Vibration modes of a resonant silicon tube density sensor

We present an investigation of the resonance parameters for a new sensor for on-line measurements of fluid density, The sensor consists of a tube system made of single crystalline silicon, The tube system is excited electrostatically into mechanical resonance and the vibration is detected optically, Using a simplified theoretical analysis, the resonance frequency can be shown to be proportional to 1/root rho, where rho is the density of the silicon and the fluid weighted according to their areas in a cross section of the tube, Thus, a change in fluid density results in a change in the resonance frequency, This dependence is demonstrated by measurements for four different vibrations modes, The quality of the vibration is also investigated through measurements of the Q-values of the vibration modes, The tubes are made using anisotropic silicon KOH etching and silicon-to-silicon fusion bonding micromachining techniques, The dimensions of the tube system are 8.6 x 17.7 mm with an outer tube thickness of 1 mm and a wall thickness of 100 mu m. Total tube length is 61 mm, and the sample volume is 0.035 mi, The sensor has a very good density sensitivity of the order of -200 ppm/(kgm(-3)) and a high Q on the order of 3000 for air in the tube. [142]