Modeling of the acoustic field of thermally induced ultrasonic emission from a spherical cavity surface

Highlights

• Formulas for sound field of the spherical focusing thermo-acoustic emission.

• Features of the thermo-acoustic ultrasound in an enclosed space.

• Standing wavelike resonance frequency response pattern due to interference.

• Much higher available SPL than usually flat response level out of cavity.

Abstract

Thermo-acoustic (TA) ultrasound has attracted considerable interest during the last decade for its many advantages over the conventional electro-acoustic ultrasound. In this paper, a general expression of the acoustic pressure field of thermally induced ultrasonic emission from a spherical cavity surface is derived by using a fully thermally–mechanically coupled TA model. The characteristics and regularities of ultrasound from spherical focusing TA emitter can therefore be studied in detail. It is found that, for the TA emission in sphere shell, wideband flat amplitude–frequency response pattern, the most important feature of TA ultrasound in an open space from a technical standpoint, is seriously disrupted by wave interference occurring in spherical cavity. The dependences of sound pressure of TA ultrasound in spherical cavity on the heating frequency, the inner radius of spherical cavity, the location in spherical cavity, and the thickness of TA sample layer, as well as the type and filling pressure of gas in cavity are given and discussed. The currently used planar TA solution is only the special case for spherical cavity with infinite radius of the analytical solution developed in this work, which would be of significance for more comprehensive guide to understanding and using TA ultrasound.

Introduction

The thermo-acoustic (TA) ultrasound has received a lot of attention since thermally induced intense emission of ultrasonic wave from nanocrystalline porous silicon (PS) to air was first reported by Shinoda et al. [1]. Many experimental and theoretical investigations on this phenomenon and its application were carried out [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], referring to various aspects of TA ultrasound, such as physical mechanism, characteristics, intensification, radiation pressure, three-dimensional image sensing, impulse and phased array operation, and sound reproduction, which clearly show that there exists a very wide range of constant (flat) amplitude–frequency response mostly in ultrasonic region for TA emission from any solid, and thermo-acoustic ultrasound has lots of advantages over conventional electric-acoustic ultrasound: larger frequency bandwidth and acoustic pressure, lesser reverberation and distortion, higher sensing accuracy and spatial resolution, easily integrated in micro-electro-mechanical system (MEMs) and sound signal self-demodulation, and availability and controllability for finely structured impulse and phase arrays operation. Hence, TA emitter, with comparable acoustical efficiency to piezoelectric transducer [20], is promised to developing many new concept devices, such as functional speaker, non-contact microactuator, single tip sonar, high-precision ultrasonic sensor, and vocal signal simulator.

However, the investigations of TA ultrasound so far are mainly for TA emission in an open space, with relatively little effort devoted to TA emission in an enclosure. A few work related to the intracavitary TA emission is basically for thermophones. Although Arnold and Crandall studied the sound emission from a periodically heated platinum strip and proposed the TA mechanism for both open and closed systems almost a century ago [23], the thermophones sound has been too weak to arouse enough interest due to larger heat capacity of TA material. In recent years, with the development of nanomaterials and nanofabrication techniques, nanothermophones have received favors since Xiao et al. found that carbon nanotube (CNT) thin film sheet could be a practical TA loudspeaker in 2008 [24]. Aliev and colleagues have done a fair amount of work to investigate the performances of CNT-based TA projectors in gases and under water [25], [26]. They reveal that putting the TA emitter in a small planar or spherical enclosure which is filled with inert gas having low specific heat and in turn radiates sound outwards and taking advantage of resonant features of enclosure can both provide CNT sheet protection and greatly improve sound generation efficiency at low frequency. Tong et al. have given the theoretical analysis of gas-filled encapsulated CNT film TA transducer by solving a set of coupled thermal–mechanical equations [27]. Xiao et al. have also experimentally studied the TA response of CNT films in a variety of gaseous mediums to verify the theoretical relationship of sound pressure and heat capacity of gas by placing CNT speaker in a sound proof chamber. Due to packing sound absorption material onto the inner wall of chamber, the TA emitter actually behaves just as it is in an open space [28].

Above-mentioned intracavitary TA transducers are basically put in an enclosure with the dimensions less than acoustic wavelength to emit sound wave outwards within the audio range for the purpose of building magnet-free speaker. So, the investigations of encapsulated TA emission are still incomplete and the realization of the features of TA radiation in enclosed space, especially inward emission from surface in ultrasonic range, has not been quite clear yet. In this work, thermally induced ultrasonic emission from a spherical cavity surface is studied by using a fully thermally–mechanically coupled TA model. A general expression of the acoustic pressure field for spherical focusing TA emitter is derived, therefore, systematic investigations on characteristics and regularities of TA ultrasound in an enclosed space, such as the dependences of sound pressure level (SPL) of TA ultrasound in spherical cavity on the heating frequency, the inner radius of spherical cavity, the thickness of TA sample layer, the location in spherical cavity, as well as the types and filling pressure of gas in cavity can be carried out, which would be of significance in complete understanding of TA features and better guiding to the further experimental investigation of TA ultrasound.