Tunable Spontaneous Droplet Motion in Flexible Channels

Spontaneous and directional droplet transport has attracted considerable attention for its potential applications such as self-cleaning surfaces and microfluidics. Previous studies on the droplet motion between rigid or parallel flexible channels established that the movement direction can be predetermined by the initial channel configuration and wettability. However, in this study, we experimentally show that the direction of droplet movement in nonparallel deformable channels can be carefully tuned, even under the same geometric and wetting conditions. This advanced feature arises from the interplay between initial system conditions and the subsequent solid-liquid interaction, depending on the initial channel configuration, channel flexibility, droplet conditions, wettability, and contact angle hysteresis. Combining the capillary pressure determined from the Young-Laplace equation with the structural deformation described by Euler-Bernoulli beam theory, we developed a general mathematical model capable of accurately predicting the droplet movement direction under a wide range of conditions. The model does not need any fitting parameters and is validated by our experiments. Additionally, our results lead to the identification of a phase diagram encompassing three distinct modes of droplet movement: toward the free end, toward the fixed end, and a stationary state. The proposed phase diagram serves as a predictive tool, offering new insights into controlling the direction of spontaneous droplet motion in flexible channels, with applications in the design and optimization of microfluidic devices.