Ferrofluid droplet generation on a zero-thickness nozzle by a magnetic field using a wedge-shaped functional surface.

Digital microfluidics for ferrofluids enables the manipulation of discrete droplets on open surfaces and has garnered significant interest as an alternative to traditional continuous-flow microfluidic systems. However, droplet generation within digital microfluidics remain underdeveloped. This study introduces a novel method for droplet generation using a wedge-shaped surface with hydrophilic-hydrophobic patterning, which functions as a two-dimensional flat nozzle. We first demonstrated the concept by investigating gravity-driven water droplet generation on a sloping surface, revealing that smaller droplets form at higher tilting angles, while droplet size remains constant with increasing flow rate. Frequency of droplet formation decreases by 60% with decreasing the tilting angle from 90° to 30°. The proposed method results in significant improvement in frequency (10 Hz) compared to nozzle-based droplet generation (1-5 Hz). We then extend this approach to ferrofluid droplets under an external magnetic field, observing five distinct steps in the formation process. Additionally, a scale analysis of both water and ferrofluid droplet generation provides a deeper theoretical understanding of the governing forces, showing a strong correlation between non-dimensional droplet diameter and the Bond number, following a -1/3 power law (R2 > 0.95). The derived empirical factor offers precise droplet diameter predictions, with an average error of 3.9%. Finally, inspired by cactus structures, we demonstrate parallelization of the flat nozzles, highlighting the potential for high-throughput droplet generation in digital microfluidic applications.