Grieser / Choi / Enomoto Sonochemistry and the Acoustic Bubble

1. Auflage 2015
ISBN: 978-0-12-801726-5
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 298 Seiten

Sonochemistry and the Acoustic Bubble provides an introduction to the way ultrasound acts on bubbles in a liquid to cause bubbles to collapse violently, leading to localized 'hot spots' in the liquid with temperatures of 5000ø celcius and under pressures of several hundred atmospheres. These extreme conditions produce events such as the emission of light, sonoluminescence, with a lifetime of less than a nanosecond, and free radicals that can initiate a host of varied chemical reactions (sonochemistry) in the liquid, all at room temperature. The physics and chemistry behind the phenomena are simply, but comprehensively presented. In addition, potential industrial and medical applications of acoustic cavitation and its chemical effects are described and reviewed. The book is suitable for graduate students working with ultrasound, and for potential chemists and chemical engineers wanting to understand the basics of how ultrasound acts in a liquid to cause chemical and physical effects. - Experimental methods on acoustic cavitation and sonochemistry - Helps users understand how to readily begin experiments in the field - Provides an understanding of the physics behind the phenomenon - Contains examples of (possible) industrial applications in chemical engineering and environmental technologies - Presents the possibilities for adopting the action of acoustic cavitation with respect to industrial applications

Autoren/Hrsg.

Grieser, Franz

Choi, Pak-Kon

Enomoto, Naoya

Harada, Hisashi

Okitsu, Kenji

Yasui, Kyuichi

Leseproben

Chapter 2

Ultrasound Field and Bubbles

Shigemi Saito     School of Marine Science and Technology, Tokai University, Shizuoka, Japan

Abstract

The fundamentals of ultrasound in a fluid are presented. Ultrasound propagates in a fluid as a longitudinal wave, where the fluid particles vibrate along the direction of propagation. A sound wave is partially reflected at the boundary between two media with different characteristic impedances. In particular, almost all of a sound wave is reflected at the boundary between water and air and the reflected sound is superposed on the incident wave to produce a standing wave. A fluid medium exhibits elastic nonlinearity. Primarily as a result of this nonlinearity, nonlinear distortion of the sound waveform occurs. A gas bubble in a liquid vibrates in the presence of sound and reradiates the sound, resulting in strong scattering of the sound. In addition, when the bubble resonates with the incident ultrasound, at a frequency specified by certain parameters, e.g., bubble size, the bubble exhibits significant elastic nonlinearity.

Keywords

Attenuation; Characteristic impedance; Longitudinal wave; Minnaert equation; Nonlinear propagation; Particle velocity; Plane wave; Reflection; Scattering; Second harmonic; Sound intensity; Sound pressure; Standing wave; Velocity dispersion

Chapter Outline

2.1 Fundamentals of a Sound Wave 11

2.1.1 Basic Equations 12

2.1.2 Physical Quantities of Sound 14

2.1.3 Complex Notation for Variable Quantities and Constant Values 15

2.1.4 Relationship between Sound Pressure and Particle Velocity 17

2.1.5 Sound Reflection and Transmission 18

2.1.6 Nonlinear Propagation of Sound 24

2.1.7 Sound Radiation from a Point Source 26

2.1.8 Scattering of Sound 28

2.1.9 Attenuation of a Sound Wave 29

2.2 Sound Propagation in a Bubbly Liquid 32

2.2.1 Basic Acoustic Equations for a Bubbly Liquid 32

2.2.2 Equation for an Oscillating Bubble 32

2.2.3 Oscillation Characteristics of a Bubble 34

2.2.4 Velocity Dispersion and Sound Absorption in a Bubbly Liquid 36

2.2.5 Nonlinearity in a Bubbly Liquid 37

Further Reading 39

Sonochemistry is a research field involving the analysis and application of chemical reactions induced by the effect of ultrasonic irradiation on small gas bubbles or solid particles mixed in a liquid medium. Hence, in addition to the chemical properties of materials, the physical properties of the ultrasound emitted in the liquid must be considered in sonochemistry. In addition, bubbles in a liquid affect the physical properties determining sound propagation. The fundamentals underpinning the physics of ultrasound are presented in this chapter.

