Archives of Acoustics, 44, 4, pp. 659–668, 2019
10.24425/aoa.2019.129722

The Forces Driving Streaming in the Presence of Scatterers Mimicking the Blood Cells and the Contrast Agents

Janusz WÓJCIK
Institute of Fundamental Technological Research, Polish Academy of Sciences
Poland

Wojciech SECOMSKI
Institute of Fundamental Technological Research, Polish Academy of Sciences
Poland

Norbert ZOŁEK
Institute of Fundamental Technological Research, Polish Academy of Sciences
Poland

Acoustical Driving Forces (ADF), induced by propagating waves in a homogeneous and inhomogeneous lossy fluid (suspension), are determined and compared depending on the concentration of suspended particles. Using integral equations of the scattering theory, the single particle (inclusion) ADF was calculated as the integral of the flux of the momentum density tensor components over the heterogeneity surface. The possibility of negative ADF was indicated. Originally derived, the total ADF acting on inclusions only, stochastically distributed in ambient fluid, was determined as a function of its concentration. The formula for the relative increase in ADF, resulting from increased concentration was derived. Numerical ADF calculations are presented. In experiments the streaming velocities in a blood-mimicking starch suspension (2 μm radius) in water and Bracco BR14 contrast agent (SF6 gas capsules, 1 μm radius) were measured as the function of different inclusions concentration. The source of the streaming and ADF was a plane 2 mm diameter 20 MHz ultrasonic transducer. Velocity was estimated from the averaged Doppler spectrum obtained from originally developed pulsed Doppler flowmeter. Numerical calculations of the theoretically derived formula showed very good agreement with the experimental results.
Keywords: streaming suspension; scattering; acoustical driving force; Doppler measurements; contrast agents
Full Text: PDF
Copyright © The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0).

References

Brekhovskikh L.M., Godin O.A. (1990), Acoustics of Layered Media I:plane and quasi-plane waves, Chapter 1, par. 1, Berlin: Springer-Verlag, Berlin, Heidelberg.

Cannell D.S., Sarid D. (1974), Sound propagation in SF6 near the critical point, Physical Review A, 10, 6, 2280–2289.

Czyz H., Gudra T. (1992), Forces due to diffraction of sound wave on small diameter cylindrical, particles, Journal de Physique IV Colloque, 2, C1, 741–744, doi: 10.1051/jp4:19921161.

Eckart C. (1948), Vortices and streams caused by sound waves, Physical Review, 73, 68–76.

Estrada-Alexanders A.F., Hurly J.J. (2008), Kinematic viscosity and speed of sound in gaseous CO, CO2, SiF4, SF6, C4F8, and NH3 from 220 K to 375 K and pressures up to 3.4 MPa, Journal of Chemical Thermodynamics, 40, 2, 193–202, doi: 10.1016/j.jct.2007.07.002.

Lei J., Glynne-Jones P., Hill M. (2013), Acoustic streaming in the transducer plane in ultrasonic particle manipulation devices, Lab on a Chip, 13, 2013, 2133–2143, doi:10.1039/c3lc00010a.

Mitri F.G. (2012), Interaction of an Acoustical Quasi-Gaussian Beam With a Rigid Sphere: Linear Axial Scattering, Instantaneous Force, and Time-Averaged Radiation Force, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 59, 10, 2347–2351, doi: 10.1109/TUFFC.2012.2460.

Nowicki A., Kowalewski T., Secomski W., Wójcik J. (1998), Estimation of acoustical streaming: theoretical model, Doppler measurements and optical visualization, European Journal of Ultrasound, Vol. 7, 73–81.

Nowicki A., Secomski W., Wójcik J. (1997), Acoustic streaming: comparison of low amplitude linear model with streaming velocities measured by means of 32 MHz Doppler, Ultrasound in Medicine and Biology, 23, 5, 783–91.

Settnes M., Bruus H. (2012), Forces acting on a small particle in an acoustical field in a viscous fluid, Physical Review E, 85, article ID: 016327, doi: 10.1103/PhysRevE.85.016327.

The Engineering Toolbox (2008), Gases – Speed of Sound, available at: https://www.engineeringtoolbox.com/speed-sound-gases-d_1160.html/.

Tjotta S. (1959), On some non-linear effects in sound fields with special emphasis on generation of vorticity and the formation of streaming patterns, Archiv for Mathematik og Naturvidenskab, 55, 1–68.

Wójcik J., Gambin B. (2017), Theoretical and numerical aspects of nonlinear reflection– transmission phenomena in acoustics, Applied Mathematical Modelling, 42, 100–113, doi: 10.1016/j.apm.2016.10.026.

Wójcik J., Litniewski J., Nowicki A. (2011), Modeling and analysis of multiple scattering of acoustic waves in complex media: Application to the trabecular bone, Journal of the Acoustical Society of America, 130, 4, 1908–1918, doi: 10.1121/1.3625285.

Wu J., Du G. (1993), Acoustic streaming generated by focused Gaussian beam and finite amplitude tone burs, Ultrasound in Medicine and Biology, 19, 2, 167–176.

Yoshida T. et al. (2012), Blood-mimicking fluid for the Doppler test objects of medical diagnostic instruments, 2012 IEEE International Ultrasonics Symposium, doi: 10.1109/ULTSYM.2012.0403, 1–4.

Zarembo L.K., Krasilnikow W.A. (1966), Introduction to Nonlinear Acoustics [in Russian], Nauka, Moscow.

Zhang D.Z., Prosperetti A. (1994), Averaged equations for inviscid disperse two-phase flow, Journal of Fluid Mechanics, 267, 185–219.

Zhang D.Z., Prosperetti A. (1997), Momentum and energy equations for disperse two-phase flows and their closure for dilute suspensions, International Journal of Multiphase Flow, 23, 3, 425–453.




DOI: 10.24425/aoa.2019.129722