A lattice Boltzmann modelling of electrohydrodynamic conduction phenomenon in dielectric liquids

•A unified lattice Boltzmann model is constructed for EHD conduction problem.•The numerical results obtained from present model agree well with the analytical solutions and experimental data.•The geometric scale and charge mobility have a great impact on conduction pumping. In this work, we propose a lattice Boltzmann method to model the electrohydrodynamic (EHD) conduction phenomenon in dielectric liquids. To incorporate the effect of the source term appeared in the charge conservation equations, some unified force terms that can be implemented locally are delicately designed in the charge evolution equations. We further validate the present model against some analytical solutions as well as experimental data for several problems, and a good agreement is obtained. Then it is used to study the fluid circulation in a square cavity generated by EHD conduction phenomenon, and the numerical results indicate that the geometric scale and the difference in the mobilities of the positive and negative charges could play an important role in studying EHD conduction phenomenon. Further, to analyze the characteristics of the EHD conduction mechanisms in the ohmic and saturation regimes, the influences of the conduction number W0 as well as the parameter β, which is related to Onsager effect, are also investigated, and the numerical results fit well with previous work.