Full Text:   <3080>

CLC number: TB5

On-line Access: 2007-11-10

Received: 2007-02-10

Revision Accepted: 2007-07-15

Crosschecked: 0000-00-00

Cited: 2

Clicked: 5542

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Journal of Zhejiang University SCIENCE A 2008 Vol.9 No.1 P.65-78

http://doi.org/10.1631/jzus.A072053


Eccentricity and thermoviscous effects on ultrasonic scattering from a liquid-coated fluid cylinder


Author(s):  Seyyed M. HASHEMINEJAD, M. A. ALIBAKHSHI

Affiliation(s):  Acoustics Research Lab., Department of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran 16844, Iran

Corresponding email(s):   hashemi@iust.ac.ir

Key Words:  Thremoviscous effects, Eccentric fluid cylinder, Acoustic scattering


Seyyed M. HASHEMINEJAD, M. A. ALIBAKHSHI. Eccentricity and thermoviscous effects on ultrasonic scattering from a liquid-coated fluid cylinder[J]. Journal of Zhejiang University Science A, 2008, 9(1): 65-78.

@article{title="Eccentricity and thermoviscous effects on ultrasonic scattering from a liquid-coated fluid cylinder",
author="Seyyed M. HASHEMINEJAD, M. A. ALIBAKHSHI",
journal="Journal of Zhejiang University Science A",
volume="9",
number="1",
pages="65-78",
year="2008",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A072053"
}

%0 Journal Article
%T Eccentricity and thermoviscous effects on ultrasonic scattering from a liquid-coated fluid cylinder
%A Seyyed M. HASHEMINEJAD
%A M. A. ALIBAKHSHI
%J Journal of Zhejiang University SCIENCE A
%V 9
%N 1
%P 65-78
%@ 1673-565X
%D 2008
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A072053

TY - JOUR
T1 - Eccentricity and thermoviscous effects on ultrasonic scattering from a liquid-coated fluid cylinder
A1 - Seyyed M. HASHEMINEJAD
A1 - M. A. ALIBAKHSHI
J0 - Journal of Zhejiang University Science A
VL - 9
IS - 1
SP - 65
EP - 78
%@ 1673-565X
Y1 - 2008
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A072053


Abstract: 
Calculation of the scattered field of the eccentric scatterers is an old problem with numerous applications. This study considers the interaction of a plane compressional sound wave with a liquid-encapsulated thermoviscous fluid cylinder submerged in an unbounded viscous thermally conducting medium. The translational addition theorem for cylindrical wave functions, the appropriate wave field expansions and the pertinent boundary conditions are employed to develop a closed-form solution in the form of infinite series. The analytical results are illustrated with a numerical example in which the compound cylinder is insonified by a plane sound wave at selected angles of incidence in a wide range of dimensionless frequencies. The backscattered far-field acoustic pressure amplitude and the spatial distribution of the total acoustic pressure in the vicinity of the cylinder are evaluated and discussed for representative values of the parameters characterizing the system. The effects of incident wave frequency, angle of incidence, fluid thermoviscosity, core eccentricity and size are thoroughly examined. Limiting case involving an ideal compressible liquid-coated cylinder is considered and fair agreement with a well-known solution is established.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Abramowitz, M., Stegun, I.A., 1965. Handbook of Mathematical Functions. National Bureau of Standards. Washington, DC.

[2] Alemar, J.D., Delsanto, P.P., Rosario, E., Nagel, A., Uberal, H., 1986a. Spectral analysis of the scattering of acoustic waves from a fluid cylinder, I: Denser fluid loading. Acustica, 61:1-6.

[3] Alemar, J.D., Delsanto, P.P., Rosario, E., Nagel, A., Uberal, H., 1986b. Spectral analysis of the scattering of acoustic waves from a fluid cylinder, II: Denser fluid inside. Acustica, 61:7-13.

[4] Babick, F., Hinze, F., Ripperger, S., 2000. Dependence of ultrasonic attenuation on the material properties. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 172(1-3):33-46.

[5] Bailey, D.H., 1995. A FORTRAN-90 based multiprecision system. ACM Trans. Math. Soft., 21(4):379-387.

[6] Boag, A., Levitan, Y., Boag, A., 1988. Analysis of acoustic scattering from fluid cylinders using a multifilament source model. J. Acoust. Soc. Am., 83(1):1-8.

[7] Cai, L.W., 2004. Multiple scattering in single scatterers. J. Acoust. Soc. Am., 115(3):986-995.

[8] Chandra, K., Thompson, C., 1992. Improved perturbation method for scattering from a fluid cylinder. J. Acoust. Soc. Am., 92(2):1047-1055.

[9] Chung, S.K., Trinh, E.H., 1998. Containerless protein crystal growth in rotating levitated drops. J. Cryst. Growth, 194(3-4):384-397.

