Aspect ratio dependence of charge transport in turbulent electroconvection

Abstract

We present measurements of the normalized charge transport or Nusselt number $\mathrm{Nu}$ as a function of the aspect ratio $\Gamma$ for turbulent convection in an electrically driven film. In analogy with turbulent Rayleigh-B{é}nard convection, we develop the relevant theoretical framework in which we discuss the local-power-law-scaling of $\mathrm{Nu}$ with a dimensionless electrical forcing parameter $\mathcal{R}$. For these experiments where $10^4\lesssim \mathcal{R}\lesssim 2\times 10^5$ we find that $\mathrm{Nu}\sim \mathrm{F}(\Gamma ){\mathcal{R}}^{\gamma }$ with $\gamma$ either $=0.26(\pm 0.02)$ or $0.20(\pm 0.03)$, in excellent agreement with the theoretical predictions of $\gamma =1/4$ and 1/5. Our measurements of the aspect ratio-dependence of $\mathrm{Nu}$ for $0.3\le \Gamma \le 17$ compares favorably with the function $\mathrm{F}(\Gamma )$ from the scaling theory.

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