An analytical model is developed to calculate the capillary pressure as the liquid-vapor interface traverses a backward facing step in an open microchannel. The developed model is validated against results from Surface Evolver liquid-vapor surface simulations and ANSYS Fluent two-phase flow simulations using the volume of fluid approach. Three different aspect ratios (inlet channel height by channel width) were studied. The analytical model shows good agreement with the simulation results from both modeling methods for all geometries. The analytical model is used to derive an expression for the critical aspect ratio (the minimum channel aspect ratio for flow to proceed across the backward facing step) as a function of contact angle.
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Ahmed Taher, Benjamin Jones, Paolo Fiorini, Liesbet Lagae, "Investigation of the capillary flow through open surface microfluidic structures," Proc. SPIE 10061, Microfluidics, BioMEMS, and Medical Microsystems XV, 1006108 (28 February 2017);