Coupled electrical and acoustic modeling of viscous fluid ejectors
Loney, Drew Allan
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The focus of this dissertation is the development of a fundamental understanding of the acoustics and piezoelectric transducer governing the operation of piezoelectric inkjets and horn-based ultrasonic atomizers when utilizing high viscosity working fluids. This work creates coupled, electro-mechanical analytical models of the acoustic behavior of these devices by extending models from the literature which make minimal simplifications in the handling terms that account for viscous losses. Models are created for each component of the considered fluid ejectors: piezoelectric transducers, acoustic pipes, and acoustic horns. The acoustic pipe models consider the two limited cases when either the acoustic boundary layer or attenuation losses dominate the acoustic field and are adapted to account for changes in cross-sectional area present in acoustic horns. A full electro-mechanical analytical model of the fluid ejectors is formed by coupling the component models using appropriate boundary conditions. The developed electro-mechanical model is applied to understand the acoustic response of the fluid cavity alone and when combined with the transducer in horn-based ultrasonic atomizers. An understanding of the individual and combined acoustic response of the fluid cavity and piezoelectric transducer allow for an optimal geometry to be selected for the ejection of high viscosity working fluids. The maximum pressure gradient magnitude produced by the atomizer is compared to the pressure gradient threshold required for fluid ejection predicted by a hydrodynamic scaling analysis. The maximum working fluid viscosity of the standard horn-based ultrasonic atomizer and those with dual working fluid combinations, a low viscosity and a high viscosity working fluid to minimize viscous dissipation, is established to be on the order of 100mPas. The developed electro-mechanical model is also applied to understand the acoustic response of the fluid cavity and annular piezoelectric transducer in squeeze type ejectors with high viscosity working fluids. The maximum pressure gradient generated by the ejector is examined as a function of the principle geometric properties. The maximum pressure gradient magnitude produced by the ejector is again compared to the pressure gradient threshold derived from hydrodynamic scaling. The upper limit on working fluid viscosity is established as 100 mPas.