Effects of interface slip and viscoelasticity on the dynamic response of droplet quartz crystal microbalances

In the present paper we first present a derivation based on the time-dependent perturbation theory to develop the dynamical equations which can be applied to model the response of a droplet quartz crystal microbalance (QCM) in contact with a single viscoelastic media. Moreover, the no-slip boundary condition across the device-viscoelastic media interface has been relaxed in the present model by using the Ellis-Hayward slip length approach. The model is then used to illustrate the characteristic changes in the frequency and attenuation of the QCM with and without the boundary slippage due to the changes in viscoelasticity as the coated media varies from Newtonian liquid to solid. To complement the theory, experiments have been conducted with microliter droplets of aqueous glycerol solutions and silicone oils with a viscosity in the range of 50 approximately 10,000 cS. The results have confirmed the Newtonian characteristics of the glycerol solutions. In contrast, the acoustic properties of the silicones oils as reflected in the impedance analysis are different from the glycerol solutions. More importantly, it was found that for the silicone oils the frequency steadily increased for several hours and even exceeded the initial value of the unloaded crystal as reflected in the positive frequency shift. Collaborative effects of interfacial slippage and viscoelasticity have been introduced to qualitatively interpret the measured frequency up-shifts for the silicone oils. The present work shows the potential importance of the combined effects of viscoelasticity and interfacial slippage when using the droplet QCM to investigate the rheological behavior of more complex fluids.