Autonomous transport and splitting of a droplet on an open surface

Pumpless transport of droplets on open surfaces has gained significant attention because of its applications starting from vapor condensation to Lab-on-a-Chip systems. Mixing two droplets on open surfaces can be carried out quickly by using wettability patterning. However, it is quite challenging to split a droplet in the absence of external stimuli because of the interfacial energy of the droplet. Here, we demonstrate a standalone power-free technique for transport and splitting of droplets on open surfaces using continuous wettability gradients. A droplet moves continuously from a low to a high wettability region on the wettability-gradient surface. A Y-shaped wettability-gradient track - laid on a superhydrophobic background - is used to investigate the dynamics of the splitting process. A three-dimensional phase-field Cahn-Hilliard model for interfaces and the Navier-Stokes equations for transport are employed and solved numerically using the finite element method. Numerical results are used to decipher the motion and splitting of droplet at the Y junction using the principle of energy conservation. It is observed that droplet splitting depends on the configuration of the Y junction; droplets split faster for the superhydrophobic wedge angle of 90. and the splitting ratio (ratio of the sizes of daughter droplets) depends on the widths of the Y branches. A critical branch-width ratio (w(2)/w(1) = 0.79) is identified below which the droplet does not split and moves towards the branch of higher width and settles there. The present study provides the required theoretical underpinnings to achieve autonomous transport and splitting of droplets on open surfaces, which has clear potential for applications in Lab-on-a-Chip devices.