Experimental and analytical study of the interaction between short acoustic pulses and small clouds of microbubbles

Abstract

Bubbles appear in many technological and industrial applications, in the fields of medicine, pharmacology, material science and in the chemical industry. In medicine, microbubbles are used as contrast agents in combination with ultrasound waves, since they enhance the backscatterd signal, improving the quality of the images. They are also applied in novel therapeutical techniques oriented to the elimination of thrombi or to tumor ablation, since they can be selectively driven towards precise targets. These important applications emphasize the relevance of knowing the physical behavior of bubbles under ultrasound waves. One of the most important properties of bubbles is that they behave as oscillators when they are excited with a pressure wave, and they can act as nonlinear resonators. The resonance frequency of a bubble is strongly related to its size, but also to the properties of the surrounding medium, being the ambient pressure one of the most relevant ones. In theory, analyzing the acoustical spectrum of a bubble and determining the resonance frequency, we can determine the pressure of the medium. This is precisely the main goal of this thesis: to study the accuracy with which the pressure can be determined. It is well known that an isolated bubble subjected to ultrasound behaves differently than a group of bubbles forming a cloud and interacting among them. Consequently, their acoustic responses are totally different. This means that the knowledge acquired when studying a single bubble cannot directly be applied to a cloud. Nevertheless, under some conditions multiple interactions among neighboring bubbles can be neglected, and the collective response can be approximated as the addition of the individual response of each of the bubbles forming the cloud. But even in this case, the response will be different depending on the properties of the cloud. In this thesis, we study the influence of the properties of the bubble cloud on the acoustical response and on the resonance frequency. In the first part of the thesis, we explain the different equations used to model the oscillatory motion of bubbles under the influence of ultrasound waves. We then focus on collective effects present in clouds of bubbles in order to determine under which conditions these effects can be neglected, concluding that if the cloud is very diluted, multiple interactions do not significantly affect its properties. We also examine the importance of the thermal effects in the acoustic response of bubbles, concluding that these cannot be ignored since they play a fundamental role in the damping of the bubble oscillations and consequently in the acoustic response. In the second part, we study numerically the acoustic spectra of different polydisperse bubble clouds. We examine how the parameters of the size distribution affect the spectra and consequently the accuracy in the determination of the resonance frequency. We are also interested in selecting the acoustic excitation parameters that maximize the response of the bubbles. We conclude that bubble populations with a small polydispersion have a stronger acoustic response than highly polydisperse clouds. Moreover, we found that to use a frequency chirp is the best option to excite the resonance behavior of the bubbles. In order to find a less expensive method—from the computational point of view—to study the acoustic spectrum of bubble clouds, we developed an analytic formulation for the pressure radiated by a cloud, based on a linear analysis of the equations. In the third part of the thesis, hydrogen microbubbles are generated using water electrolysis. We show how mini clusters of bubbles with a size of a few tens of microns can be produced in an easy and inexpensive manner. The technique consists of using a train of short intensity pulses to produce the electrolysis, instead of using a continuous voltage. In this way, only a few bubbles are produced. Moreover, they are sufficiently distant from each other to be considered as isolated. The bubbles produced by electrolysis are used to study experimentally the displacement suffered by the bubble as a consequence of the radiation force produced by an ultrasound wave. In chapter 6, we study the displacement achieved by bubbles of different sizes, as well as the maximum velocities that they attain. The most relevant result is that a same bubble, subjected to two consecutive and identical pulses, can reach different maximum velocities and consequently can experience different displacements. Through a numerical study of the Bjerknes force, we show that the initial condition of the velocity of the bubble has a significant effect on the experienced radiation force, and therefore on the maximum velocity. Finally, monodisperse microbubbles produced using flow-focusing techniques are excited with an ultrasound wave. Their backscatterd signal is analyzed in order to detect their resonance frequency. Although we are able to detect a peak around the expected resonance frequency in some cases, unfortunately no conclusive results are obtained, as shown in chapter 4.