Accurate and Wide-Voltage-Range Modeling of Electrowetting with a Lattice Boltzmann Approach

The lattice Boltzmann method (LBM) has been widely used in multi-phase fluid mechanics and is known to be more computationally efficient than the traditional method of numerically solving Navier-Stokes and Cahn-Hilliard equations. Electrowetting is an important component of interfacial sciences, in which the liquid-liquid and solid-liquid interfaces are tuned by electrostatics. Modeling electrowetting using the LBM can be categorized into surface and bulk methods. By modifying the surface tension scalar, the surface method easily reproduces the fundamental Young-Lippmann (YL) equation at low voltages but fails to capture contact angle saturation at high voltages. With fully coupled hydrodynamics and electrostatics in the form of spatially dependent matrices, the bulk method can successfully show contact angle saturation, but it is often unable to reproduce the YL equation due to its intrinsic inaccuracies. The inaccuracies are mainly due to the fact that while the hydrodynamics are all described by continuous physical quantities in the framework of diffusive interfaces, the interfacial electrostatics are governed by discontinuous electric fields caused by sheet charge density. In this paper, we show that accurately modeling electrowetting using the LBM is non-trivial. Additional modeling work, especially the treatment of interfacial electric fields, is needed to recover the fundamental YL equation at low voltages and predict contact angle saturation at high voltages, with a systematic model validation over key parameters and applications.