Theoretical model for droplet self-motion in hydrophilic and hydrophobic microchannels with wettability gradient surfaces

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Spontaneous liquid transport in microchannels driven by wettability gradient surfaces has received considerable interest for microfluidic applications. In this paper, a theoretical model was developed to investigate the self-motion behaviors of droplet in square microchannels featured by wettability gradient surfaces using 3D (three dimensional) morphological construction and virtual work principle. The effects of wettability gradient and contact angle range on droplet movement were compared and evaluated. A larger wettability gradient contributes to a higher droplet velocity, and the droplet velocity could reach several centimeters per second. In a wettability-gradient microchannel, the droplet velocity increased and decreased along the channel length in the hydrophobic and hydrophilic channels, respectively. For a droplet moving in a microchannel with its surface wettability continuously changing from hydrophobic to hydrophilic zones, the maximum droplet velocity appears at the contact angle of 90°, and it could be about 2.7 cm/s in the 100 μm width channel under a wettability gradient of 4°/mm. At a same wettability gradient, a lower initial contact angle is associated with higher droplet velocity for hydrophobic channels, while it is opposite in hydrophilic channels. Dimensionless correlations were developed to predict the self-motion velocities in hydrophobic and hydrophilic microchannels, and droplet self-motion characteristics at different wettability gradient conditions were elucidated. The droplet velocities obtained from the theoretical model are in good agreement with that from a 3D numerical simulation, but featured by tens of times smaller in time consumption of computation, showing the reliability and high computation efficiency of the theoretical model.