Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Effects of crystalline anisotropy on resonant acoustic loss of torsional quartz viscometers

Published

Author(s)

Paul Heyliger, Clemens Junker, Karsten Meier, Ward L. Johnson

Abstract

Vibrational modes of unrestrained elastic cylinders of trigonal crystals are studied using Ritz-based polynomial approximations for displacements formulated in rectangular Cartesian coordinates. The selected orientation of the threefold trigonal axis is perpendicular to the cylinder axis, corresponding to the configuration employed in torsional quartz viscometry (TQV) for characterizing Newtonian fluids. A revised working equation for TQV is derived, incorporating effects of crystalline anisotropy, and Ritz results are used to numerically quantify effects of acoustic radiation from surface-normal displacements and viscous loss from nontorsional surface-parallel displacements of resonant modes corresponding to the purely torsional modes of isotropic cylinders traditionally employed as an approximation in TQV analysis. For a cylinder typical of TQV, with 3 mm diameter and 50 mm length, the anisotropy-related correction to the extracted fluid viscosity is a positive shift of 36 ppm relative to the isotropic approximation, if radiative losses are neglected. This contribution is independent of fluid properties. Radiative losses depend on the properties of the fluid and reduce the extracted viscosity. The total magnitude of corrections varies between several tens of parts per million for low density gases to values on the order of 0.01% for normal liquids near atmospheric pressure and 0.06% for superfluid helium.
Citation
Journal of the Acoustical Society of America

Keywords

quartz resonators, Ritz calculations, torsional modes, torsional quartz visometers, trigonal crystals, vibrational modes, viscosity

Citation

Heyliger, P. , Junker, C. , Meier, K. and Johnson, W. (2022), Effects of crystalline anisotropy on resonant acoustic loss of torsional quartz viscometers, Journal of the Acoustical Society of America, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=932727 (Accessed March 30, 2023)
Created March 25, 2022, Updated January 20, 2023