Dynamic meniscus models for MEMS elements

The dynamics of a liquid meniscus bridge between solid surfaces were analyzed based on the continuum lubrication theory assuming a small vibration of the spacing. The geometry of the meniscus considered in this study was the finite meniscus ring. The following two meniscus models were considered: (1) the fixed boundary position of the meniscus and variable contact angle (VCA) model and (2) the fixed contact angle and variable boundary position (VBP) model. The time-dependent Reynolds equation was solved under the boundary condition considering the Laplace pressure, assuming that the mass of the liquid in the meniscus is conserved. It was found by linearization that the pressures and the load-carrying capacities of both models have three terms, i.e., a time-dependent squeeze term due to the viscosity of the liquid, a spring term due to the dynamic Laplace pressure and a static meniscus force term. The comparisons between these models and experimental results were also presented.