Deformation, speed, and stability of droplet motion in closed electrowetting-based digital microfluidics

Electrowetting-based microdrop manipulation has received considerable attention owing to its wide applications in numerous scientific areas based on the digital microfluidics (DMF) technology. However, the techniques for highly precise droplet handling in such microscopic systems are still unclear. In this work, the deformation, speed, and stability of droplet transporting in closed electrowetting-based DMF systems are comprehensively investigated with both theoretical and numerical analyses. First, a theoretical model is derived which governs the droplet motion and includes the influences of the key electrowetting system parameters. After that, a finite volume formulation with a two-step projection method is used for solving the microfluidic flow on a fixed numerical domain. The liquid-gas interface of the droplet is tracked by a coupled level-set and volume-of-fluid method, and the surface tension at the interface is computed by the continuum surface force scheme. A parametric study has been carried out to examine the effects of the static contact angles (theta(s,ON) and theta(s,OFF)), hysteresis effect (Delta theta), channel height (H), and electrode size (L-E) on droplet shape, speed, and deformation during transport, which unanimously shows that droplet length, neck width, and transport stability are directly related to a dimensionless parameter kappa* that only comprises theta(s,ON), theta(s,OFF), H, L-E, and the hysteresis angle Delta theta. Based on the results, the scaling laws for estimating droplet shape and stability of the transport process have been developed, which can be used for promoting the accuracy and efficiency of droplet manipulation in a large variety of droplet-based DMF applications.