The influence of surface adsorption on microbubble dynamics

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Jun 2008

In a pure liquid, the behaviour of a gas or vapour microbubble is determined primarily by its size, the ambient pressure and the properties of the surrounding liquid. In practice, however, adsorption of a dissolved substance from the surrounding liquid onto the microbubble surface will often take place, producing a thin coating which can significantly affect both the microbubble's stability and its dynamic response. This can have important implications in a wide range of applications, including underwater acoustics, cavitation detection, medical imaging and drug delivery. The aim of this paper is to review the existing theoretical treatments of coated microbubbles and to present and discuss some recent developments. It will be shown that the presence of the coating can substantially modify the amplitude of microbubble volumetric oscillation, resonance characteristics and relative amplitude in tension and compression. Finally, the need for improved understanding of the dynamic behaviour of surface coatings at high frequencies will be discussed.

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The influence of surface adsorption on microbubble dynamics

BY E. STRIDE 0 0 Department of Mechanical Engineering, University College London , Torrington Place, London WC1E 7JE , UK In a pure liquid, the behaviour of a gas or vapour microbubble is determined primarily by its size, the ambient pressure and the properties of the surrounding liquid. In practice, however, adsorption of a dissolved substance from the surrounding liquid onto the microbubble surface will often take place, producing a thin coating which can significantly affect both the microbubble's stability and its dynamic response. This can have important implications in a wide range of applications, including underwater acoustics, cavitation detection, medical imaging and drug delivery. The aim of this paper is to review the existing theoretical treatments of coated microbubbles and to present and discuss some recent developments. It will be shown that the presence of the coating can substantially modify the amplitude of microbubble volumetric oscillation, resonance characteristics and relative amplitude in tension and compression. Finally, the need for improved understanding of the dynamic behaviour of surface coatings at high frequencies will be discussed. The behaviour of bubbles is a subject which has long excited the interest of physicists, mathematicians and engineers, whether to explain the origins of cavitation damage (Besant 1859; Lord Rayleigh 1917), the sounds of the natural world (Minnaert 1933; Leighton & White 2004) or phenomena such as sonoluminescence (Lohse 2005). In a pure liquid, the motion of a gas- or vapour-filled cavity is determined primarily by its size, the ambient pressure and the properties of the surrounding liquid. Rarely, however, are such 'clean' bubbles encountered in practice. Adsorption of molecules of a dissolved substance from the surrounding liquid onto the gas-water interface results in the formation of a thin coating on the bubble surface. This may be due to the deliberate addition of surfactants to produce stabilized bubble suspensions and foams, or it may be incidental due to the natural occurrence of these substances, for example in biological tissue (Moore 1953; Pattle 1960). In either case, the presence of this film or coating can have a significant effect upon both the stability of the bubble and its dynamic behaviour, particularly if the bubble diameter is smaller than 1 mm. 1. Introduction A microbubble suspended in a liquid is inherently unstable due to the action of interfacial tension. This effect can be expressed in terms of the Laplace pressure acting on the microbubble surface where R is the instantaneous radius of the microbubble and s is the interfacial tension. For the sake of simplicity, this discussion will be restricted to the behaviour of gas microbubbles. Under constant ambient pressure in an unsaturated liquid, the radius of a microbubble will decay exponentially as gas diffuses into the surroundings, with the rate of dissolution depending on the magnitude of the interfacial tension, the size of the microbubble, the ambient temperature and pressure, and the concentration and diffusivity of the gas in the liquid (Epstein & Plesset 1950; Readey & Cooper 1966). If the microbubble is subjected to a fluctuating pressure such as a sound field, however, it will undergo volumetric oscillations and, depending on its location and its size relative to the wavelength of the sound field, it may also experience surface oscillations and/or translation. These oscillations may be highly nonlinear on account of the microbubbles high compressibility and both the hydrodynamic and acoustic consequences of this motion may be of great significance. It is well known that cavitation can produce serious damage in hydraulic machinery ( Young 1989), whilst, at lower levels, the erosion caused by microbubble oscillations can be exploited for cleaning and is being investigated as a means of enhancing drug uptake in certain types of therapy (Mitragotri et al. 1995). In underwater acoustics, the distinctive signature of bubbles is used in wake detection; and in diagnostic medical imaging, suspensions of microbubbles are used intravenously as contrast agents, where their ability to scatter ultrasound nonlinearly enables them to be distinguished from the surrounding tissue (Stride & Saffari 2003). In the case of either a constant or a fluctuating pressure, the presence of a coating at the gasliquid interface can significantly affect the microbubbles behaviour. Firstly, it can reduce the Laplace pressure (equation (1.1)) by lowering the interfacial tension. Secondly, it can alter the rate of diffusion of the gas across the interface and hence the rate of change of microbubble size (Fyrillas & Szeri 1995, 1996). Thirdly, it can impart additional resistance to the motion of the interface. The aim of this paper is to discuss the third of these phenomena and, in particular, the effect of a surface coating on the volumetric oscillations of a microbubble. 2. Review of exist (...truncated)


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E Stride. The influence of surface adsorption on microbubble dynamics, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2008, pp. 2103-2115, 366/1873, DOI: 10.1098/rsta.2008.0001