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

The lattice Boltzmann method (LBM) has been widely usedin multi-phasefluid mechanics and is known to be more computationally efficientthan the traditional method of numerically solving Navier-Stokesand Cahn-Hilliard equations. Electrowetting is an importantcomponent of interfacial sciences, in which the liquid-liquidand solid-liquid interfaces are tuned by electrostatics. Modelingelectrowetting using the LBM can be categorized into surface and bulkmethods. By modifying the surface tension scalar, the surface methodeasily reproduces the fundamental Young-Lippmann (YL) equationat low voltages but fails to capture contact angle saturation at highvoltages. With fully coupled hydrodynamics and electrostatics in theform of spatially dependent matrices, the bulk method can successfullyshow contact angle saturation, but it is often unable to reproducethe YL equation due to its intrinsic inaccuracies. The inaccuraciesare mainly due to the fact that while the hydrodynamics are all describedby continuous physical quantities in the framework of diffusive interfaces,the interfacial electrostatics are governed by discontinuous electricfields caused by sheet charge density. In this paper, we show thataccurately modeling electrowetting using the LBM is non-trivial. Additionalmodeling work, especially the treatment of interfacial electric fields,is needed to recover the fundamental YL equation at low voltages andpredict contact angle saturation at high voltages, with a systematicmodel validation over key parameters and applications.

Automated summary

The lattice Boltzmann method is more computationally efficient than traditional methods for numerically solving fluid mechanics equations. Electrowetting, a component of interfacial sciences, can be modeled using the lattice Boltzmann method through surface and bulk methods. However, accurately modeling electrowetting using the lattice Boltzmann method is challenging due to inaccuracies caused by the discontinuous electric fields at the interface. Additional modeling work, especially regarding the treatment of interfacial electric fields, is needed to improve the accuracy of the method.