Small telecentric Schlieren stroboscopically viewing capillary waves

[davekni]

Looking for ways to measure surface tension of surfactant/water mixtures, I ran across capillary waves as a measurement technique.  Read a paper about a smart-phone app for that using phone's vibrator, flash, and camera.  It has a few drawbacks, however.  Key one for me is that I don't own a smart phone

Since I had some small 25mm diameter off-axis parabolic mirrors, decided to make a small telecentric Schlieren setup to view capillary waves in plastic petri dishes.  A stepper motor driver generates sine wave current feeding a small E-core coil.  Coil field vibrates a permanent magnet taped to petri dish, generating capillary waves in water inside dish.  LED pulses synchronously with sine wave, imaging capillary waves at the same phase each cycle.  (Red LED to match gold-plated mirrors.)  A 2mm pitch scale below the dish provides a measurement reference.  Due to telecentric optics, scale is viewed at the same magnification as waves.  Frequency is manually adjusted to make 2mm wavelength.  Measured frequency is used to calculate surface tension using formula (edited from Wikipedia):
        surface_tension = density * frequency^2 * wavelength^3 / (2 * PI)

The entire setup, measuring water at 242Hz:


Side view to show optical path.  LED reflects down to lower mirror, forming parallel beam up towards upper mirror.  Upper mirror images parallel beam to small rectangular aperture (hole in black paper) above LED.  Lens just past aperture (behind wood frame) images the object space (parallel beam) onto a finite-distance screen.  (Would otherwise image at infinity.)  The aperture is reverse-imaged at infinity by the upper mirror, which makes the setup telecentric.


With pure water (low viscosity), the image is quite clear as shown above.  With detergent-water, viscosity is higher, which damps waves.  It still works, but is a bit harder to view and adjust accurately to 2mm wavelength.

Even though the result is fairly simple, this project took much longer than I'd expected - especially trying different ways to vibrate the petri dish or vibrate an object within the dish.  Advantage of vibrating the dish is avoiding another surface that needs cleaning between testing different surfactant solutions.  Final goal is to optimize surfactant solutions for making bubbles.  Perhaps became more of a project than this goal warrants.  Measuring bubble film strength may be more relevant than surface tension.

[MRMILSTAR]

Very interesting. I'm also glad to hear that I'm not the only person that doesn't own a Smartphone. I and my wife own old-fashioned flip phones and use a land-line at home. Its all we need or want.

[Da_Stier]

Very interesting.
I always assumed that you would need a stable surface table and nicely machined brackets for every piece of optics.
But seeing you getting good results with such simple to replicate and modify fixtures is actually quite interesting.


Greetings,
Michael

[davekni]

I always assumed that you would need a stable surface table and nicely machined brackets for every piece of optics.
But seeing you getting good results with such simple to replicate and modify fixtures is actually quite interesting.

If this were a Schlieren diffraction interferometer or other interferometry setup requiring fractional-light-wavelength precision, this construction would not be practical.  Required precision for basic Schlieren is tied to the light source size, ~1mm in this case.  Smaller light sources and longer optical paths increase sensitivity, as in my previous Schlieren setup:
https://highvoltageforum.net/index.php?topic=1376.msg10223#msg10223
This one is viewing water rather than air.  Index of refraction is ~1000 times higher for water than air (difference from 1.0).  That allows this short optical path.

There are many interferometric experiments that would be fun to try, but I don't have ability or equipment for such precision mechanical construction and alignment.

[Uspring]

That is a nicely designed experiment providing me with some incentive to brush up my memories of fluid dynamics and optics. The dispersion relation you quoted looks inaccurate at the wavelengths you're measuring due to gravity wave contributions.
Keep us updated on perfect bubble mixtures 

[davekni]

That is a nicely designed experiment providing me with some incentive to brush up my memories of fluid dynamics and optics. The dispersion relation you quoted looks inaccurate at the wavelengths you're measuring due to gravity wave contributions.
Keep us updated on perfect bubble mixtures 

I haven't taken time to derive water wave equations myself, so am relying on Wikipedia formulas on its capillary wave page.  Presuming those are accurate, yes, there is a 2-3% error due to gravity for my chosen 2mm wavelength.  That is a compromise wavelength choice.  I made reference scales at 1.5, 2, and 2.5mm.  Higher frequencies are damped more due to viscosity, so are harder to measure.  If I've made a calculation mistake and errors are more significant, I'd certainly appreciate correction here.

My primary interest is in comparing differences, with (I think) the goal of minimizing surface tension.  Thus absolute error is not too important.  As I've played a bit with this, now realizing that measuring bubble film strength is probably much more useful than surface tension.  Will be scabbing something together for that soon.  Making hemispherical (roughly) bubbles of known diameter on the end of a small pipe (~20mm diameter) and measuring the pressure.  Expected pressures are in the 1-2Pa range.  Plan to use a milligram scale and thin polyethylene diaphragm.

[Uspring]

If I've made a calculation mistake and errors are more significant, I'd certainly appreciate correction here.

You didn't err, I did. I somehow lost a factor of two pi squared in my numerics. I am sorry for the false alarm.

[davekni]

Thank you for the update.  Although the error to to ignoring gravity is small, it turns out to be very easy to correct.  With my choice of fixed wavelength (2mm) and adjusting frequency (opposite the smart-phone app), gravity contribution is an offset to computed surface tension.  Offset is very close to 0.001N/m.  Thus all I need to do is subtract 0.001N/m from my results.  Some surfactant solution values get down to 23N/m, 22N/m after correction, so up to 4.5% error if uncorrected.  Given manual viewing of wavelength match to 2mm scale, my repeatability error is at least +-2%.  Good enough for now, especially presuming film strength is more significant.