Sensing of liquid level at micron resolution using self-excited millimeter-sized PZT-cantilever

Composite resonant millimeter-sized piezoelectric cantilevers were fabricated and their mass change sensitivity was evaluated using liquid evaporation experiments. The cantilever sensor was immersed to 1 mm depth in two volatile fluids, and one non-volatile fluid. Deionized water and 50% ethanol-water solution showed a resonant frequency change of 19 ± 1 and 23 ± 1 Hz/min, respectively. The cantilever liquid level change sensitivity (ϕ) was determined as 0.26 ± 0.01 μm/Hz. Experimental measurement of liquid level change of deionized water at room temperature and humidity was found to be 5.0 ± 0.1 μm/min, and is in good agreement with first principles model prediction of 5.5 μm/min. We have modeled the added mass effects as proportional to displaced liquid mass. Such a model agrees with experimental results for immersion depths of less than 1 mm. The model provides a method for determining cantilever's spring constant and the added mass coefficient. The significance of the results we report is that millimeter-sized piezoelectric-actuated cantilevers have the sensitivity for measuring micron-level liquid level changes.