Viscous flow in variable cross-section microchannels of arbitrary shapes

This paper outlines a novel approximate model for determining the pressure drop of laminar, single-phase flow in slowly-varying microchannels of arbitrary cross-section based on the solution of a channel of elliptical cross-section. A new nondimensional parameter is introduced as a criterion to identify the significance of frictional and inertial effects. This criterion is a function of the Reynolds number and geometrical parameters of the cross-section; i.e., perimeter, area, cross-sectional polar moment of inertia, and channel length. It is shown that for the general case of arbitrary cross-section, the cross-sectional perimeter is a more suitable length scale. An experimental investigation is conducted to verify the present model; 5 sets of rectangular microchannels with converging–diverging linear wall profiles are fabricated and tested. The collected pressure drop data are shown to be in good agreement with the proposed model. Furthermore, the presented model is compared with the numerical and experimental data available in the literature for a hyperbolic contraction with rectangular cross-section.