Effective viscosity for nematic-liquid-crystal viscosity measurement using a shear horizontal wave

We investigate the effective viscosity of a nematic-liquid-crystal (NLC) for viscosity measurement using a shear horizontal (SH) wave propagating through a glass substrate loaded with the NLC. The phase measurement of the SH wave determines the NLC viscosity because SH wave propagation depends on loaded material viscosity. Using this viscosity measurement, we can also determine the viscosity anisotropy of the NLC with director reorientation. In experiment, phase shifts are detected when voltages are applied to a NLC layer. The measured phases show an unpredictable shift which cannot be explained by conventional director angular dependence of viscosity. To analyze the phase shifts quantitatively, we introduce average effective viscosity for the viscosity measurement using SH wave. This effective viscosity is calculated considering the NLC director configuration and SH wave penetration into the NLC layer. The phase shifts calculated from the effective viscosity well agree with the measured phase shifts. The use of effective viscosity enables quantitative analysis for NLC viscosity measurement using the SH wave and also clarifies the mechanism of the unpredictable SH wave phase shift with director reorientation.