I’m thrilled you did what you proposed and we discussed there, Rob!
When I tried to rely mostly on the mechanical advantage that the ultrasonic waves provide, without using many chemicals, I got frustrated with a glass jar I was using. I just wasn’t getting the results I expected. Intuitively, I thought that glass would transmit the waves well since it doesn’t dampen vibrations, it’s a rigid container.
However, I also noticed that when I had a cut on my finger, I could feel the ultrasonic waves as a distinct sting when I immersed it. My quick and dirty test was to compare whether the sting was different in a yogurt cup than it was in a thicker plastic lunch box (I moved from the glass jar to this), and I could definitely feel the difference. Yet, the flimsy yogurt container seemed much more damping than the lunch box; surely it would “vibrate” itself and thus absorb the energy.
I thought I must be missing something here and looked into the subject, admittedly very simplistically. I wish
@Angelo Farina could weigh in here, as I’m sure he would correct me from a multitude of angles, this was his subject.
Here is how my rudimentary interpretation of the physics led me to believe that a yogurt cup is a great practical solution:
Every medium has something called acoustic impedance. It is a fundamental property of the material that indicates its resistance to the propagation of sound waves. If two materials have impedances that are very close to each other, the sound waves travel nearly uninterrupted from one into the other. If their impedances differ greatly, much of the acoustic wave is reflected at the boundary.
This acoustic impedance is defined as: Z = p × c
Z = Acoustic impedance
p = Density of the material
c = Speed of sound within the material
When I saw that simple formula, I thought, “Hey, that’s easy enough to calculate!”, as values for density and speed of sound are readily available for many materials. Since I was floating my containers in water, I calculated the impedance for water first (density = 1000 kg/m³; speed of sound = 1481 m/s):
Z
W = 1000 kg/m³ × 1481m/s
Z
W = 1481000 kg/m²s
That’s an unusual unit for all but
@Angelo Farina, but apparently that unit (kg/m²s) is called a Rayl, so our result is 1.48 MRayl.
Next, I calculated the same for glass, although I hit my first roadblock, there are many more grades of glass than I ever imagined. Still,
MatWeb is a brilliant resource for material properties. Here are the values I picked for soda-lime glass:
Z
G = 2500 kg/m³ × 5000 m/s
Z
G = 12.5 MRayl
Looking at these numbers, 1.48 MRayl for water versus 12.5 MRayl for glass, there is a huge difference between the two. Did my lunch box do any better? I assumed it was polypropylene, although I admit this was a wild guess:
Z
P = 900 kg/m³ x 2740 m/s
Z
P = 2.45 MRayl
That looked really promising, as the 2.45 MRayl from the polypropylene was relatively close to the 1.48 MRayl of water. There is a formula for calculating the reflection coefficient for those interested, but at its core it simply states: The greater the difference between impedances, the greater the reflection:
Reflection = ((Z
2 - Z
1)/(Z
2 + Z
1))²
It’s rather obvious from this formula that little reflection takes place as Z
2 approaches Z
1
So the core of the issue was not that glass doesn't allow sound to travel effectively, it does so much better than most plastics. The problem was that the sound waves largely didn't enter the glass to begin with, due to the high impedance mismatch.
Of course, the above isn’t the whole story, as the thickness of the material also plays a role. If it isn’t shorter than the sound wavelength, or by some miracle exactly the same length as the wavelength, waves will reflect off the opposite wall and bounce back and forth within the material.
It’s also worth remembering that the ultrasonic waves have to traverse the barrier twice, water to container and back, so any impedance mismatches are doubly annoying.
Back then, I finally experimented with thin flimsy garbage bags, and they gave me the absolute best results. (Appearantly they are often made from LPDE with 1.7 MRayl, although I did not verify that back then or now). However, they were such a pain to work with that I settled on yogurt cups. The zip-lock bag is something that never occurred to me, but it seems like a great solution.
After our last discussion, I went down a bit of a rabbit hole and thought to myself, surely there must be materials that impedance-match water. Sure enough, there’s a whole industry around this.
While specialized compounds virtually match the impedance of water, I was happy to see that
polyethylene is a really good fit at about 1.73 MRayl. Why? Because most take-out food plastic containers are made of it, something easy to find anywhere for anyone.
Yogurt cups are often made from PP or PET, which have slightly less ideal impedances than PE. I will go and try a PE box and I'm rather confident I will settle to it from the yogurt cups.
So thanks again for nudging me in the right direction, something I will definitely incorporate into my writings!
)
).
