Identification of viscoelastic properties with fluid inertia in a parallel plate with effective mechanical system analyses

Measurement of viscoelastic properties in small amplitude oscillatory shear (SAOS) can be affected by fluid inertia, especially at high frequencies. In this study, we introduce an effective mechanical system approach to address the effects of fluid inertia on the viscoelastic measurement with a SAOS test, employing a parallel plate geometry. In the effective mechanical system approach, viscous, elastic, and inertial properties of a fluid system are modeled systematically by a rotational drag coefficient, a torsional spring constant, and a second moment of inertia, respectively. In this way, we established the analytic solution for the linear viscoelastic behavior of a fluid in the presence of fluid inertia. The shear modulus on the frequency, obtained by the effective mechanical system, reveals that fluid inertia only affects the storage modulus and not the loss modulus. We investigate the behavior of the storage modulus as a function of the gap size, the oscillation frequency, and the disk radius, demonstrating the dependence on the gap size and the frequency. Comparison was made for the shear modulus from the effective mechanical system with viscoelastic flow simulation, employing two viscoelastic (Oldroyd-B and Giesekus) fluid models to validate the accuracy of this approach. The maximum error was found less than 3.3% over the frequency range from 1 to 100 rad/s.