Aspect-Ratio Dependence of Charge Transport in Turbulent Electroconvection

We present measurements of the normalized charge transport or Nusselt number Nu as a function of the aspect ratio Γ for turbulent convection in an electrically driven film. In analogy with turbulent Rayleigh-B\'enard convection, we develop the relevant theoretical framework in which we discuss the local power-law scaling of Nu with a dimensionless electrical forcing parameter R. For these experiments where 10⁴R2×10⁵ we find that Nu~F(Γ)R^γ with either γ=0.26 (±0.02) or γ=0.20 (±0.03), in excellent agreement with the theoretical predictions of γ=1/4 and $1/5$. Our measurements of the aspect-ratio dependence of Nu for 0.3≤Γ≤17 compares favorably with the function F(Γ) from the scaling theory.