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Deriving the Speed of Sound in a Liquid

As with waves on a string, the speed of sound or a mechanical wave in a fluid depends on the fluid's elastic modulus and inertia. The two relevant physical quantities are the bulk modulus and the density of the material. Indeed, it turns out that the relationship between speed and the bulk modulus and density in fluids is the same as that between the speed and the Young's modulus and density in solids.
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Bulk viscosity and compressibility measurement using acoustic spectroscopy.

Andrei S Dukhin1, Philip J Goetz

  • 1Dispersion Technology Inc., Bedford Hills, New York 10507, USA. adukhin@dispersion.com

The Journal of Chemical Physics
|April 2, 2009
PubMed
Summary

Bulk viscosity, reflecting molecular relaxation, is challenging to measure. Acoustic spectroscopy is identified as the most suitable method, revealing it as an independent liquid property.

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Area of Science:

  • Fluid dynamics
  • Physical chemistry
  • Rheology

Background:

  • Bulk viscosity is crucial for Newtonian liquids with compressibility, controlling sound attenuation alongside dynamic viscosity.
  • It reflects molecular rotational and vibrational relaxation, unlike dynamic viscosity's focus on translational motion.
  • Experimental data for bulk viscosity is scarce compared to dynamic viscosity.

Purpose of the Study:

  • To compare experimental techniques for measuring bulk viscosity: Brillouin spectroscopy, Laser transient grating spectroscopy, and acoustic spectroscopy.
  • To identify the most suitable technique for bulk viscosity measurement and verification.
  • To investigate the relationship between bulk viscosity, compressibility, and other liquid properties.

Main Methods:

  • Comparison of Brillouin spectroscopy, Laser transient grating spectroscopy, and acoustic spectroscopy for bulk viscosity measurement.
  • Application of acoustic spectroscopy to measure bulk viscosity and compressibility in twelve Newtonian liquids.
  • Testing the Newtonian hypothesis using a verification procedure within acoustic spectroscopy.

Main Results:

  • Acoustic spectroscopy is deemed the most suitable technique for measuring bulk viscosity and verifying its theoretical definition.
  • Two of the twelve tested liquids unexpectedly failed the Newtonian hypothesis verification.
  • No significant correlation was found between bulk viscosity and other intensive liquid properties like density or dynamic viscosity.

Conclusions:

  • Acoustic spectroscopy is the preferred method for accurate bulk viscosity measurements and Newtonian liquid verification.
  • Bulk viscosity appears to be an independent parameter reflecting unique liquid characteristics.
  • Further research is needed to understand the implications of bulk viscosity as an independent molecular interaction descriptor.