Aspect ratio dependence of charge transport in turbulent electroconvection
Abstract
We present measurements of the normalized charge transport or Nusselt number \rm 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 \rm Nu with a dimensionless electrical forcing parameter \cal R. For these experiments where 10^4 \lesssim {\cal R} \lesssim 2 \times 10^5 we find that {\rm Nu} \sim {\rm F}(\Gamma){\cal 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 {\rm Nu} for 0.3 \leq \Gamma \leq 17 compares favorably with the function {\rm F}(\Gamma) from the scaling theory.