Bulk viscosity and compressibility measurement using acoustic spectroscopy

Bulk viscosity is a somewhat obscure parameter that appears in the hydrodynamic equations for Newtonian liquids when compressibility is important and, together with the dynamic viscosity, controls sound attenuation. Whereas dynamic viscosity reflects only "translational" molecular motion, in contrast the bulk viscosity reflects the relaxation of both "rotational" and "vibrational" degrees of molecular freedom. Several molecular theories yield predictive expressions for both bulk and dynamic viscosities, but experimentally the situation is quite out of balance, in that there is extensive data for the dynamic viscosity of all sorts of liquids, but a paucity of data for bulk viscosity, just a few values for water and a handful of exotic liquids. We compare three possible experimental techniques for measuring bulk viscosity, namely, Brillouin spectroscopy, Laser transient grating spectroscopy, and acoustic spectroscopy. We then formulate some arguments suggesting that acoustic spectroscopy is not only the most suitable for measuring bulk viscosity, but that it also offers a verification procedure that can confirm that the measured parameter agrees with theoretical definition of bulk viscosity for a Newtonian liquid. In addition, acoustic spectroscopy provides a measurement of sound speed, which cannot only improve the attenuation measurement but as a side benefit can also be used to calculate liquid compressibility. We apply this technique for measuring the bulk viscosity and compressibility of twelve commonly assumed Newtonian liquids, two of which surprisingly fails to pass a verification test described here to test the Newtonian hypothesis. Then, we test correlation between measured bulk viscosity and several other intensive properties of these liquids, such as density, dynamic viscosity, dielectric permittivity, and compressibility. We have not discovered any meaningful correlation. This suggests that bulk viscosity is an independent parameter that reflects peculiar properties of liquids and can be used in the set of independent equations describing molecular interaction in liquids.