Multiscale flow in an electro-hydrodynamically driven oil-in-oil emulsion.

Efficient mixing strategies in a fluid involve generation of multi-scale flows which are strongly suppressed in highly viscous systems. In this work, we report a novel form of multi-scale flow, driven by an external electric field, in a highly viscous (η∼ 1 Pa s) oil-in-oil emulsion system consisting of micron-size droplets. This electro-hydrodynamic flow leads to dynamical organization at spatial scales much larger than that of the individual droplets. We characterize the dynamics associated with these structures by measuring the time variation of the bulk Reynolds stress in a rheometer, as well as through a micro-scale rheometric measurement by probing the spectrum of fluctuations of a thin fiber cantilever driven by these flows. The results display scale invariance in the energy spectra over three decades with a power law reminiscent of turbulent convection. We also demonstrate the mixing efficiency in such micro-scale systems.