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We characterize the super-diffusive dynamics of tracer particles in anelectrohydrodynamically driven emulsion of oil droplets in an immiscible oilmedium, where the amplitude and frequency of an external electric field are thecontrol parameters. In the weakly-driven electrohydrodynamic regime, thedroplets are trapped dielectrophoretically on a patterned electrode, and thedriving is therefore spatially varying. We find excellent agreement with a$\langle x^2 \rangle \sim t^{1.5}$ power law, and find that this superdiffusivedynamics arises from an underlying displacement distribution that is distinctlynon-Gaussian, and exponential for small displacements and short times. Whilethese results are comparable with a random-velocity field model, the tracerparticle speeds are in fact spatially varying in 2 dimensions, arising from aspatially varying electrohydrodynamic driving force. This suggests that theimportant ingredient for the super-diffusive $t^{1.5}$ behaviour observed is avelocity field that is isotropic in the plane and spatially correlated.Finally, we can extract, from the superdiffusive dynamics, a experimentallengthscale that corresponds to the lateral range of the hydrodynamic flows.This experimental length scale is only non-zero above a threshold ion mobilitylength.

Anomalous dynamics in tracer-particle motions in an electrohydrodynamically driven oil-in-oil system