As an environment for rich pattern formation, the electroconvection (EC) of nematic liquid crystals (LCs) is studied via fully nonlinear simulations for the first time. Previously, EC was mostly studied by experiments or
by linear/weakly nonlinear hydrodynamic theory for its instability criteria. While the negative dielectric LCs are used in most EC analytical and experimental investigations, EC with positive dielectric LCs is limited to
experiments only, due to their more complex nonlinear behavior. In this work we take a step beyond the existing weakly nonlinear EC research by using a fully nonlinear particle-based simulation. To investigate
the distinct dynamics of positive and negative dielectric LCs, we modified the molecular potential in the LC stochastic rotational model (LC SRD) [Lee et al., J. Chem. Phys., 2015, 142, 164110] to incorporate the
dielectric characteristics and the field-particle interaction. As a result, different convection patterns known in the EC experiments were observed in our simulations, for which those patterns appeared orderly, as a function of external field strength. The simulated director and flow fields correspond to each other well, as found in our experiments. For the positive dielectric LC, we discovered a net directional flow accompanying the travelling EC rolls. This numerical model and its hydrodynamic analysis could be used for precise flow control at the micro-scale, such as nematic colloidal transportation in microfluidics.
