Effects of gradient and nonlocality on the dynamics of nonlinear Bleustein-Gulyaev wave in the 6 mm piezoelectric crystal adjacent to viscous and non-conducting liquid

Liquid sensing applications involve identifying, assessing, and measuring various liquid properties. These applications are utilized across numerous industries, including industrial operations, healthcare, environmental monitoring, and more. In this paper, we investigate the potential application of nonlinear wave particularly, Bleustein-Gulyaev (BG) wave in 6 mm PZT-5H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$PZT-5H$$\end{document} piezoelectric ceramic crystals for liquid sensing. For both metalized surface boundary conditions (i.e., open and short circuit), the exact dispersion relations are provided. The numerical solutions for velocity profiles are obtained subject to the boundary conditions. These numerical outcomes are dependent on embedded parameters viz., viscosity, density of the liquid, nonlocal factor and dimensionless material gradient variable. The authors manifest these embedded parameters on the dissemination of nonlinear wave at nanoscale dimension, which can offer novel perspectives for the development and utilization of nanoscale wave devices. The authors explored the transference of nonlinear Bleustein-Gulyaev (NLBG) wave, in a piezoelectric crystal with nonlocal (PCNL) effect based on the Eringen's nonlocal elasticity theory (ENLET) in the vicinity of Newtonian viscous and non-conducting (VNCL) liquid. The findings demonstrate that wave propagation is significantly impacted by nanoscale size effects because of the nonlocality present in the media.