Im Michael Stullick, Ill be presen6ng on acous6c tweezers tonight. I - PDF document

I’m Michael Stullick, I’ll be presen6ng on acous6c tweezers tonight. I chose this topic because most of what we hear about sound waves are how the world around them affects them, or how we can detect them. This sort of turns that around, so it’s how the sound waves affect the world, and I thought that was a preAy neat idea. 1

The physics behind these tweezers is preAy complicated, and I don’t want to spend too much 6me on it, I’d rather show you what they can do, so I’ll keep this part short. Star6ng off with the thermodynamic equa6on of state, the con6nuity equa6on, and the Navier-Stokes equa6on, we can perturb them, 6me average the variables, and treat this as a scaAering problem, then assume the waves incident on the par6cles we want to affect are plane waves to come up with this force equa6on. It’s sort of spring-like, there’s a sinusoid in there. There’s also this crazy factor of Phi in there. That’s called the acous6c control factor, and it’s actually important. 2

The acous6c control factor is a func6on of the ra6os of par6cle density and compressibility to the vibra6ng medium’s density and compressibility, and determines if the force traps par6cles or creates an unstable balance. The picture on the leI demonstrates this with a pressure plane wave of wavelength twice the length of the chamber it’s in. The top arrows are the direc6on of the force when the control factor is greater than 0, and the boAom is when it’s less than 0. The doAed sine wave is the pressure amplitude in the chamber. The contour plot on the right shows rough values of the acous6c control factor for density and compressibility ra6os between 0 and 2. First off, no6ce the singularity at the density ra6o of 1:2. Also, no6ce that the region of nega6ve acous6c control is very small, and below that line. So in reality, this may never be an issue, because you’d need to be manipula6ng objects that are less than half as dense as the medium in which they’re being suspended. 3

Here the forces are shown for a single transducer without and with reflec6on off a surface. A, B, and C are not the situa6on we want, but if a microscope slide, say, is put under the par6cle, then we see in E and F the radial and transverse forces demonstrate trapping. The liAle green dots are where the par6cle would be in the picture. 4

The tweezers are controlled by this algorithm called “itera6ve backpropaga6on”. It works by telling it what trap geometry you want set up, then the algorithm feeds each transducer’s pressure amplitude and phase informa6on into a control point, a kind of digital analog, then it normalizes the control point’s amplitude, feeds it back into the transducer, and normalizes the transducer’s new amplitude, then repeats over again. To get it to work for a 3 dimensional arrangement, the transducers need an addi6onal phase offset of pi radians to change the plane that the par6cle is on. There’s three kinds of traps, you can see them in the picture. There’s focus traps, in (a), those ones hold a par6cle at some point in space. They only require a single control point, or transducer, to maintain. There’s also twin traps, shown in b and c. Those ones can orient a par6cle in a certain direc6on. No6ce that for a twin trap, the two transducers have to be exactly pi radians out of phase with each other, regardless of their orienta6on. Then, there’s vortex traps. Those are either clockwise or counterclockwise based on the direc6on the phase increases; in d the phase increases clockwise, and in e the phase increases counterclockwise. 5

I want to show some videos soon, and to do that I want to make sure we have context for them, so we can appreciate it fully. The transducers generate a 40kHz ultrasound wave in air, which gives a wavelength of about 8.6mm. At some of the highest voltages they used, the pressure generated was around 2 pascals. The tweezers are essen6ally a box with pairs of transducers on the top and boAom, oriented in a 16 by 16 grid for a total of 256 transducer elements, that are approximately 1 cen6meter across each. The balls you’ll see floa6ng around are between 1 and 3 mm. 6

The par6cles move in 3 dimensions by changing focus traps between transducers. The array can manipulate mul6ple par6cles at once, but the closest they can get to one another is about 1.3 cm, which we can no6ce in this video; 7

You can see the balls move, change orienta6on. And you can see some cheesy graphics. Here’s a shot of the tweezer chamber. You can see the par6cles sort of shake, that’s due to the spring nature of the forces involved. The par6cles can be manipulated in 2 dimensions as well as 3 dimensions. And they can be manipulated into a smiley face, of course. You could use these balls as liAle handles to perform tasks, like puang these strings together. You can also use them to put objects through one another, like threading a needle. 8

To rotate an object, twin traps can orient an asymmetric object in a certain direc6on, or vor6ces could con6nuously rotate an object. These too can be set up at mul6ple loca6ons, and also can only get so close to each other. I’d also like to point out that the rota6onal trap symmetries have much weaker transverse forces, so to rotate an object the trap needs to switch quickly between focus traps and the rota6onal trap of choice. 9

Here the bars show the direc6on the par6cle should be oriented in, and here comes a pencil. You can see the trap re-orients a par6cle aIer being adjusted. You can see the boAom leI par6cle got knocked out of the right trap; it can just be bumped back into the right one with the same pencil. 10

So aIer all this, we s6ll have laser tweezers, and we have for a long 6me; so why worry about acous6c tweezers? Well, we talked a liAle about how liAle energy is imparted by sound waves, and it turns out it’s one one hundred thousandth of the energy from laser tweezers in this case. Tuesday we learned sound waves are excellent at penetra6ng the body as well. The par6cle size affected by the acous6c trap ranges from microns to millimeters as well, so all these traits combined hint at medical applica6ons. It hasn’t been demonstrated yet, but in theory these could poten6ally be the next evolu6on in laparoscopic surgery. 11

I don’t know if the colors of the other videos were too drab or what, but this one really makes these things real to me; seang par6cles in place with tweezers on top of each other is really neat, and shows two things; first, it shows that the waves have no problem moving past the par6cles to con6nue to work further down, and it also shows that it really isn’t a magic trick-no wires involved. 12

Any ques6ons? 13

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