Measurement of Shear Elasticity and Viscosity of Liquids at Ultrasonic Frequencies

Abstract

It has long been suspected that if liquids were sheared sufficiently rapidly they would exhibit a shear elastic effect as well as a viscous effect. This supposition was verified recently by one of the writers (see reference 8) by employing a torsionally vibrating crystal and measuring the mechanical loading for the shear wave by observing the increased resistance at resonance and the change in the resonant frequency. By this method it was shown that long chain polymer liquids had shear configurational elasticities in the order of ${10}^{7}$ dynes/${\mathrm{cm}}^{2}$. The use of a torsional crystal is limited in frequency to about 2 to 3\ifmmode\times\else\texttimes\fi{}${10}^{5}$ cycles on account of the small sizes needed. In the present paper the range of shear wave measurements in liquids has been extended up to 60 megacycles by observing the effect, on a series of shear waves in a fused quartz rod, of terminating the rod by a thin layer of a liquid. The shear wave in the rod is altered in magnitude and phase by the boundary layer impedance of the liquid. By observing the reflection loss and the change in phase caused by the liquid layer, a measure is obtained of the shear impedance of the liquid. By employing a fused quartz rod for which the shear wave strikes the reflecting surface at an angle from the normal of about 79 degrees, the effect of the shear wave impedance on the boundary is greatly enhanced and a more accurate measurement obtained. Both the torsional crystal and high frequency shear wave techniques applied to polyisobutylene and poly-$\ensuremath{\alpha}$-methyl-styrene liquids, show that there are two main relaxation frequencies in these liquids. At frequencies under 100 kc, the shear stiffness is in the order of 3\ifmmode\times\else\texttimes\fi{}${10}^{7}$ dynes/${\mathrm{cm}}^{2}$, while in the high megacycle range it has increased to 5\ifmmode\times\else\texttimes\fi{}${10}^{9}$ dynes/${\mathrm{cm}}^{2}$. The low shear elasticity appears to be associated with a composite motion of molecular rotation and translation that allows a configurational change to occur from the most probable chain shape. When the shear stress is removed, the molecule quickly returns to its most probable shape. This results in a low shear stiffness. At high frequencies this motion cannot take place, and the shear stiffness is determined by motions within single potential wells, and the value approaches that for a crystal. It is shown that the dispersion for longitudinal waves measured recently (see reference 11) is primarily due to the shear mechanisms investigated.