Measurement of a micro-scale fluid physical properties using torsional vibration of a micro shaft

Abstract

The purpose of this study is presenting a novel micro-electromechanical (MEM) sensor for measurement of a micro-scale fluid physical properties. A mathematical model is proposed for this study which consists of a micro-shaft with one end fixed and a sensing element in the form of a cylinder at its free end. The fluid is bounded between the micro-cylinder as sensing element and the outer fixed cylinder. As fluids behave differently in micro-scale than macro, the fluid in the gap is modeled based on micro-polar fluid theory. The sensor can be actuated torsionally via applying an AC voltage to the pair of capacitive plates situated around the micro-shaft and the outer fixed cylinder. After deriving the equations of motion of the micro-shaft and also micro-scale fluid media, these coupled partial differential equations have been solved simultaneously using Galerkin based reduced order model. The dynamic response of the micro-shaft for different exciting frequencies has been investigated. It has been shown that inertial and damping effects of fluid, causes resonance frequency and resonance amplitude of the shaft to decrease. By calculating resonance frequency and resonance amplitude changes, physical properties of a fluid can be measured. Effects of geometrical parameters of the sensing element on the force response of the sensor have also been studied. Through this study it was found that a sensor with large surface area of sensing element and small fluid gap, could measure fluid properties with high accuracy.