We present a detailed acoustic model of the Greenspan acoustic viscometer, a practical instrument for accurately measuring the viscosity eta of gases. As conceived by Greenspan, the viscometer is a Helmholtz resonator composed of two chambers coupled by a duct of radius rdu. In the lowest order, h = pfr( rd/Q)2 where f and Q are the frequency and quality factor of the isolated Greenspan mode, and r is the gas density. Thus the viscosity can be determined without calibration by measuring the duct radius and frequency response of the resonator. In the full acoustic model of the resonator, the duct is represented by a T-equivalent circuit, the chambers as lumped impedances, and the effects of the diverging fields at the duct ends by lumped end impedances with inertial and resistive components. The model accounts for contributions to 1/Q from thermal dissipation (primarily localized in the chambers) and from a judiciously-located capillary used for filling and evacuating the resonator. A robust, prototype instrument is being used for measuring the viscosity of reactive gases used in semiconductor processing. For well-characterized surrogate gases, the prototype viscometer generated values of h that were 0 to 1 % higher than published reference values throughout the pressure range 0.2--3.2~MPa.
Journal of the Acoustical Society of America
acoustic resonator, acoustics, gases, process gases, resonator, thermophysical properties, transport properties, viscometer, viscosity
, Mehl, J.
and Moldover, M.
Theory of the Greenspan Viscometer, Journal of the Acoustical Society of America
(Accessed October 22, 2021)