Hostname: page-component-8448b6f56d-m8qmq Total loading time: 0 Render date: 2024-04-20T15:23:17.063Z Has data issue: false hasContentIssue false
  • English
  • Français

Acoustic Scattering by a Fluid-Encapsulating Spherical Viscoelastic Membrane Including Thermoviscous Effects

Published online by Cambridge University Press:  05 May 2011

Seyyed M. Hasheminejad
Seyyed M. Hasheminejad*
Affiliation:
Department of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran 16844, Iran
*
* Associate Professor
Get access

Abstract

This study provides a general analysis for scattering of a planar monochromatic compressional sound wave by a fluid-filled viscoelastic spherical membrane immersed in an unbounded viscous heat-conducting compressible fluid. The thermoviscous effects in the fluid are incorporated by application of a thin boundary layer model. The dynamic viscoelastic properties of the spherical membrane are rigorously taken into account in the solution of the acoustic-scattering problem. Havriliak-Negami model for viscoelastic material behaviour along with the appropriate wave-harmonic field expansions and the pertinent boundary conditions are employed to develop a closed-form solution in form of infinite series. Subsequently, the basic acoustic quantities, such as the scattered far-field pressure directivity pattern, and the scattering cross section are evaluated for given sets of viscoelastic material properties. Numerical results clearly indicate that, in addition to the traditional fluid thermoviscosity-related mechanisms, dynamic viscoelastic properties of the obstacle can be of significance in sound scattering. The presented analysis is of practical interest in development of contrast agents for echocardiographic research with potential clinical applications.

