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Jun 1998

Volume 103, Issue 6, pp. 3121-3736

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Resonator frequency shift due to ultrasonically induced microparticle migration in an aqueous suspension: Observations and model for the maximum frequency shift

Christopher S. Kwiatkowski and Philip L. Marston

J. Acoust. Soc. Am. Volume 103, Issue 6, pp. 3290-3300 (1998); (11 pages)

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Aqueous suspensions of plastic and hollow-glass microspheres are subjected to the radiation pressure of an ultrasonic standing wave. It is well known that the particles are attracted to the pressure nodes of the standing wave for the particle and host properties considered. We demonstrated that the radiation pressure induced migration of particles leads to a significant shift in the resonant frequency of a suitably designed chamber. This shift is easily resolved with a phase-locked loop even if the particle volume fraction is as small as 0.001. For sufficient ultrasonic amplitudes, the shift is found to saturate at a limiting value. To approximate the limiting frequency shift, the principle of adiabatic invariance is first applied to the case of a single compressible sphere in a standing wave and then superposition is used to give the collective shift for the suspension. The measured limiting shifts are typically within 25% of the calculated value and this method may have application to the characterization of dilute suspensions since the shift is proportional to the volume fraction and to a material contrast factor. The applicability of adiabatic invariance is confirmed by comparing frequency shifts for certain cases of idealized particle spatial distributions with results based on transfer matrix eigenvalues combined with an effective-medium approximation. © 1998 Acoustical Society of America.
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43.35.Bf Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in liquids, liquid crystals, suspensions, and emulsions
43.35.Ty Other physical effects of sound
43.25.Qp Radiation pressure

The natural frequency of oscillation of gas bubbles in tubes

H. N. Og̃uz and A. Prosperetti

J. Acoust. Soc. Am. Volume 103, Issue 6, pp. 3301-3308 (1998); (8 pages) | Cited 19 times

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A numerical study is presented of the natural frequency of the volume oscillations of gas bubbles in a liquid contained in a finite-length tube, when the bubble is not small with respect to the tube diameter. Tubes rigidly terminated at one end, or open at both ends, are considered. The open ends may be open to the atmosphere or in contact with a large mass of liquid. The numerical results are compared with a simple approximation in which the bubble consists of a cylindrical mass of gas filling up the cross section of the tube. It is found that this approximation is very good except when the bubble radius is much smaller than that of the tube. An alternative approximate solution is developed for this case. The viscous energy dissipation in the tube is also estimated and found generally small compared with the thermal damping of the bubble. This work is motivated by the possibility of using gas bubbles as actuators in fluid-handling microdevices. © 1998 Acoustical Society of America.
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43.35.Pt Surface waves in solids and liquids

Linear thermoacoustic instability in the time domain

S. Karpov and A. Prosperetti

J. Acoust. Soc. Am. Volume 103, Issue 6, pp. 3309-3317 (1998); (9 pages) | Cited 2 times

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An approximate time-domain description of the development of the thermoacoustic instability in gas-filled tubes is developed by exploiting the difference between the instability time scale and the period of standing waves. The perturbation results compare very favorably with the exact frequency-domain theory of Rott. The perturbation results are further simplified by introducing a short-stack approximation which is numerically much simpler and only slightly less accurate. An approximate expression for the critical temperature gradient accounting for viscous effects and other design features is also derived. In addition to the fundamental mode of a tube closed at both ends, the theory includes higher modes as well as open-end boundary conditions. © 1998 Acoustical Society of America.
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43.35.Ud Thermoacoustics, high temperature acoustics, photoacoustic effect

A model for transverse heat transfer in thermoacoustics

George Mozurkewich

J. Acoust. Soc. Am. Volume 103, Issue 6, pp. 3318-3326 (1998); (9 pages) | Cited 6 times

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A model for transverse heat transfer in parallel thermoacoustic pores is developed. The model is one-dimensional, in the sense that the temperatures in the gas, Tg, and in the solid walls, Tw, are assumed to be fully represented by their dependences on the pore’s axial coordinate, z. All effects of transverse variation across the cross section of the pore are subsumed into a transverse heat-transfer coefficient, h1, that couples the temperatures according to q(z) = h1[Tg(z)−Tw(z)], where q is the transverse heat transfer per unit area. First the model is applied to thermally isolated pores, and results are compared to a recent three-dimensional analysis of this case [G. Mozurkewich, J. Acoust. Soc. Am. 103, 380–388 (1998)]. Then it is extended to the case of heat-exchanger pores immediately adjacent to the end of a long stack. The heat-transfer results are cast in nondimensional form as the product of two factors. One factor depends on gas properties and the geometry of the heat exchanger, the other on the length of the stack and on a parameter related to the relative total heat pumping capacity of heat exchanger and stack. Plots of both factors are given for the special case of planar pores. The results may be applied to the design of heat exchangers for practical thermoacoustic devices. © 1998 Acoustical Society of America.
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43.35.Ud Thermoacoustics, high temperature acoustics, photoacoustic effect

Laser-modulated phase-stepping digital shearography for quantitative full-field imaging of ultrasonic waves

Benjamin A. Bard, Grant A. Gordon, and Shudong Wu

J. Acoust. Soc. Am. Volume 103, Issue 6, pp. 3327-3335 (1998); (9 pages) | Cited 1 time

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Measurement of surface displacements due to ultrasonic wave propagation in elastic solids has traditionally been studied using single-point measurement techniques such as ultrasonic transducers or interferometers. Full-field methods, excluding scanning techniques, are uncommon; examples include holographic interferometry and Schlieren imaging. In many cases, these techniques have been used to yield qualitative results due to inherent difficulties in processing the data. Laser-modulated phase-stepping digital shearography is a full-field, common-path, interferometric method which can be used to quickly visualize ultrasonic wave fields. A shearography system will be described that provides not only whole-field images of ultrasonic waves, but quantitative displacement data within these fields. Images are shown of propagating plate and bar waves, and mathematics relating the calculated optical phase to the ultrasonic wave parameters are presented. © 1998 Acoustical Society of America.
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43.35.Yb Ultrasonic instrumentation and measurement techniques
43.35.Sx Acoustooptical effects, optoacoustics, acoustical visualization, acoustical microscopy, and acoustical holography
43.35.Pt Surface waves in solids and liquids
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