Miniaturized high frequency plate resonators for rheometric applications

Abstract

Conventional rotational rheometers are typically limited to around 100Hz. In order to extent the frequency domain, a couple of methods have been proposed [1]. These are however typically stand alone instruments and only a few have been commercially available. In the present work we pursue an approach aimed at miniaturizing in-plane plate resonators for possible add-on integration into standard rheometers. The lithographically structured plates have primary mechanical resonance frequencies up to 10 kHz. Lorentz force excitation and an inductive readout mechanism allow the measurement of the frequency response by monitoring the electrical two port behavior [2]. The fluid-structure interaction is dominated by decaying shear waves with penetration depths of typically a few to tens of micrometers, exact values depend on the mass density and viscoelastic moduli. The resonance frequency and damping are sensitive to the fluid forces and therefore can be used to measure the rheological properties of liquids. In our work, we will present the modeling approach including the eigenmode solution of the mechanical resonance, the fluid-structure interaction, and the electrical equivalent circuit describing the excitation and readout mechanisms. The theoretical model is verified using a set of low to intermediate viscosity liquids demonstrating the measurement technique and consistency of the modeling approach. For an aqueous silica suspension it is shown that the resonator damping is determined by the steady shear viscosity. This result is compared to measurements obtained with a high frequency quartz thickness shear mode sensor where the high-frequency viscosity determines the damping. Further experiments will focus on the behavior in non-Newtonian (viscoelastic) media and the effect of a reflecting wall placed at a distance below the shear-wave penetration depth. [1] Kirschenmann et al, Rheol. Acta 41, 2002 [2] Reichel et al, submitted to Sens. and Act. A, Elsevier, 2009status: publishe