Correlation between the toroidal modes of an elastic sphere and the viscosity of liquids

Vibration characteristics of elastic nanostructures embedded in fluid medium have been used for biological and mechanical sensing also to investigate materials properties. An analytical approach has developed this paper accurately predict toroidal vibrations an nanosphere water–glycerol mixture. The Maxwell Kelvin–Voigt models are describe the viscoelasticity fluid. influence key parameters such as glycerol mass fraction, sphere radius, angular mode number studied. We demonstrate that radius plays a significant role on quality factor. Results highlight three behavior zones: viscous fluid, transition, solid. In addition, these investigations can serve benchmark solution design liquid sensors.