Simulation reproduces decades-old hexagonal cell pattern observed in an electroconvection system

Electroconvection of dielectric liquids is an inducible behavior using charge injection, occurring when electrodes create an electric field that exerts Coulombic force on free space charges. A better understanding of this fundamental problem in electrohydrodynamics deepens our insight into the interaction between external electric fields and flow.

An article in the journal Physics of Fluids reports on the numerical reproduction of the now well-known hexagonal cell flow pattern in an electroconvection system. Forty years ago, after this pattern was first observed, a subsequent stability analysis successfully predicted the appearance of hexagonal cells. However, the new study represents the first reproduction of such a flow pattern by numerical simulation, serving as a bridge between the worlds of theory and experiment.

The authors simulated charge injection-induced electroconvection in a perfectly insulating liquid layer between two parallel planar electrodes in three dimensions by extending their unified lattice Boltzmann model. The 3-D lattice Boltzmann method code was first validated by three cases: the hydrostatic solution, quasi-two-dimensional roll flows and 3-D electrohydrodynamic flow in a cube. Then, the authors looked at electroconvection due to both strong and weak unipolar injection of ions to study the roll, polygon and square flow patterns.

For a strong injection, they found that the cellular patterns were related to the size of the computational domain, but were surprised that the finite amplitude stability criteria from different cellular patterns remained very similar. A hexagonal cell pattern with the central region being empty of charge and centrally downward flow is preferred in a symmetric system under random initial disturbance. For a weak injection, the system transitioned from a rest state to turbulence once it lost linear stability.

Source: “Three-dimensional finite amplitude electroconvection in dielectric liquids,” by Kang Luo, Jian Wu, Hong-Liang Yi, and He-Ping Tan, Physics of Fluids (2018). The article can be accessed at https://doi.org/10.1063/1.5010421 .