Shear-Wave Interference observed by Optical Birefringence Induced in a Viscoelastic Liquid

Abstract

A theoretical and experimental study of the shear‐wave field and the associated optical birefringence produced by interfering primary and reflected wavetrains propagating in a viscoelastic medium is presented. The shear‐wave field is generated by two parallel planes, one oscillating sinusoidally in its own plane, the other held motionless at a fixed distance from the driving plane. The shear‐wave propagation is characterized by a complex propagation constant, while the optical birefringence is related to the shear strain rate in the field by a complex mechano‐optic constant. The shear‐wave‐induced birefringence is analyzed by a determination of the modification of the state of polarization of incident circularly polarized light upon passage through the medium. The limiting cases of small and large separation between generating surface and reflecting surface with respect to the shear wavelengths in the medium are useful for determination of the propagation constant and the mechano‐optic constant, while intermediate values of separation of surfaces are useful for demonstrations of the character of the stationary wave patterns. Theoretical determinations of the velocity gradient distribution in the medium for various ratios of surface separation to shear wavelength are presented, together with experimental determinations for an aqueous suspension of milling yellow.