About sonofusion via ultrasonic fusion
Sonofusion
August 20, 2005
You probably know how an airplane flies. If not, read "If We Could Fly," also known as "The Aspirisouffle". A depression forms on the upper surface of the wing, its "extrados."
Airplane wing
By the way, what is the order of magnitude of the depression acting on this wing's surface? Let's take a small single-seat touring aircraft. Suppose its loaded weight is 300 kilograms and its wing area is 18 square meters. That gives it a wing loading of 16 kilograms per square meter, or 1.6 grams per square centimeter. Since atmospheric pressure at sea level is about 1,000 grams per square centimeter, the average pressure difference between the extrados and intrados of the wing is on the order of a few millibars. This explains why we can fly with fabric-covered aircraft and why it's not recommended to step on the wing, except on designated areas—otherwise you'd go right through.
What happens in water? It's a thousand times denser than air. At the same speed, we can "fly in water" using much smaller "wings." These are called "foils."
Wings and foils
If we can sustain ourselves on such small surfaces, it's because pressure variations are much greater. Imagine these foils moving very close to the liquid surface, where ambient pressure is nearly one kilogram per square centimeter. The boat on the right sustains itself thanks to pressure differences far greater than those measured around an airplane wing profile. This is why foils aren't fabric-covered but made of solid, robust steel.
Why, by the way, is there a depression on the extrados of the wing? In water, this is easier to understand. The fluid mass hits the profile at the "stagnation point" and then accelerates again. In doing so, it gains speed and also experiences centrifugal force effects.
What happens when a liquid is subjected to a depression? We can demonstrate this using a cylinder and a piston. If, by pulling the piston, we reduce the pressure in the liquid below the saturation vapor pressure at the given temperature, tiny bubbles will form. These have nothing to do with Champagne bubbles, which indicate dissolved gas in the drink. These bubbles are filled with water vapor. This is the phenomenon of cavitation.
Cavitation phenomenon
Here is a photograph of the phenomenon, induced inside a cylinder.
Cavitation bubbles
In 1917, the British Admiralty summoned physicist William Strutt, also known as Lord Raleigh, to address a strange problem. The bronze propellers of His Majesty's ships were all damaged, covered in tiny holes, despite being nearly new. The Admirals wondered if the sea might harbor unknown parasites capable of attacking the metal of the propellers. Below is a more recent photo showing the damage cavitation can cause on the blades of a centrifugal pump.
Damage caused by cavitation on a centrifugal pump. Quite impressive, isn't it?
Here is a close-up view, showing the "pitting" observed in the metal.
Cavitation damage on a bronze blade.
Contrary to what the British Admirals initially thought, this wasn't due to some unknown species of "hydro-wasps." Lord Raleigh performed some calculations and provided the explanation. The depressions created on the propeller blades were strong enough that locally, pressure dropped below the saturation vapor pressure of water. Water thus locally boiled. One detail: what is the saturation vapor pressure of water at ambient temperature?
Answer: a few pascals, or about one-hundredth of a millibar. The depressions forming around propeller blades in hydraulics are extremely intense. This is why we can propel a small outboard motor with such a ridiculously small object as a propeller. Here is a rotating propeller blade. The arrow indicates the presence of water vapor bubbles corresponding to the cavitation phenomenon.
Cavitation near the leading edge of a rotating propeller blade.
A stream of water vapor bubbles is visible, forming at the blade's edge. But their origin is different. They result from the tip vortex and resemble the condensation trails forming at the tips of airplane wings. We won't discuss this here. Let's consider the pressure variation along the extrados of a propeller blade:
Pressure variation along the extrados of a propeller blade
The curve is schematic. We see that pressure drops rapidly along the chord of the profile. When it falls below the liquid's saturation vapor pressure (water, in this case), bubbles appear and grow as pressure continues to drop. Even though the rest of the profile remains under depression relative to ambient pressure, pressure eventually rises again and becomes greater than the saturation vapor pressure in water. Then the water vapor tends to disappear, as seen in the photograph.
Everyone knows that in fluid mechanics, expansion phenomena do not behave the same way as compression (or recompression) phenomena. When pressure starts to increase, the bubble wall behaves like a spherical piston acting on a gas, competing with water vapor. If the collapse speed of the bubble exceeds the speed of sound in the vapor mass (and it does), a spherical shock wave forms, converging toward the geometric center of the object, carrying significant energy—enough to create those "pits" in the blade metal and, ultimately, cause damage as severe as that seen on the pump blades above.
Explanation of cavitation-related damage.
We know about so-called "hollow charge" systems. In these, an explosive is detonated across the entire surface of a conical wall (using a detonating material with very high propagation speed). The cone surface then emits a very intense shock wave, whose energy focuses along the system's axis. A "dart" forms, capable of piercing steel armor whose thickness is roughly equal to the cone's diameter (though the dart creates a hole much smaller in diameter). The implosion of the bubble, as Christophe Tardy pointed out to me, resembles the focusing of energy carried by a spherical shock wave. If hollow charges were designed around non-conical, but spherical cavities, we could concentrate enormous energy at the center of the sphere, at the focal point. This is exactly what happens during cavitation.
As we mentioned, the cavitation phenomenon was discovered in 1917. In 1930, it became possible to generate intense ultrasonic waves. In 1934, a new phenomenon emerged at the University of Cologne, which greatly puzzled physicists. When a liquid, such as water, was subjected to ultrasonic waves, the fluid emitted... light. This phenomenon was named sonoluminescence.
At first...