Analytical, numerical and experimental study on capillary flow in a microchannel traversing a backward facing step. (October 2018) - Taher, Ahmed; Jones, Benjamin; Fiorini, Paolo; Lagae, Liesbet
Highlights: Capillary flow traversing a backward facing step in a microchannel is modeled analytically. Spontaneous flow can be checked by a geometric condition. The analytical model and the spontaneous flow condition are in good agreement with experimental and numerical validation. The developed model is an enabling tool for designers of capillary microfluidic systems. Abstract: Capillary flow traversing a backward facing step (BFS) in a microchannel at low Capillary and Weber numbers is investigated in detail using analytical, numerical and experimental techniques. The BFS's under study included both open surface, where a free surface is formed at the top to the channel, and closed surface, where a lid with a different contact angle than the base material is used. An analytical model valid for both geometries was derived to determine the capillary pressure as a function of the liquid-gas interface position as it traverses the BFS. The model was validated against two different numerical simulation techniques: (1) surface energy minimization of the meniscus shape and (2) CFD simulation using the volume of fluid method. Comparison between the simulations and analytically derived model for a range of aspect ratios (0.5–3) and contact angles of the base material (60°–80°) revealed that the analytical model works best at high contact angles ( > 70°) and high aspect ratios ( > 2). Furthermore, an analytically derived geometric condition required for spontaneous capillary flow over a BFS was developed. To validate the flow condition, experimental measurements were performed on microchannels with BFSs fabricated in silicon using deep reactive ion etching with aspect ratios ranging from 1.5 to 3.8. The contact angle of surfactant/water solutions ranged from 50° to 85° on the silane-treated silicon surfaces and from 93° to 100° on the PDMS top surface for the closed structure experiments. The experimental results were in good agreement with the analytically derived condition. The developed model is an enabling tool for designers of capillary-driven microfluidic systems.