Mathematical modelling of Love waves propagation in viscoelastic waveguide loaded with complex fluids

Abstract

Love waves propagation in a viscoelastic waveguide loaded on its surface with viscoelastic fluids of finite thickness is investigated in this paper. The Maxwell and Kelvin-Voigt constitutive equations are employed in order to describe the fluid viscoelasticity. By solving the equations of motion in the different media (viscoelastic fluid, viscoelastic waveguide and elastic substrate) and imposing the suitable boundary conditions, an accurate and simple generalized complex dispersion equation is established for Love waves. Subsequently, a comparison is made with the published complex dispersion equations in the literature in some particular cases, and a very good agreement is showed. A detailed study was conducted by varying key parameters such as operating frequency, waveguide thickness and fluid thickness. The waveguide surface was subjected to various glycerol concentrations, with a wide range of dynamic viscosity, representing both Newtonian and viscoelastic behaviors. Theoretical analysis shows that to reasonably predict the characteristics responses of Love waves, the Maxwell fluid is more appropriate for low glycerol concentration and, the Kelvin-Voigt fluid is more suitable for high glycerol concentration and at high frequency. Results also evaluated the influence of layer thickness on the dispersion curves. The obtained results can be very useful in the design and optimization of Love wave fluid sensors.