Dipolar solvent contributions for transient nanoscale electroosmotic flow

Abstract

Electrohydrodynamic flows of weak electrolytes at the nanoscale are significantly influenced by the molecular structure of water-like polar solvents within the electric double layer (EDL). Moreover, unlike in microfluidics, at these length scales the time scale of evolution of EDL often becomes comparable to the consequent fluidic phenomena of interest. While continuum descriptions to model such phenomena typically assume a constant dielectric and viscous solvent background, this study incorporates dipolar solvent physics, specifically both dielectric saturation and the viscoelectric effect together, into a Poisson-Nernst-Planck-Stokes (PNP-S) framework, using the Langevin-Bikerman solvent permittivity distribution and empirical viscoelectric coefficients, respectively. Numerical simulations in a one-dimensional geometry reveal substantial modifications to the electrohydrodynamic body force density and transient electroosmotic mobility during EDL evolution. The magnitude and temporal evolution of these corrections are characterized across parametric regimes, revealing systematic departures from standard constant-permittivity and constant-viscosity models, with electroosmotic mobility reductions of up to 50% governed by a characteristic dimensionless parameter. The results provide a solvent-consistent continuum framework for transient nanoscale electroosmotic flows and quantify the impact of molecular solvent structure on electrohydrodynamic transport relevant to modern nanofluidic applications.

Figures (7)

• Figure 1: Illustration of the electrolytic cell (a) before and (b) after applying external voltage ($2V_0$). (c) Transient growth of EOF velocity profile ($u_{eo}$) under a small lateral electric field ($\mathbf{E}_l$), with range of dipolar solvent corrections highlighted.
• Figure 2: (a) Temporal evolution of the total EDL charge predicted by the different models for Case I. (b) Spatial variation of the electric potential as a function of distance from the electrode surface for Case I, shown at two representative times. The region $\hat{x}<0.006$corresponds to the Stern layer. (Color online.)
• Figure 3: (a, b) Distributions of charge density from different models, at $\hat{t} = 2.7$ for case I (red) & IV (blue) near and away from the surface, respectively. See Figure \ref{['fig:2']}(a) for the legend. (Color online.)
• Figure 4: (a) The scaled space charge density and (b) normalized EHD force density profiles at $\hat{t} = 5$ for case I. (Color online.)
• Figure 5: Transient EOF with dielectric saturation and no viscoelectric effect of LBFT model. (a) Spatio-temporal profiles of EOF velocity from different models for case I and corresponding (b) EOF mobility evolutions with time. (c) Evolution of correction factors for EOF mobility for LBFT, MPNP models relative to PNP for the different cases shown in different colors. (Color online.)