[10] Danila, E.B., Conoir, J.M., Izbicki, J.L., 1995. Generalized Debye series expansion: Treatment of the concentric and nonconcentric cylindrical fluid-fluid interfaces. J. Acoust. Soc. Am., 98(6):3326-3342.

[11] Danila, E.B., Conoir, J.M., Izbicki, J.L., 1998. Generalized Debye series expansion. Part II, Treatment of eccentric fluid-solid cylindrical interfaces. Acta Acustica, 84:38-44.

[12] Doi, T., Koster, J.N., 1993. Thermocapillary convection in two immiscible liquid layers with free surface. Phys. Fluids A, 5(8):1914-1927.

[13] Dongarra, J., Bunch, J., Moler, C., Stewart, G.W., 1979. LINPACK User’s Guide. SIAM.

[14] Eyer, A., Leiste, H., 1985. Striation-free silicon crystal by float-zoning with surface coated melt. J. Cryst. Growth, 71(1):249-252.

[15] Faran, J.J., 1951. Sound scattering by solid cylinders and spheres. J. Acoust. Soc. Am., 23(4):405-418.

[16] Gao, J.R., Wei, B.B., 1999. Containerless solidification of undercooled NdFeZrB alloy droplets in a drop tube. J. Alloys Compd., 285(1-2):229-232.

[17] Hasegawa, T., Yasutaka, H., Akio, H.A., Hideki, N., Massahiko, K., 1993. Acoustic radiation pressure acting on spherical and cylindrical shells. J. Acoust. Soc. Am., 93(1):154-160.

[18] Hasheminejad, M., Geers, T.L., 1993. Modal impedance for two spheres in a thermoviscous fluid. J. Acoust. Soc. Am., 94(4):2205-2214.

[19] Hasheminejad, M., Azarpeyvand, M., 2003. Energy distribution and radiation loading of a cylindrical source suspended within a nonconcentric fluid cylinder. Acta Mechanica, 164(1-2):15-30.

[20] Hasheminejad, M., Badsar, A., 2004. Acoustic scattering by a pair of poroelastic spheres. Quart. J. Mech. Appl. Math., 57(1):95-113.

[21] Janele, P.J., Mioduchowski, A., Haddow, J.B., 1991. A note on finite dynamic deformation of concentric cylinders. Int. J. Eng. Sci., 29(12):1585-1592.

[22] Johnson, D.T., 2002. Viscous effects in liquid encapsulated liquid bridges. Int. J. Heat Fluid Flow, 23(6):844-854.

[23] Kanevskii, I.N., Surikov, B.S., 1976. Two-layer acoustic lenses. Acoustics, 22:292-294.

[24] Lamb, H., 1945. Hydrodynamics. Dover.

[25] Lane, M., Forest, K.T., Lyons, E.A., Bavister, B.D., 1999. Live births following vitrification of hamster embryos using a novel containerless technique. Theriogenology, 51(1):167.

[26] Li, M.W., Zeng, D.L., Zhu, T.X., 2002. Instability of the Marangoni convection in a liquid bridge with liquid encapsulation under microgravity condition. Int. J. Heat Mass Transfer, 45(1):157-164.

[27] Li, Y.R., Liu, Y.J., Peng, L., Wang, Y., 2006. Three-dimensional oscillatory thermocapillary flow in encapsulated liquid bridge. Phys. Fluids, 18(7):074108-1-074108-6.

[28] Lin, W.H., Raptis, A.C., 1983. Acoustic scattering by elastic solid cylinders and spheres in viscous fluids. J. Acoust. Soc. Am., 73(3):736-748.

[29] Lorber, B., Giege, R., 1996. Containerless protein crystallization in floating drops—Application to crystal-growth monitoring under reduced nucleation conditions. J. Cryst. Growth, 168(1-4):204-215.

[30] Mai, J., Yamane, R., Früh, W.G., Oshima, S., Ando, A., 2002. Unstable waves at the interface of a diamagnetic liquid column contained in a magnetic fluid. European Journal of Mechanics-B/Fluids, 21(2):237-246.

[31] Marr-Lyon, M.J., Thiessen, D.B., Marston, P.L., 1997. Stabilization of a cylindrical capillary bridge far beyond the Rayleigh-Plateau limit using acoustic radiation pressure and active feedback. J. Fluid Mech., 351:345-357.

[32] Marr-Lyon, M.J., Thiessen, D.B., Blonigen, F.J., Marston, P.L., 2000. Stabilization of electrically conducting capillary bridges using feedback control of radial electrostatic stresses and the shapes of extended bridges. Phys. Fluids, 12(5):986-995.

[33] Marr-Lyon, M.J., Thiessen, D.B., Marston, P.L., 2001. Passive stabilization of capillary bridges in air with acoustic radiation pressure. Phys. Rev. Lett., 86(11):2293-2296.

[34] Montanero, J.M., 2003. Theoretical analysis of the vibration of axisymmetric liquid bridges of arbitrary shape. Theoret. Comput. Fluid Dynamics, 16(3):171-186.

