This work describes the modeling and simulation of a parallel-plate Electrowetting On Dielectric (EWOD) device that moves fluid droplets through surface tension effects. The fluid dynamics are modeled by Hele-Shaw type equations with a focus on including the relevant boundary phenomena. Specifically, we include contact angle saturation, hysteresis, and contact line pinning into our model. We show that these extra boundary effects are needed to make reasonable predictions of the correct shape and time scale of droplet motion. We compare our simulation to experimental data for five different cases of droplet motion that include splitting and joining of droplets. Without these boundary effects, the simulation predicts droplet motion that is much faster than in experiment (up to 10-20 times faster).

We present two different numerical implementations of our model. The first uses a level set method, and the second uses a variational method. The level set method provides a straightforward way of simulating droplet motion with topological changes. However, the variational method was pursued for its robust handling of curvature and mass conservation, in addition to being able to easily include a phenomenological model of contact line pinning using a variational inequality. We are also able to show that the variational form of the time-discrete model satisfies a well-posedness result. Our numerical implementations are fast and are being used to design algorithms for the precise control of micro-droplet motion, mixing, and splitting.

We demonstrate micro-fluidic control by developing an algorithm to steer individual particles inside the EWOD system by control of actuators already present in the system. Particles are steered by creating time-varying flow fields that carry the particles along their desired trajectories. Results are demonstrated using the model given above. We show that the current EWOD system at the University of California in Los Angeles (UCLA) contains enough control authority to steer a single particle along arbitrary trajectories and to steer two particles, at once, along simple paths. We also show that particle steering is limited by contact angle saturation and by the small number of actuators available in the EWOD system.