Bubble dynamics and High Intensity Focused Ultrasound: experimental observations and numerical simulations using Boundary Element Method

摘要

We present an experimental study of High Intensity Focused Ultrasound (HIFU) using a parabolic shaped transducer and high speed photography (Ohl et al, 2015). The transducer (Sonic Concept Inc.) has a diameter of 60 mm, and a resonant frequency of 250kHz. When it is driven between 120 to 150 Volt peak-to-peak, concentrated rings of bubbles are formed on top of the transducer. The distance between the rings is about 3 mm, which is half the wavelength of the sound wave produced by the transducer at 250 kHz. The bubbles within the rings are not stable. They move or jump between the rings, or coalesce, or float toward the free surface. To stabilise the rings, we use a reflector which is made of stainless steel, and have the same shape and dimensions as the transducer. At lower driving voltages (80 to 100 Vpp), streams of bubbles are seen moving towards the free surface. This indicates that no standing waves are present. When driven in a burst mode (500 cycles), small bubble clouds are formed. We captured the nucleation and expansion of these clouds using the high speed photography and a long distance microscopic lens. In an attempt to understand some of these observed phenomena, we employed numerical simulations based on the Boundary Element Method (BEM). The Boundary Element Method is an established numerical method for the simulation of bubble dynamics (Blake et al, 1986, 1987). Recently Klaseboer et al (2012) and Sun et al (2014) have improved the numerical solution methodology by eliminating the singularities in the Boundary Integral equation. By using an analytical function, and subtracting this from the original Boundary Integral Method in a specific manner, the method is desingularized, with the added advantage of eliminating the solid angle. This breakthrough significantly reduces the computational complexity and cost, making the use of higher order elements becomes straight forward. The same analytics is applied then to develop a three-dimensional BEM code to solve the Helmholtz equation. The code is used to simulate the ultrasound field generated by the HIFU transducer which is used in the experiments previously mentioned. From the simulation, the focused ultrasound field is clearly described.