Density and viscosity of liquids determination using an inverse method for Love wave propagation

The aim of this work was to establish an inversion procedure for the simultaneous determination of the viscosity and density of liquids. To this end, measurements of dispersion curves of the phase velocity and attenuation of shear horizontal Love waves were applied. Love waves propagate in an elastic layered waveguide covered on its surface with an investigated viscous (Newtonian) liquid. Firstly, the Direct Sturm-Liouville Problem of the Love wave propagation in a such waveguide was formulated and solved. Subsequently, the Inverse Problem was formulated and solved as an Optimization Problem. The appropriately constructed objective function that depends on the material properties of a waveguide of the Love wave, material properties of an investigated liquid (viscosity and density), and the experimental data was employed. The simultaneous determination of both liquid density and viscosity is important in the monitoring of technological processes in many industries (e.g. chemical, petroleum, pharmaceutical industry) as well as in geophysics.