The influence of Navier-slip boundary conditions on two-dimensional electroconvective flows in a dielectric liquid confined between two infinite parallel plates is investigated, highlighting their pivotal role in modulating flow stability and transport characteristics. The presence of Navier-slip conditions significantly reduces both the linear and nonlinear instability thresholds, offering a plausible explanation for the persistent discrepancies between experimental observations and numerical predictions of these criteria. A critical slip-length range, $l_s\in [{10}^{-3},10]$, is identified, within which instability thresholds and macroscopic flow features exhibit pronounced sensitivity to $l_s$. In the turbulent regime, the electric Nusselt number scales with the electric Rayleigh number as $\text{Ne}\propto T^{0.5}$ under partial- and free-slip boundary conditions, in contrast to the no-slip case, where a weaker scaling $\text{Ne}\propto T^{0.15}$ is observed. At sufficiently high electric Rayleigh numbers, a transition from convective states to zonal flow states, characterized by large-scale horizontal flows, emerges. Notably, this transition occurs at lower $T$ values as $l_s$ increases. In the zonal flow regime, the observed saturation of the electric Nusselt number provides a possible interpretation of the asymptotic behavior reported in former experimental studies. These results establish a comprehensive framework for understanding the interplay between Navier-slip boundary conditions and electroconvective dynamics, providing critical insights for future experimental validation and theoretical advancements.

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• Electrokinetic flows
• Flow instability
• Turbulence