Electrowetting with contact line pinning: Computational modeling and comparisons with experiments

This work describes the modeling and simulation of planar electrowetting on dielectric devices that move fluid droplets by modulating 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 and a contact line force threshold model that can account for hysteresis and pinning effects. These extra boundary effects are needed to make reasonable predictions of the correct shape and time scale of liquid motion. Without them the simulations can predict droplet motion that is much faster than in experiments (up to 10–20 times faster). We present a variational method for our model, and a corresponding finite element discretization, which is able to handle surface tension, conservation of mass, and the nonlinear contact line pinning in a straightforward and numerically robust way. In particular, the contact line pinning is captured by a variational inequality. We note that all the parameters in our model are derived from first principles or from independent experiments except one (the parameter Dvisc that accounts for the extra resistive effect of contact angle hysteresis and is difficult to measure directly). We quantitatively compare our simulation to available experimental data for four different cases of droplet motion that include splitting and joining of droplets and find good agreement with experiments.