Gas flows in rectangular microchannels and a capacitive micro flow sensor using differential pressure

Jaesung Jang, Purdue University

Abstract

Flows often behave differently at small length scales than macroscopic intuition. These behavior changes can have serious implications for microfluidic devices. In gas flows, these differences are rarefaction and compressibility, among others. The goal of this thesis is to derive the theoretical mass flow rate and pressure distribution in rectangular microchannels considering those differences. These results are applied to designing and fabricating a micro gas flow sensor. Analytical expressions for mass flow rates and pressure distribution in long, straight and uniform rectangular cross section microchannels in the slip flow regime are presented. This analytical model is based on the assumption that the flow is steady state, two-dimensional, isothermal with negligible transverse velocities. Inertial effects are assumed to be negligible, and a first order slip boundary condition is used. These theoretical expressions are compared with experimental measurements of air flowing in microchannels fabricated using DRIE. There is close agreement between the measurements of mass flow/pressure and calculations by the slip flow formulae. These analytical formulae can be used to extract a channel height and a TMAC. The dimensionless location of the maximum pressure deviation from the linear pressure distribution is found analytically and compared with the measurements. The dimensionless location of the maximum deviation depends mostly on the pressure ratio and it increases with the increasing pressure ratios. μPIV measurements are conducted to find the entrance length in water flows. A capacitive micro gas flow sensor is also presented with slip flow analysis. This sensor consists of a pair of capacitors that measure the pressure difference between the inlet and outlet along with the absolute pressure at the outlet, inlet/outlet reservoirs, and the main microchannel which causes a pressure difference between the reservoirs. The main microchannel is 128.0μm wide, 4.64μm deep, and 5680μm long, where the outlet Knudsen number is 0.0137. As the pressure difference increases, the capacitance of the differential pressure sensing capacitor increases. Sensitivity of this sensor and the TMAC are discussed. The laminar friction constant f·Re varies from the no-slip case and hysteresis is important for dynamic flow rate measurements, both of which are also discussed.

Degree

Ph.D.

Advisors

Wereley, Purdue University.

Subject Area

Mechanical engineering

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