Numerical modeling of electrowetting transport processes for digital microfluidics

Electrical actuation and control of liquid droplets in Hele-Shaw cells have significant importance for microfluidics and lab-on-chip devices. Numerical modeling of complex physical phenomena like contact line dynamics, dynamic contact angles or contact angle hysteresis involved in these processes do challenge in a significant manner classical numerical approaches based on macroscopic Navier-Stokes partial differential equations. In this paper, we analyze the efficiency of a numerical lattice Boltzmann model to simulate basic transport operations of sub-millimeter liquid droplets in electrowetting actuated Hele-Shaw cells. We use a two-phase three-dimensional D3Q19 lattice Boltzmann scheme driven by a Shan-Chen-type mesoscopic potential in order to simulate the gas-liquid equilibrium state of a liquid droplet confined between two solid plates. The contact angles at the liquid-solid-gas interface are simulated by taking into consideration the interaction between fluid particles and solid nodes. The electrodes are designed as regions of tunable wettability on the bottom plate and the contact angles adjusted by changing the interaction strength of the liquid with these regions. The transport velocities obtained with this approach are compared to predictions from analytical models and very good agreement is obtained.