Keywords

ScatteringViscoelasticThermoviscousContrast agentsEncapsulated bubble
Type
Articles
Information
Journal of Mechanics , Volume 21 , Issue 4 , December 2005 , pp. 205 - 215
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Lord, Rayleigh, The Theory of Sound, 2, Dover, New York (1945).Google Scholar
2.Lamb, H., Hydrodynamics, Dover, New York (1945).Google Scholar
3.Morse, P. M., Vibration and Sound, McGraw-Hill, New York (1948).Google Scholar
4.King, L. V., “On the Acoustic Radiation Pressure on Spheres,” Proc. Royal Soc. London Ser A, 137, pp. 212–240 (1934).Google Scholar
5.Faran, J. J., “Sound Scattering by Solid Cylinders and Spheres,” J. Acoust. Soc. Am., 23, pp. 405–418 (1951).CrossRefGoogle Scholar
6.Yosioka, K. and Kawasima, Y., “Acoustic Radiation Pressure on a Compressible Sphere,” Acustica, 5, pp. 167–173.Google Scholar
7.Hickling, R., “Analysis of Echoes From a Solid Elastic Sphere in Water,” J. Acoust. Soc. Am., 34, pp. 1582–1601 (1962).CrossRefGoogle Scholar
8.Hasegawa, T. and Yosioka, K., “Acoustic-Radiation Force on a Solid Elastic Sphere,” J. Acoust. Soc. Am., 46, pp. 1139–1143 (1969).CrossRefGoogle Scholar
9.Junger, M. C., “Sound Scattering by Thin Elastic Shells,” J. Acoust. Soc. Am., 24, pp. 366–373 (1952).CrossRefGoogle Scholar
10.Goodman, R. R. and Stern, R., “Reflection and Transmission of Sound by Elastic Spherical Shells,” J. Acoust. Soc. Am., 34, pp. 338–344 (1962).CrossRefGoogle Scholar
11.Hickling, R., “Analysis of Echoes from a Hollow Metallic Sphere in Water,” J. Acoust. Soc. Am., 36, pp. 1124–1137 (1964).CrossRefGoogle Scholar
12.Diercks, K. J. and Hickling, R., “Echoes from Hollow Aluminium Spheres in Water,” J. Acoust. Soc. Am., 41, pp. 380–393 (1967).CrossRefGoogle Scholar
13.Hickling, R., “Scattering of Frequency-Modulated Pulses by Spherical Elastic Shells in Water,” J. Acoust. Soc. Am., 44, pp. 1246–1252 (1968).CrossRefGoogle Scholar
14.Williams, K. L. and Marston, P. L., “Backscattering from an Elastic Sphere: Sommerfeld-Watson Transfer and Experimental Confirmation,” J. Acous. Soc. Am., 79, pp. 2091–2099 (1986).CrossRefGoogle Scholar
15.Flax, L., Dragonette, L. R., Varadan, V. K. and Varadan, V. V., “Analysis and Computation of the Acoustic Scattering by an Elastic Spheroid Obtained from the T-Matrix Formulation,” J. Acoust. Soc. Am., 71, pp. 1077–1082 (1982).CrossRefGoogle Scholar
16.Werby, M. F. and Green, L. H., “A Comparison of Acoustical Scattering from Fluid Loaded Elastic Shells and Sound Soft Objects,” J. Acoust. Soc. Am., 76, pp. 1227–1230 (1984).CrossRefGoogle Scholar
17.Murphy, J., George, J., Nagl, A. and Uberali, H., “Isolation of the Resonant Components in Acoustic Scattering from Fluid Loaded Elastic Spherical Shells,” J. Acoust. Soc. Am., 65, pp. 368–373 (1979).CrossRefGoogle Scholar
18.Flax, L. and Gaunaurd, G. C., “Theory of Resonance Scattering,” Physical Acoustics, XV, Mason, W. P. and Thurston, R. N. Eds., Academic Press, New York, pp. 191–294 (1990).Google Scholar
19.Gaunaurd, G. C. and Kalmins, A., “Resonances in the Sonar Cross Sections of Coated Spherical Shells,” Int. J. Solids Structures, 18, pp. 1083–1102 (1982).CrossRefGoogle Scholar
20.Hinders, M. K., “Extinction of Sound by Spherical Scatterers in a Viscous Fluid,” Physical Rev. A., 43(10), pp. 5628–5637 (1991).CrossRefGoogle Scholar
21.Lin, W. H. and Raptis, A. C., “Themoviscous Effects on Acoustic Scattering by Thermoelastic Solid Cylinders and Spheres in Viscous Fluid,” J. Acoust. Soc. Am., 74(5), pp. 241–250 (1983).CrossRefGoogle Scholar
22.Danilov, S. D. and Mironov, M. A., “Mean Force on a Small Sphere in Sound Field in a Viscous Fluid,” J. Acoust. Soc. Am., 107(1), pp. 143–153 (2000).CrossRefGoogle Scholar
