Added-Mass Effect in Modeling of Cilia-Based (Vibrating Cantilever-Type) Devices for Microfluidic Systems

This article shows that the added mass due to fluid structure interaction significantly affects the vibrational dynamics of cilia-based (vibrating cantilever-type) devices for handling micro/nano-scale fluid flows. Commonly, the hydrodynamic interaction between the cilia-based actuator and fluid is modeled as a Stokes drag force that is proportional to the velocity. Our main contribution is to show that such a drag effect cannot explain the substantial reduction in the resonant frequency of the cilia actuator operating in liquid when compared to the natural frequency of the cilia in air. It is shown that an added-mass approach can explain this reduction in the resonant frequency when operating cantilever-type devices in fluid. Thus, this article shows the need to model the added-mass effect, both, theoretically and by using experimental results.