Insights into the electrorheological and electrohydrodynamic regimes in electrically driven emulsions

Recently, we reported the electrorheoimaging technique [Bahraminasr and Yethiraj, Phys. Rev. Res. 8, 013231 (2026)] and found that the frequency-dependent electric field of an oil-in-oil emulsion yields two distinct regimes: a high-frequency dipolar, electrorheological (ER) regime and a low-frequency electrohydrodynamic (EHD) regime. In this work, we identify a phenomenological model to fit the results in the ER regime to a classic yield-stress fluid and find collapse onto a master curve upon rescaling, consistent with a yield stress that grows approximately as E2. Macroscopic small-amplitude oscillatory shear (SAOS) rheology is compared with passive microrheology employing differential dynamic microscopy, with the close agreement implying scale independence of the ER behavior, and indicating that, unlike steady shear, SAOS measurements do not restructure these samples and probe underlying material properties. Finally, under the presence of both steady shear and electric fields in the EHD regime, the emulsion forms banded structures composed of alternating droplet-rich and droplet-depleted regions. We explore recurrence and divergence in the location of these bands: they emerge within seconds of field application and decay rapidly after the field is switched off. Using the Jensen-Shannon divergence between radial intensity profiles, we show that the driven structure loses memory on timescales of order 1 s, commensurate with the timescale of the EHD convection roll. For much longer field-off intervals, successive banding events become statistically independent.