer
[Laboratories, Equipment and Tools]
klugesmith
July 04, 2024, 12:31:40 AM
post Re: FIRST DRSSTC SKM400GB128D OCD SETTING
[Dual Resonant Solid State Tesla coils (DRSSTC)]
Alex_1996
July 04, 2024, 12:07:21 AM
post Re: FIRST DRSSTC SKM400GB128D OCD SETTING
[Dual Resonant Solid State Tesla coils (DRSSTC)]
Alex_1996
July 04, 2024, 12:06:17 AM
post Re: FIRST DRSSTC SKM400GB128D OCD SETTING
[Dual Resonant Solid State Tesla coils (DRSSTC)]
Benjamin Lockhart
July 03, 2024, 10:51:23 PM
post Re: FIRST DRSSTC SKM400GB128D OCD SETTING
[Dual Resonant Solid State Tesla coils (DRSSTC)]
Mads Barnkob
July 03, 2024, 09:44:14 PM
post Re: Coax cable for DRSSTC interrupter?
[Dual Resonant Solid State Tesla coils (DRSSTC)]
Admiral Aaron Ravensdale
July 03, 2024, 08:48:13 PM
post Re: Coax cable for DRSSTC interrupter?
[Dual Resonant Solid State Tesla coils (DRSSTC)]
Simranjit
July 03, 2024, 08:24:50 PM
post Re: FIRST DRSSTC SKM400GB128D OCD SETTING
[Dual Resonant Solid State Tesla coils (DRSSTC)]
Alex_1996
July 03, 2024, 08:12:55 PM
post Re: Coax cable for DRSSTC interrupter?
[Dual Resonant Solid State Tesla coils (DRSSTC)]
Admiral Aaron Ravensdale
July 03, 2024, 07:29:53 PM
post Re: FIRST DRSSTC SKM400GB128D OCD SETTING
[Dual Resonant Solid State Tesla coils (DRSSTC)]
Admiral Aaron Ravensdale
July 03, 2024, 07:21:38 PM
post Re: FIRST DRSSTC SKM400GB128D OCD SETTING
[Dual Resonant Solid State Tesla coils (DRSSTC)]
flyingperson23
July 03, 2024, 05:05:39 PM
post Re: FIRST DRSSTC SKM400GB128D OCD SETTING
[Dual Resonant Solid State Tesla coils (DRSSTC)]
Alex_1996
July 03, 2024, 04:29:53 PM
post Re: FIRST DRSSTC SKM400GB128D OCD SETTING
[Dual Resonant Solid State Tesla coils (DRSSTC)]
flyingperson23
July 03, 2024, 04:09:11 PM
post FIRST DRSSTC SKM400GB128D OCD SETTING
[Dual Resonant Solid State Tesla coils (DRSSTC)]
Alex_1996
July 03, 2024, 02:47:18 PM
post Re: Eliminating discharges from a SSTC
[Solid State Tesla Coils (SSTC)]
Alex_1996
July 03, 2024, 01:35:24 PM
post Re: Coax cable for DRSSTC interrupter?
[Dual Resonant Solid State Tesla coils (DRSSTC)]
flyingperson23
July 03, 2024, 02:19:03 AM
post Re: Coax cable for DRSSTC interrupter?
[Dual Resonant Solid State Tesla coils (DRSSTC)]
verliebt_in_neukölln17
July 03, 2024, 01:19:50 AM
post Coax cable for DRSSTC interrupter?
[Dual Resonant Solid State Tesla coils (DRSSTC)]
Simranjit
July 02, 2024, 11:29:18 PM
post Re: Is this a good pulse experiment capacitor?
[Capacitor Banks]
Mads Barnkob
July 02, 2024, 09:59:07 PM
post Re: LabCoatz Staccato QCW No straight sparks
[Dual Resonant Solid State Tesla coils (DRSSTC)]
ZakW
July 02, 2024, 09:55:53 PM
post Re: Capacitor wiring for single phase 240 to split phase (180 degree) 240v
[Capacitor Banks]
klugesmith
July 02, 2024, 09:44:55 PM
post Re: LabCoatz Staccato QCW No straight sparks
[Dual Resonant Solid State Tesla coils (DRSSTC)]
Admiral Aaron Ravensdale
July 02, 2024, 07:51:37 PM
post Re: LabCoatz Staccato QCW No straight sparks
[Dual Resonant Solid State Tesla coils (DRSSTC)]
ZakW
July 02, 2024, 06:14:07 PM
post Is this a good pulse experiment capacitor?
[Capacitor Banks]
FPS
July 02, 2024, 06:02:38 PM
post Re: LabCoatz Staccato QCW No straight sparks
[Dual Resonant Solid State Tesla coils (DRSSTC)]
Admiral Aaron Ravensdale
July 02, 2024, 11:37:46 AM
post Re: Building my first DRSSTC
[Dual Resonant Solid State Tesla coils (DRSSTC)]
davekni
July 02, 2024, 05:22:10 AM
post Re: Coulometric hourmeters
[Laboratories, Equipment and Tools]
davekni
July 02, 2024, 05:16:30 AM
post Re: Building my first DRSSTC
[Dual Resonant Solid State Tesla coils (DRSSTC)]
drobotk
July 01, 2024, 11:50:12 PM
post Re: Restoring a Rogowski coil calibrator
[Capacitor Banks]
klugesmith
July 01, 2024, 08:48:53 PM
post Uses for Weston's Little Bee probe
[Laboratories, Equipment and Tools]
klugesmith
July 01, 2024, 08:40:59 AM
post Re: Coulometric hourmeters
[Laboratories, Equipment and Tools]
klugesmith
July 01, 2024, 08:09:42 AM
post Re: Coulometric hourmeters
[Laboratories, Equipment and Tools]
davekni
June 30, 2024, 06:49:45 AM

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