Influence of hydrophobic effects on streaming potential

We study the influence of hydrophobic effects on streaming potential mediated flow through a narrow confinement. In a clear departure from the approach used in prior works, we use a phase-field model to capture the hydrophobicity-induced depletion in the near wall region, and express the variation of viscosity and permittivity across the interfacial layer in terms of the phase-field variable. We then use these in the determination of the flow velocity, and highlight the sensitive interplay between the intrinsic length scale of the electrical double layer and that of the depletion in terms of the variations of an effective normalized viscosity that captures the electroviscous effect. We expect that this work will be an important step forward in the realistic continuum modeling of interfacial physics in the particular context of streaming potential mediated flows.