Investigation of Oscillating Micro U-Tube-Based Fluid Density Sensor

The fluid-density sensor is realized using the oscillating U-tube method. This sensor is composed of a U-shaped tube, a piezoelectric actuator, a micropump, and a U-tube housing for the inlet and outlet of the fluid. The U-tube was excited to the oscillation mode using a piezoelectric actuator. The sensing principle is based on the dependency of resonant frequency on the measuring fluid density, where changes in density alter the inertial mass of the oscillating tube system. A theoretical analysis reveals that the resonant frequency is directly influenced by the effective density (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho $ </tex-math></inline-formula>) of the measuring fluid. A new mathematical relationship has been derived and proposed between resonance frequency (f) and center-to-center gap (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${D} _{c}$ </tex-math></inline-formula>) between of U-tube open ends. This U-tube has been designed for the resonance frequency of 2.269 kHz, and the empty tube quality (Q) factor was ~51.59. The density sensor exhibits a superior sensitivity of 0.05351 Hz/(kg<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\cdot $ </tex-math></inline-formula><inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathrm {m}}^{-{3}}$ </tex-math></inline-formula>), a high mechanical quality factor of 114.48. It operates effectively in a broad range of density 784–1463 kg<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\cdot $ </tex-math></inline-formula><inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathrm {m}}^{-{3}}$ </tex-math></inline-formula> with deflection amplitudes spanning 20.05–53 nm. The design model has been developed and correlated with the experimental results. The U-tube requires only a small volume of sample (2.416 nL), making it suitable for a variety of applications with limited sample volume availability. The compact design and robust performance characteristics position this sensor as a highly effective solution for advanced applications in precision density measurement.