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

This article focuses on the theoretical investigation of spontaneous droplet self-motion in square microchannels driven by wettability gradient surfaces, using three-dimensional morphological modeling and the virtual work principle. It establishes correlations relating droplet wetting length, cap volume, and surface areas to contact angle, enabling calculation of surface potential energy and prediction of droplet velocity under varying wettability gradients and contact angle ranges (45°–135°). The study finds that droplet velocity increases with wettability gradient, exhibiting opposite trends in hydrophilic versus hydrophobic channels, with a maximum velocity at a contact angle of 90°. Two dimensionless correlations are developed to predict droplet velocities in hydrophilic and hydrophobic microchannels, and the theoretical model shows good agreement with 3D numerical simulations while requiring significantly less computational time. This work provides insights and design strategies for directional droplet transport in microfluidic applications.