# Microcannons firing Nanobullets

Original Paper: Acoustic Microcannons: Toward Advanced Microballistics

Sometimes I read papers that enhance my understanding of how the universe works, and sometimes I read papers about fundamental research leading to promising new technologies. Occasionally though, I read a paper that is just inherently cool. The paper by Fernando Soto, Aida Martin, and friends in ACS Nano, titled “Acoustic Microcannons: Toward Advanced Microballistics” is such a paper.

The grand scheme of this research is developing a tool that can selectively shoot drugs into cells at a microscopic level. This is hard because everything happens really slowly at the microscopic scale in a liquid, in ways that meter-sized beings who live in air would not necessarily expect. For example, it is impossible for small organisms to move through a fluid using a repetitive motion that looks the same in reverse. The way we move our feet back and forth to walk would not work for a tiny aquatic human, because the forward motion in the first phase of movement would be nullified by backwards motion in the second phase. This is why bacteria use things like rotating flagella to move*.

Digressions aside, if you tried to shoot a tiny bullet through a cell wall, it would quickly halt and diffuse away before even hitting the cell wall. Soto, Martin, and collaborators wanted to beat this. Perhaps inspired by the likely unrelated Rodrigo Ruiz Soto, a Costa Rican competitive pistol shooter in the 1968 Olympics, Soto sought to develop a cannon that would change the game in the microscopic world in the same way that gunpowder technology changed things in  the macroscopic world.

The researchers developed a “microcannon,” starting with a thin membrane of polycarbonate plastic studded with small pores, which is a thing you can buy and don’t have to make. The pores would eventually serve as the molds for the barrels of the cannons. They deposited graphene oxide onto the inside of the pores using electrochemistry, and then sputtered gold onto the inside of that graphene layer.  While they were still in the plastic membrane, the cannon pores were filled with a gel (literally gelatin from the supermarket) loaded with micron-sized plastic beads to act as bullets, and the “gunpowder,” which I’ll describe after the next image. The polycarbonate is then washed away with acid, leaving free-floating carbon and gold cannon barrels a few microns in size.

While it is generally difficult to make small things move quickly in a fluid, bubbles are somewhat of an exception to this rule. Their collapse can lead to rapid motion on tiny scales. Taking advantage of this, the authors used perfluorocarbon (molecules with the same structure as hydrocarbons but with fluorine connected to carbon atoms instead of hydrogen) droplets as a propellant, which they turned into bubbles with an ultrasound-induced phase transition (essentially blasting them with soundwaves until they vaporized). When they initiated the collapse of the bubbles, they emitted a pressure wave which drove the nanobullets out of the barrel towards their target**.

The authors performed two tests to characterize how powerful these things were. First, they embedded the cannons in an agar gel (an algae-based substance that Japanese desserts are made of) and loaded them with fluorescent beads. They looked at where the beads were before firing the ultrasound trigger at the cannon, and after. They observed that the beads had penetrated an average of 17 microns through the gel. However, this is about the thickness of a human cell layer, so this could be used, for example, to shoot a small amount of medication through the layer of cells on the wall of a blood vessel. In some more direct studies of the damage caused by collapsing bubbles (which is a common mechanism of damage to ship propellers), the jets that formed when bubbles collapse were shown with high-speed photography to penetrate about a millimeter into a gel. However, these bubbles were 1000 times bigger than those formed in the microcannons, and it’s not out of the question to assume that the penetration depth scales with bubble size.

The bullets were too fast to record with a microscope camera, so their second test involved recording the motion of the cannon after it fired the bullets. Naively, one would expect to be able to calculate the bullet speed with conservation of momentum from knowing the cannon’s speed, but momentum isn’t conserved in a noisy viscous environment (which brings us back to why it’s so hard for microorganisms to move around). They modeled the fluid dynamical forces acting on the system, measured that the terminal speed of the cannon was about 2 meters per second, and concluded that the initial speed of the bullets is 42 meters per second or 150 kilometers per hour (see appendix). Pretty fast, especially for something so small in a draggy environment.

After finding this paper I emailed the first author, Fernando Soto, saying that I enjoyed his paper, and he responded by saying that he was glad that other people liked his “very sci-fi nanodream.” I don’t know if this technology will succeed in the authors’ goal of localized drug delivery to cells, but I think it’s awesome that they made a functioning microscale cannon.

*I recommend reading Life at Low Reynolds Number if this interests you.

**Or just in whatever direction it was pointing, I guess.

Appendix: Velocity calculation

The researchers wanted to figure out how fast the bullets were moving based on their measurement of how fast the cannons were moving. Normally you could just use conservation of momentum, but because of the surrounding fluid, momentum is not necessarily conserved (unless you know the momentum of the fluid as well).

However, we understand how velocity decreases in a fluid based on drag: if the velocity is low, the drag force arises from separating the water molecules from each other, and the force is linear with velocity. If the velocity is high, the force arises mainly from accelerating the water to the speed of object, and the force is quadratic with velocity. To figure out which rule applies you can calculate what’s called the Reynold’s number, Re, which is the ratio of inertial to viscous forces in a fluid. If Re is in the thousands or higher,the flow is turbulent. f it’s below 100, the flow is smooth, or laminar. Specifically, the Reynold’s number is calculated as:

$Re=\frac{\rho L v}{\mu}$

where $\rho$ is the density of the fluid, L is the length of the object in the flow, v is its velocity, and $\mu$ is the viscosity. The microcannon was seen moving at about a micron per second, it was about 15 microns long, and the high speed photograph was done in water (density of 1 kg/L, viscosity of about 0.001 pascal seconds). This means the Reynold’s number was about 13, in the laminar regime, and that drag is due to viscosity and linear.

The equation of motion for a slowing object undergoing viscous drag with an initial velocity is

$v(t)=v(0)e^{-kt/m}$

where m is the mass of the cannon (known from stoichiometry) and k is the drag coefficient which depends on the viscosity as well as the geometry of the object experiencing drag. Because they know v(t) (as determined from high speed videography), t (the time since detonation), k, and m, they can find v(0).

Then it is assumed that momentum is conserved during the detonation, so the nanobullets with known mass can have their velocity calculated from

$v_{c}m{c}=v_{b}m_{b}$

where the indices c and b refer to cannon and bullet. The velocity was calculated to be 42 m/s. Pretty fast.