Physics behind circular cracking caused by high-velocity water droplet impacts leads Duke University team to more efficient potential method for breaking up mineral deposits in the body
Powerful soundwaves have been used for some years to break up kidney stones, one of the most painful conditions known to medicine. But the method is not perfect: if the stone is not reduced to a fine powder, remaining fragments can still cause pain and potential infections, and surgery is often necessary to remove them with all the attendant risks.
Engineers from Duke University in North Carolina now believe they have found a more efficient way to destroy the stones, using a phenomenon that was first seen when testing supersonic aircraft.
When high-speed aircraft were first tested it was found that raindrops striking the canopy can sometimes cause circular cracks. The cause of this was mysterious for some time, until two researchers from Cambridge University, Frank Philip Bowden and John Field, discovered that the culprit was surface waves: these propagate in only two dimensions rather than three, and therefore pack a more powerful punch. However, the mathematics to describe this phenomenon remained elusive, and it proved difficult to design experiments to test theories of their behaviour.
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The Duke team, led by mechanical engineer Prof Pei Zhong and his then-graduate student Ying Zhang, who now works for Bose Acoustics, designed experiments using a lithotripsy device: an acoustic generator used to treat kidney stones.
They explain in Physics Review Research how they placed the device in a vat of water covered with a sheet of glass, and triggered a burst of soundwaves that expanded through the water as a spherical shockwave. Depending on the angle at which the shockwave hits the glass sheet, it can create a surface wave that spreads along the water-glass boundary.
Zhang and Zhong used a high-speed camera to measure the velocity of the elements of the shockwave during the very short period as they spread through the glass. Zhang then used the multi-physics software package COMSOL to validate a finite-element model of the characteristics of both bulk and surface waves, which led to the discovery that a particular type of wave – called a leaky Rayleigh wave – that propagates much faster than a second type of wave called an evanescent wave, even though they are created at the same time on the water-glass boundary.
As the Rayleigh wave pulls away from the evanescent wave, a very high tensile stress is generated, and if there is an existing imperfection in the glass, a crack propagates from this point in a circular shape identical to those seen when raindrops crack supersonic windshields.
“The challenge for treating kidney stones is to reduce the stones to very fine fragments so the doctors don’t have to follow up with any ancillary procedures,” said Zhong. “Based on the insight gained through this model, we may be able to optimise the shape of the shock waves and lithotripter design to create more tension on the surface of the kidney stones to open up the defects more efficiently.”