A novel solution for pressure drop in singly connected microchannels of arbitrary cross-section

This paper outlines a novel approximate solution for determining the pressure drop of fully developed, laminar, single-phase flow in singly connected microchannels of arbitrary cross-section. Using a “bottom-up” approach, it is shown that for constant fluid properties and flow rate in fixed cross-section channels, the Poiseuille number is only a function of geometrical parameters of the cross-section, i.e., perimeter, area, and polar moment of inertia. The proposed model is validated with experimental data for rectangular, trapezoidal, and triangular microchannels. The model is also compared against numerical results for a wide variety of channel cross-sections including: hyperellipse, trapezoid, sine, square duct with two adjacent round corners, rhombic, circular sector, circular segment, annular sector, rectangular with semi-circular ends, and moon-shaped channels. The model predicts the pressure drop for the cross-sections listed within 8% of the values published.