[35] Montanero, J.M., Cabezas, G., Acero, J., Perales, J.M., 2002. Theoretical and experimental analysis of the equilibrium contours of liquid bridges of arbitrary shape. Phys. Fluids, 14(2):682-693.

[36] Morse, P., Ingard, K., 1968. Theoretical Acoustics. McGraw-Hill.

[37] Morse, S.F., Feng, Z.W., Marston, P.L., 1995. High-frequency threshold processes for leaky waves on cylinders of variable thickness: Fluid shell case. J. Acoust. Soc. Am., 98(5):2928.

[38] Moseler, M., Landman, U., 2000. Formation, stability, and breakup of nanojets. Science, 289(5482):1165-1169.

[39] Nagashio, K., Takamura, Y., Kuribayashi, K., Shiohara, Y., 1999. Microstructural control of NdBa3Cu3O7-delta superconducting oxide from highly undercooled melt by containerless processing. J. Cryst. Growth, 200(1-2):118-125.

[40] Perales, J.M., Meseguer, J., 1992. Theoretical and experimental study of the vibration of axisymmetric viscous liquid bridges. Phys. Fluids A, 4(6):1110-1130.

[41] Rayleigh, L., 1945. Theory of Sound. Dover.

[42] Reese, J.M., Thompson, W., 1986. Acoustic diffraction by a variable thickness fluid layer. J. Acoust. Soc. Am., 80(6):1810-1815.

[43] Rhim, W.K., Ohsaka, K., Paradis, P.F., Spjut, R.E., 1999. Noncontact technique for measuring surface-tension and viscosity of molten materials using high-temperature electrostatic levitation. Rev. Sci. Instrum., 70(6):2796-2801.

[44] Roumeliotis, J.A., Kakogiannos, B., 1995. Acoustic scattering from an infinite cylinder of small radius coated by a penetrable one. J. Acoust. Soc. Am., 97(4):2074-2081.

[45] Roumeliotis, J.A., Ziotopoulos, A.P., Kokkorakis, G.C., 2001. Acoustic scattering by a circular cylinder parallel with another of small radius. J. Acoust. Soc. Am., 109(3):870-877.

[46] Rousselot, J.L., 1994. Field diffracted by a fluid cylinder: Comparison between the geometrical theory of diffraction and a model solution. Acustica, 80:14-20.

[47] Sanz, A., 1985. The influence of the outer bath in the dynamics of axisymmetric liquid bridges. J. Fluid. Mech., 156:101-140.

[48] Schuster, G.T., 1990. A fast exact numerical solution for the acoustic response of concentric cylinders with penetrable interfaces. J. Acoust. Soc. Am., 87(2):495-502.

[49] Scotti, T., Wirgin, A., 2004. Reconstruction of the three mechanical material constants of a lossy fluid-like cylinder from low-frequency scattered acoustic fields. Comptes Rendus Mécanique, 332(9):717-724.

[50] Shaw, R.P., Tai, G., 1974. Time harmonic acoustic radiation from nonconcentric circular cylinder. J. Acoust. Soc. Am., 56(5):1437-1443.

[51] Sinai, J., Waag, R.C., 1988. Ultrasonic scattering by two concentric cylinders. J. Acoust. Soc. Am., 83(5):1728-1735.

[52] Stratton, J.A., 1941. Electromagnetic Theory. McGraw-Hill.

[53] Temkin, S., 1981. Elements of Acoustics. Wiley, New York.

[54] Thiessen, D.B., Marr-Lyon, M.J., Marston, P.L., 2002. Active electrostatic stabilization of liquid bridges in low gravity. J. Fluid Mech., 457:285-294.

[55] Varadan, V.V., Ma, Y., Varadan, V.K., Lakhtakia, A., 1991. Scattering of Waves by Spheres and Cylinders. In: Varadan, V.V., Lakhtakia, A., Varadan, V.K. (Eds.), Field Representation and Introduction to Scattering. Elsevier, Amsterdam, p.211-324.

[56] Viviani, A., Golia, C., 2003. Thermocapillary flows in two-fluids liquid bridges. Acta Astronautica, 53(11):879-897.

[57] Walker, J.S., Henry, D., BenHadid, H., 2002. Magnetic stabilization of the buoyant convection in the liquid-encapsulated Czochralski process. J. Cryst. Growth, 243(1):108-116.

[58] Wei, W., Thiessen, D.B., Marston, P.L., 2004. Acoustic radiation force on a compressible cylinder in a standing wave. J. Acoust. Soc. Am., 116(1):201-208.

[59] Zayas, F., Alexander, J.I.D., Meseguer, J., Ramus, J.F., 2000. On the stability limits of long nonaxisymmetric cylindrical liquid bridges. Phys. Fluids, 12(5):979-985.

[60] Zhang, S., Jin, J., 1996. Computation of Special Functions. John Wiley & Sons.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE