A conceptual model for acoustic microcavitation
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A conceptual model for acoustic microcavitation Sameer I. Madanshetty Aerospace and Mechanical Engineering, Boston University, Boston, Massachusetts 02215
(Received 25 May 1994; revised 8 May 1995; accepted 8 May 1995)
A conceptual model is developed to explain microcavitation events at low megahertz frequencies and low duty cycles, facilitated by smooth, spherical, submicrometer sized particles in clean water. The extremely high levels of accelerations associated with high-frequency acoustic fields, the active detector field, can, according to this model, "coax" such smooth particles to nucleate cavitation events at reduced thresholds. This conceptual model should help further experimentation exploring the phenomenon of "acoustic coaxing" for microcavitation. 1995 Acoustical Society of America.
PACS numbers: 43.35.Ei
One always thinks of cavitation in terms of a preexisting gaseous presence either as a bubble or a stabilized pocket of gas trapped in a suitable container crevice. Cavitation can occur if a sound wave imposes sufficiently strong tensile fields. The oscillating pressures of a sound wave imply re- strictions on the time duration of the available tensile field
within a period of oscillation. At high frequencies it becomes increasingly difficult to bring about cavitation because insuf- ficient time is available for bubble growth, which precedes the cavitational implosion. Consequently the cavitation thresholds of bubbles become greater at higher frequencies, and for practical purposes, it becomes very difficult to bring about cavitation (in water) at frequencies in excess of 10 MHz (cf .... in excess of 3 MHz, Neppiras). Therefore, it appears paradoxical that a high-frequency field may actually help lower the thresholds and facilitate cavitation. Such low- ering of thresholds in the presence of high-frequency fields has been reported by Madanshetty. 2
To explore the mechanism of how high-frequency acoustic fields "coax" smooth, spherical particles to nucleate cavitation events at reduced thresholds, we have selected for
discussion several experiments from earlier work. 2-5 This paper is arranged as follows: We start by giving a brief re- view of cavitation and then describe the particular experi- ment that highlighted the paradox. The central thesis of the conceptual model is then presented, and we elaborate upon the constructs that build the model. It is difficult to be fully rigorous at this stage; we therefore seek only supporting evi- dence and arguments, and present some more experiments that corroborate the thesis, at least in principle.
A. Brief review of cavitation
Cavitation is a fascinating phenomenon. It can erode metallic surfaces, help shatter kidney stones, accelerate chemical reactions, and even lead to light production-- sonoluminescence, in the case of acoustic cavitation. Acous-
tic cavitation has been exhaustively reviewed by Flynn, 6 Neppiras, Apfel, 7 and Prosperetti. 8 We will not dwell on the
details of bubble dynamics, but we will recollect in simple terms the concepts of rectified diffusion, resonance, and tran- sient cavitation.
Consider a free bubble in the path of a sound wave. The bubble expands and contracts in response to the pressure alternations of the sound wave; the energy stored during the expansion being returned concentrated during the possibly implosive collapse. Should a bubble grow to about two and a half times its original size during the negative excursion of the acoustic pressure, then during the following positive half- cycle its speed of collapse could become supersonic. 9 Such almost single cycle violent events, called transient cavita- tion, may explain the energetic manifestations of cavitation.
Unlike the dramatic bubble growth within a single acoustic cycle as seen in transient (inertial) cavitation, there exists a more gradual process, termed rectified diffusion. Un- der favorable conditions, a small bubble exposed to a con- tinuous sound wave tends to grow in size if rectified diffu- sion is dominant. According to Henry's law, for a gas soluble in liquid, the equilibrium concentration of the dissolved gas in the liquid is directly proportional to the partial pressure of the gas above the liquid surface, the constant of proportion- ality being a function of temperature only. When a bubble expands, the pressure in the bubble interior falls and gas diffuses into the bubble from the surrounding liquid. When the bubble contracts, the pressure in the interior increases and the gas diffuses into solution in the surrounding liquid. However, the area available for diffusion is larger in the expansion mode than in the contraction mode. Consequently, there is a net diffusion of the gas into the bubble from the surrounding liquid over a complete cycle and thus the bubble grows due to rectified diffusion.
However, a bubble can grow only up to a critical size-- the resonance radius determined by the frequency of the impressed sound wave. For small amplitude oscillations a bubble acts like a simple linear oscillator of mass equal to the virtual mass of the pulsating sphere, which is 3x the mass of displaced fluid, and stiffness primarily given by the internal pressure of the bubble times the ratio of specific heats. (Surface tension effects are significant for small bubbles.) Following Minnaert, ignoring surface tension, there is a simple relation for the resonance radius of air bubbles in water:
2681 J. Acoust. Soc. Am. 98 (5), Pt. 1, November 1995 0001-4966/95/98(5)/2681/9/$6.00 1995 Acoustical Society of America 2681
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 188.8.131.52 On: Mon, 22 Dec 2014 06:23:17
(Resonance radius in /m)
X (insonification frequency in MHz)= 3.2.
This relation is valid to within 5% even for bubbles of radius
10/m. The bubble response becomes increasingly vigorous at resonance radius, and is limited by the damping mecha- nisms in the bubble environment--viscous damping, acous- tic radiation damping, and thermal damping. A postresonance bubble may exhibit nonlinear modes of oscillations or be- come transient if the forcing acoustic pressure amplitude is adequately high.
The above discussion presupposes the presence of a free bubble in the path of a sound wave. Free bubbles, however, do not last long in a standing body of water. The larger ones are rapidly removed due to buoyancy and the smaller ones dissolve even in slightly undersaturated water. While a 10-/m air bubble rises in water at a terminal speed of 300 /m/s, it can survive for about 5 s before dissolving com- pletely. The dissolution of bubbles is driven essentially by the excess pressure inside the bubble due to the surface ten- sion.
It is very difficult to cavitate clean liquids. A pure liq- uid purged of all particulate impurities and stored in a per- fectly smooth container can attain its theoretical tensile strength before undergoing cavitation or fracture. Under ideal conditions water can be as strong as aluminum; the tensile strength of water based on the homogeneous nucle- ation theory exceeds 1000 bars. (In cavitation studies tensile strengths are often quoted in terms of negative pressures, and threshold is understood as the pressure amplitude at which the first occurrence of cavitation is detected.) The observed strengths (thresholds) in practice, however, are very much lower, rarely exceeding a few bars for reasonably clean liq- uids. This is because there exist gas pockets within the liquid which provide the necessary seeding for cavitation. A gas site is often stabilized in a crevice, 2 either in the container wall or on a fluidborne particle. Incomplete wetting traps gas at the root of a sharp crevice, stabilizing it against dissolu- tion. Unlike a free bubble, surface tension in this case acts on
a meniscus which is concave toward the liquid. Overpressur- ing the liquid for sufficient duration prior to insonification can force the meniscus further into the crevice and may cause full wetting of the crevice, which then gives rise to increased thresholds.
II. THE EXPERIMENT
While researching acoustic microcavitation 2 in water primarily at 0.75-MHz frequency and 1% duty cycle--as a precursor to the work to follow at more diagnostically rel- evant frequencies--two kinds of acoustic detectors were used to detect cavitation (see schematic of the test cell, Fig. 1). The first one was an unfocused, untuned 1-MHz trans- ducer which served as a "passive detector." The second was a focused 30-MHz transducer used in a pulse-echo mode as the "active detector." Cavitation itself was brought about by a focused PZT-8, 0.75-MHz transducer driven in pulse mode. Focused systems have the advantage that the zone of cavita- tion is localized within the bulk of the liquid, away from the walls of the container and the rough transducer face. The
acoustically transpaten DIAPHRAGM
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FIG. 1. Schematic of the test cell. The test cell is divided into two compart- ments so that the rho-c TM impedance matching rubber wall immersed in water provides a nonreflecting boundary while remaining isolated from the cavitation chamber. An acoustically transparent stainless shim stock forms a watertight seal between the two compartments. To detect cavitation two kinds of acoustic detectors are used. The first one is an unfocused, untuned 1-MHz receiver transducer which serves as a passive detector. The other one is a focused 30-MHz transducer which