Dynamic model of micropipettes in piezo-assisted ICSI

In this paper, the full nonlinear equations of motion of an immersed glass micropipette driven longitudinally by a piezoelectric actuator are derived, based on Kane's method. The Morison equation is adopted to model the hydrodynamic forces in which the drag force is approximated with a viscous damping force. The model presented shows that the longitudinal vibration of a micropipette results in excitation of its out-of-plane, lateral eigenmodes. The nonlinear dynamic model is in good agreement with experimental observations in the literature. Furthermore, an immersed glass micropipette with imbedded mercury is also considered. Simulation results show that the lateral deflection of a micropipette tip increases by adding mercury. This result, however, is inconsistent with the experimental results. The discrepancy is possibly attributed to the assumption of zero relative motion between the mercury contained in the glass micropipette and the glass micropipette. Consequently, it is suggested that a more general nonlinear dynamic model should include the dynamic coupling effects of mercury due to its motion within the micropipette, as it vibrates longitudinally.