23.Dukhin, A. S., Goetz, P. J., Wines, T. H. and Somasundaran, P., “Acoustic and Electroacoustic Spectroscopy,” Colloids and Surfaces, 173, pp. 127–158 (2000).CrossRefGoogle Scholar
24.Temkin, S., “Attenuation and Dispersion of Sound in Dilute Suspensions of Spherical Particles,” J. Acoust. Soc. Am., 108(1), pp. 126–146 (2000).CrossRefGoogle ScholarPubMed
25.Sewell, C. J. T., “The Extinction of Sound in a Viscous Atmosphere by Small Obstacles of Cylindrical and Spherical Form,” Philo. Trans. R. Soc. London, A. 210, pp. 239–270 (1910).Google Scholar
26.Hertzfeld, K. F., Philo. Mag., 9, p. 741 (1930).CrossRefGoogle Scholar
27.Epstein, P. S. and Carhart, J., “The Absorption of Sound in Suspensions and Emulsions,” J. Acoust. Soc. Am., 25, pp. 553–565 (1953).CrossRefGoogle Scholar
28.Allegra, J. R. and Hawley, S. A., “Attenuation of Sound in Suspensions and Emulsions: Theory and Experiments,” J. Acoust. Soc. Am., 51, pp. 1545–1564 (1972).CrossRefGoogle Scholar
29.Anson, L. W. and Chivers, R. C., “Ultrasonic Scattering from Spherical Shells Including Viscous and Thermal Effects,” J. Acoust. Soc. Am., 93(4), pp. 1687–1699 (1993).CrossRefGoogle Scholar
30.Ferry, J. D., Viscoelastic Properties of Polymers, Wiley, New York (1980).Google Scholar
31.Read, J. D., The Determination of Dynamic Properties of Polymers and Composites, Adam Hilger, Bristol (1978).Google Scholar
32.Nashif, A. D., Vibration Damping, Wiley, New York (1985).Google Scholar
33.Capps, R. N., “Elastomeric Materials for Acoustical Applications,” Naval Research Lab.-Underwater Sound Reference Detachment (1989).Google Scholar
34.Piquette, J. C., “Determination of the Complex Dynamic Bulk Modulus of Elastomers by Inverse Scattering,” J. Acoust. Soc. Am., 77(5), pp. 1665–1673 (1985).CrossRefGoogle Scholar
35.Simmonds, D. J. and Humphrey, V. F., “Estimation of the Dynamic Plate Modulus of Viscoelastic Materials by Inversion of the Impedance Tube Measurements,” Proc. Inst. Acoust., 15(6), pp. 104–114 (1993).Google Scholar
36.Zhong, W. F., Tang, S. B. and Chen, B. H., “The Multi-Parameter Inversion of Elastic Wave in Half-Space,” Acta Mech. Sin., 12(2), pp. 129–135 (1999).Google Scholar
37.Willis, R. L., Wu, Lei and Berthelot, Y. H., “Determination of the complex Young's and Shear Dynamic Moduli of Viscoelastic Materials,” J. Acoust. Soc. Am., 109(2), pp. 1–11 (2001).CrossRefGoogle Scholar
38.Thrope, S. A., “Dynamical Processes of Transfer at the Sea Surface,” Prog. Oceanogr., 35, pp. 315–352 (1995).CrossRefGoogle Scholar
39.Farmer, D. M., Lemon, D. D., “The Influence of Bubbles on Ambient Noise in the Ocean at High Wind Speeds,” J. Phys. Oceangr., 14, pp. 855–863 (1984).2.0.CO;2>CrossRefGoogle Scholar
40.Ye, Z., “Acoustic Scattering from Fish Swimbladders,” J. Acoust. Soc. Am., 99, pp. 785–792 (1996).CrossRefGoogle Scholar
41.Ye, Z., “Resonant Scattering of Acoustic Waves by Ellipsoid Air Bubbles,” J. Acoust. Soc. Am., 101, pp. 681–685 (1997).CrossRefGoogle Scholar
42.de Jong, N., Ten Cate, F. J., Lancee, C. T., Roelandt, J. R. T. C. and Born, N., “Principles and Recent Developments in Ultrasound Contrast Agents,” Ultrasonics, 29(4), pp. 324–330 (1991).CrossRefGoogle ScholarPubMed
43.Hoff, L., “Acoustic Properties of Ultrasonic Contrast Agents,” Ultrasonics, 34(2–5), pp. 591–593 (1996).CrossRefGoogle Scholar
44.Allen, J. S., “Shell Waves and Acoustic Scattering from Ultrasound Contrast Agents,” LEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 48(2), pp. 409–418 (2001).CrossRefGoogle ScholarPubMed
