Investigating the impact of shear and bulk viscosity on the damping of confined acoustic modes in phononic crystal sensors

Abstract

Phononic crystal (PnC) sensors are recognized for their capability to control acoustic wave propagation through periodic structures, presenting considerable potential across various applications. Despite advancements, the effects of fluid viscosity on PnC performance remain intricate and inadequately understood. This study theoretically investigates the influence of shear (dynamic) and bulk viscosity on acoustic wave damping in defective one-dimensional phononic crystal (1D PnC) sensors designed for detecting liquid analytes. Acetic acid with varying viscosities is considered to fill a cavity layer intermediated by a multilayer stack of lead and epoxy. The effects of dynamic and bulk viscosity on the resonance characteristics of the defective mode were analyzed. Numerical results reveal that increased dynamic viscosity leads to substantial broadening and decreased intensity of resonance peaks, accompanied by a shift to higher frequencies due to enhanced elastic wave attenuation and damping. At low dynamic viscosity (η = 0.2 η d ), numerous resonance peaks with varying intensities are observed. However, at higher viscosities (η = 2.0 η d to η = 10.0 η d ), only one prominent peak appears in the spectrum. The intensity of this resonant peak starts at 98% for η = 2 η d and decreases to 58.8% as the dynamic viscosity increases to η = 10 η d . Additionally, the combined effect of dynamic and bulk viscosity introduces further damping, causing a strong shift of the resonance peak to higher frequencies, along with an increase in the full width at half maximum (FWHM) and a decrease in the quality factor (QF). These findings emphasize the necessity of incorporating both shear and bulk viscosity in the design of PnC sensors to enhance their sensitivity and accuracy in practical applications. This theoretical framework provides critical insights for optimizing sensor performance and bridging gaps between theoretical predictions and experimental observations, especially in 1D PnCs, offering potential solutions to challenges in real-world PnC sensor applications.