On the modeling of a MEMS-based capacitive wall shear stress sensor

In this paper, a microcapacitive wall shear stress sensor for the measurement of skin friction is developed. The design objective is to measure wall shear stress in the range of 1.25–2.45 kPa in laminar boundary layers. Mechanical behavior of the sensing elements, capacitive variations, and sensor’s static response has been investigated using numerical methods. The governing equation whose solution holds the answer to all our questions about the sensor’s characteristics is the nonlinear elasto-electrostatic equation. The results indicate that with this sensor design it is possible to measure wall shear stress values of 1.25 kPa and larger with a maximum uncertainty of 1.13%. Apparently, uncertainty depends on magnitude of wall shear stress. The higher the value of wall shear stress is, the smaller the uncertainty becomes. If we need the sensor to detect wall shear stress values less than 1.25 kPa with the same accuracy as cited, it is essential to replace the sensing microplate of the device with a thinner one.