45.Frinking, Peter J. A. and de Jong, Nico, “Acoustic Modeling of Shell-Encapsulated Gas-Bubbles,” Ultrasound in Medicine and Biology, 24(4), pp. 523–533 (1998).CrossRefGoogle ScholarPubMed
46.de Jong, N. and Hoff, L., “Ultrasonic Scattering Properties of Albunex Microspheres,” Ultrasonics, 31, pp. 175–181 (1993).CrossRefGoogle ScholarPubMed
47.Ye, Z., “On Sound Scattering and Attenuation of Albunex Bubbles,” J. Acoust. Soc. Am., 100, pp. 2011–2028 (1996).CrossRefGoogle Scholar
48.Church, C. C., “The Effects of an Elastic Solid Surface Layer on the Radial Pulsations of Gas Bubbles,” J. Acoust. Soc. Am., 97, pp. 1510–1521 (1995).CrossRefGoogle Scholar
49.Soula, M., Vinh, T., Chevalier, Y. and Beda, T., “Measurements of Isothermal Complex Moduli of Viscoelastic Materials Over a Large Range of Frequencies,” J. Sound Vib., 205(2), pp. 167–184 (1997).CrossRefGoogle Scholar
50.Hillstrom, L., Mossberg, M. and Lundberg, C., “Identification of Complex Modulus from Measured Strains on an Axially Impacted Bar Using Least Squares,” J. Sound Vib., 230(3), pp. 689–707 (2000).CrossRefGoogle Scholar
51.Giovagnoni, M., “On the Direct Measurement of the Dynamic Poisson's Ratio,” Mech. Mater., 17, pp. 33–46 (1994).CrossRefGoogle Scholar
52.Jarzynski, J., “Mechanisms of Sound Attenuation in Matrials,” Sound and Vibration Damping with Polymers, Cosaro, R. D. and Sperling, L. H., Eds., American Chemical Society, Washington DC, pp. 167–207 (1990).CrossRefGoogle Scholar
53.Havriliak, S. and Negami, S., “A Complex Plane Representation of Dielectric and Mechanical Relaxation Processes in Some Polymers,” Polymer, 8, pp. 161–210 (1967).CrossRefGoogle Scholar
54.Bagley, R. L. and Torvik, P. J., “Fractional Calculus: A Different Approach to the Analysis of Viscoelastically Damped Structures,” ALAA J., 21, pp. 741–748 (1983).Google Scholar
55.Bagley, R. L. and Torvik, P. J., “On the Fractional Calculus Model of Viscoelastic Behaviour,” J. Rheol, 30, pp. 133–155 (1986).CrossRefGoogle Scholar
56.Havriliak, S. and Negami, S., “A Complex Plane Analysis of α-Dispersions in Some Polymer Systems,” Transitions and Relaxations in Polymers, J. Polymer Sci., Part C, No. 14, edited by Boyer, R. F., Interscience, New York, pp. 99–117 (1966).Google Scholar
57.Hartman, B., Lee, G. F., Lee, J. D. and Fedderly, J. J., “Sound Absorption Height and Width Limits for Polymers,” J. Acoust. Soc. Am., 101(4), pp. 2008–2011 (1997).CrossRefGoogle Scholar
58.Hartman, B., Lee, G. F. and Lee, J. D., “Loss Factor Height and Width Limits for Polymer Relaxations,” J. Acoust. Soc. Am., 95(1), pp. 226–233 (1994).CrossRefGoogle Scholar
59.Morse, P. M. and Feshbach, H., Methods of Theoretical Physics, McGraw-Hill, New York (1953).Google Scholar
60.Morse, P. M. and Ingard, K. U., Theoretical Acoustics, McGraw-Hill, New York (1968).Google Scholar
61.Abramovitz, M. and Stegun, I. A., Handbook of Mathematical Functions, National Bureau of Standards, Washington D.C. (1964).Google Scholar
62.Pierce, A. D., Acoustics; An Introduction to its Physical Principles and Applications, Acoustical Soc. Am., New York (1989).Google Scholar
63.Morse, P. M. and Ingard, K. U., “Linear Acoustic Theory,” Encyclopedia of Physics, XI/1, Acoustics, Sect. 39, pp. 101–103, Springer Verlag, Berlin (1961).Google Scholar
64.Brekhovskikh, L. M. and Lysanov, Y. P., Fundamentals of Ocean Acoustics, Springer-Verlag, Berlin (1991).CrossRefGoogle Scholar
65.Thompson, I. J. and Barnett, A. R., “Modified Bessel Functions Iv (z) and Kv (z) of Real Order and Complex Argument, to Selected Accuracy,” Computer Physics Comm., 47, pp. 245–257 (1987).CrossRefGoogle Scholar
66.Vargaftik, N. B., Handbook of Physical Properties of Liquids and Gases, Springer-Verlag, Berlin (1983).Google Scholar