Application of flexural mechanical resonators to simultaneous measurements of liquid density and viscosity

Application of flexural mechanical resonators such as tuning forks, benders, etc. to liquid characterization is described. Additional complex impedance produced by a liquid environment to such resonators is considered. It is shown experimentally, that this additional impedance can be represented by the sum of two terms: one that is proportional to liquid density and a second one that is proportional to the square root the of viscosity density product. This impedance model is universally applicable to any resonator type that directly displaces liquid and has size much smaller than the acoustic wavelength in a liquid at its operation frequency. Using this model it is possible to separately extract liquid viscosity and density values from the flexural resonator frequency response, while conventional TSM resonators can measure only the viscosity density product.