Optimization for ultrafast capillary-driven flow in open rectangular microchannels

Abstract

The Lucas−Washburn (LW) equation has been extensively used to predict the imbibition length of capillary-driven flow. Using the hydraulic diameter for non-circular cross section in the LW equation is widely accepted. Accordingly, the larger the hydraulic diameter, the higher the imbibition rate. However, the validity of the LW equation for the optimization of capillary-driven flow in open rectangular microchannels remains an open question. In this study, we propose a theoretical model to predict the imbibition rate of capillary-driven flow in open rectangular microchannels. To validate the model, we conducted a series of experiments on spontaneous capillary-driven flow of water in open rectangular Si microchannels. We fabricated Si microchannels with hydraulic diameters ranging from 18 to 375 µm to investigate the dependence of the imbibition rate on the hydraulic diameter. The proposed model was consistent with the experimental results. In the case of microchannels with a fixed height, a plot of the measured imbibition rate against the hydraulic diameter was well fitted by a downward-opening parabolic curve, indicating that the imbibition rate had an optimal value at the aspect ratio (width to height) of two. For a given channel width, the imbibition rate increased with the hydraulic diameter, and it leveled off at a large hydraulic diameter for aspect ratios below 0.5. An ultrafast imbibition time of 1.97 s over an entire length of 70 mm was achieved, corresponding to the optimal imbibition rates of 40 mm/s at imbibition length x1 = 34 mm and 19 mm/s at x2 = 68 mm among the experimental cases.