2.1. Fundamentals of a Sound Wave

When an object vibrates in a fluid, be it either a gas or liquid, the fluid directly in contact with the vibrating surface is displaced by the component of the motion normal to the surface. As a consequence of this movement the pressure in a layer near the surface is instantly increased or decreased by the action of contraction or expansion, respectively. Subsequently, the transient pressure change will move the neighboring particles of the fluid beyond this layer, and so on. The periodic motion that propagates in such a manner is a sound wave. The displacement of the medium is parallel to the direction in which a sound wave propagates. Such a wave is also called a longitudinal wave or a dilatational wave.

2.1.1. Basic Equations

Take the case of a sound wave propagating in a continuous and uniform fluid. The pressure and the density of the fluid in an equilibrium state are denoted by P0 and ?0, respectively. When a sound wave is applied to a medium in this state, the particles making up the medium begin to translationally vibrate parallel to the propagating direction. The velocity of vibration u is the particle velocity. Since u varies with the location along the propagation path, so too does the density. The increment of the density from ?0 is denoted by ?. The increase in the pressure accompanying ? is defined as the sound pressure p. In order to describe the vibration of a fluid without using a vector u, the velocity potential ?, that is defined by the following equation, is often used.

=-??=-(???x,???y,???z).

(2.1)

The values of u, ?, and p change with time t. For simplicity, a one-dimensional wave, or a plane wave propagating in the x direction, is assumed here. As illustrated in Figure 2.1, the difference between the pressures that act on both sides of an element occupying the space between x and x+?x equates to p(x)–p(x+?x)˜-(?p/?x)?x. This force is effectively applied to a mass of ?0?x. Then the equation of motion for the acceleration du/dt is obtained.1

Figure 2.1 One-dimensional motion of a volume element.

0(?u?t+u?u?x)=-?p?x.

(2.2a)

When u˜0, Eqn (2.2a) is approximated as

0?u?t=-?p?x.

(2.2b)

Moreover, as seen in Figure 2.1, whilst the mass inflowing through the plane x is ?0u(x) per unit area and unit time, the mass outflowing through x+?x is ?0u(x+?x). The difference ?0[u(x)-u(x+?x)]=-?0(?u/?x)?x is basically the incremental mass in the element between x and x+?x per unit area and unit time, (??/?t)?x. Hence, the equation for continuity.

??t=-?0?u?x

(2.3)

is derived.

The change in the pressure is expressed as a function of the fractional change of the density, ?/?0, by the equation of state,

=K??0,

(2.4)

where K is the volume elasticity. For an ideal gas, K is given as K=?P0, where ? is the specific heat ratio (the ratio of the specific heat at constant pressure to that at constant volume).

The substitution of Eqn (2.1) into Eqn (2.2b) gives

=?0???t.

(2.5)

Hence the acoustic pressure can be easily obtained from the velocity potential.

By combining Eqns (2.2b), (2.3), and (2.4), to eliminate u and ?, the following is obtained.

2p?x2-1c02?2p?t2=0,

(2.6)

where

02=K?0(=?p??).

(2.7)

Equation (2.6) is called the d'Alembert's wave equation in one dimension. Equations with similar form, such as ?2u/?x2-(1/c0)2?2u/?t2=0, can also be derived for u, ?, and ? as well as p.

The solutions for p from Eqn (2.6) become the functions of x±c0t.2 Since the value of x-c0t is constant for a point that moves along the x-axis with a speed of c0, the functions of x-c0t represent waves that propagate in the x direction with a speed of c0. Similarly, the functions of x+c0t represent waves propagating in the -x direction with a speed c0. Here, c0 is the sound speed, which is a constant that is dependent on the propagating medium.

In most cases, a one-dimensional plane wave is sufficient for...