Fluids at an electrostatically active surface: Optimum in interfacial friction and electrohydrodynamic drag

Abstract

While fluids near a solid surface are at the core of applications in energy storage/conversion, electrochemistry/electrowetting and adsorption/catalysis, their nanoscale behavior remains only partially deciphered. Beyond conventional effects (e.g. adsorption/reaction, interfacial transport, phase transition shifts), recent experimental and theoretical studies on metallic surfaces have unraveled exotic peculiarities such as complex electrostatic screening, unexpected wetting transition, and interfacial quantum friction. These novel features require developing and embarking new tools to tackle the coupling between charge relaxation in the metal and molecular behavior in the vicinal fluid. Here, using the concept of Virtual Thomas-Fermi fluids, we employ a molecular simulation approach to investigate interfacial transport of fluid molecules and metal charge carriers at their interface--including the underlying electrostatically-driven dynamic friction and the coupling between charge current/hydrodynamic flow (the so-called electrohydrodynamic drag). While conventional numerical techniques consider either insulating materials or metallic materials described as polarizable, non-conducting media, our atom-scale strategy provides an effective yet realistic description of the solid excitation spectrum--including charge relaxation modes and conductivity. By applying this approach to water near metallic surfaces of various electrostatic screening lengths, we unveil a non-monotonous dependence of the fluid/solid friction on the metallicity with a maximum occurring as the charge dynamic structure factors of the solid and fluid strongly overlap. Moreover, we report a direct observation of the electrohydrodynamic drag which arises from the momentum transfer between the solid and liquid through dynamic electrostatic interactions and the underlying interfacial friction.

Figures (5)

• Figure 1: Effective Coulomb screening at a solid/fluid interface using a Virtual Thomas-Fermi fluid.a, Schematic illustration of the electrostatic screening as modeled using the concept of Virtual Thomas-Fermi fluids. The electrostatic screening induced in the vicinity of a metallic interface is characterized by a screening length $\ell_{\rm TF}$ which can take values from 0 (perfect metal) to any non-zero value (imperfect metal). With the Virtual Thomas-Fermi method, the solid is described as a set of positive and negative charges having a charge $q_{\rm TF}$. Here, we model water at the surface of the metallic system. The two systems [liquid water as the physical fluid and the Virtual Thomas-Fermi fluid to mimic the metallic surface] are separated by a reflective wall to prevent mixing. (b) Inverse screening length of the solid $\ell_{\rm TF}^{-1}$ as a function of the charge $q_{\rm TF}$ of the particles in the Virtual Thomas-Fermi fluid. The system can be tuned continuously from a perfect insulator ($\ell_{\rm TF}^{-1} = 0$) towards the perfect metal limit ($\ell_{\rm TF}^{-1} \to \infty$). (c) Solid electrical conductivity $\sigma$ as described using the Virtual Thomas-Fermi method as a function of the inverse screening length $\ell_{\rm TF}^{-1}$.
• Figure 2: Surface response functions and solid/fluid coupling at their interface. (a) Normalized charge/charge correlation function $C_{\rm cc}(k,t)$ for a wavevector $k = 0.21~$Å$^{-1}$ as a function of time $t$. The blue data correspond to the charge dynamic structure factor for the solid surface while the red data correspond to the charge dynamic structure factor for the solid surface. As shown in the legend, the dashed lines correspond to the solid and water phases in contact with vacuum while the solid lines correspond to the solid and water phases in contact with each other. The longer relaxation timescales observed when the solid and water are set in contact indicate a slowdown induced by the friction/coupling between the two phases. (b) Response function ${\rm Im}[g(k,\omega)]$ which illustrates the full wavevector $k$ and energy transfer $\hbar \omega$ spectra. The results correspond to a screening length $\ell_{\rm TF}^{-1} = 2.7~$nm$^{-1}$, which is associated with the maximum conductivity shown in Fig. \ref{['fig:fig1']}(c). These data highlight the interplay between the wavevector-dependent dynamics of the interfacial fluid and the electrostatic response function of the solid surface.
• Figure 3: Interfacial friction and overlap between the solid/fluid response functions. (a) Fluid/solid friction coefficient $\lambda$ as a function of the inverse screening length $\ell_{\rm TF}^{-1}$. $\lambda$ is calculated from equilibrium Molecular Dynamics using the Green-Kubo integral of the force time autocorrelation function. A maximum in friction is observed at a screening length of approximately $2.7~\mathrm{nm}^{-1}$. The inset shows $\lambda$ as a function of the water/solid interaction spectrum, $\Phi_{\rm ws}$, which represents the summation of the imaginary parts of the water and solid surface responses over all possible $k$ and $\omega$ values. As indicated by the black dashed line, a perfect correlation is observed: $\Phi_{\rm ws} = \lambda$. (b) Solid response functions ${\rm Im}[g_{\rm s}(k,\omega)]$ as a function of the wavevector $k$ and energy transfer $\hbar \omega$ for four different inverse screening lengths $\ell_{\rm TF}^{-1}$ [the latter values are those shown as empty markers in (a)]. The white line corresponds to the water response function $\operatorname{Im}[g_w(k,\omega)]$ taken at the following isovalue condition $\operatorname{Im}[g_w(k,\omega)] = 0.05$. As explained in the text, the overlap of these two response functions corresponds to $\Phi_{\rm ws}$ -- therefore demonstrating that the maximum friction occurs when the two spectra significantly overlap.
• Figure 4: Non-equilibrium flow as induced through electrohydrodynamic drag. Non-equilibrium flows measured for $\ell_{\rm TF}^{-1} = 2.7~\mathrm{nm}^{-1}$: (a) Water velocity profile as a function of time along with its time window-averaged value (red line). Despite large statistical fluctuations, the averaged velocity converges to a steady state for times $t \sim 10^6~\mathrm{fs}$. The inset represents a sketch of the system, where an electrostatic field $E$ is applied to the mobile negative charges in the solid to generate a charge current. (b) Solid and liquid velocity profiles across the nanochannel with $z$ representing the direction perpendicular to the solid/fluid interface. The inset illustrates the simulation setup, where the system is driven out of equilibrium by applying an electrostatic field to the negative charges, while the cations are immobile. The dynamic coupling observed in the spectra from Fig. \ref{['fig:fig2']} and Fig. \ref{['fig:fig3']} leads to an electric field-induced water flow.
• Figure 5: Linear response theory and electrohydrodynamic drag coefficient. (a-b) Linear response regime for $\ell_{\rm TF}^{-1} = 2.71~\mathrm{nm}^{-1}$ showing the response of ions (a) and water (b) to an applied electrostatic potential difference $E \sim \Delta V$. The solid line represents a linear fit where the slope is related to the electrical conductivity of the solid in (a) and the electrohydrodynamic drag in (b). (c) Onsager transport coefficient corresponding to the electrohydrodynamic drag $M_{\rm eh}$ as inferred from the following linear response relation $Q = M_{\rm eh}\Delta V$. As shown in the inset, the maximum $M_{\rm eh}$ is observed at a screening length $\ell_{\rm TF}$ which maximizes the friction parameter $\lambda$ (the latter, which was discussed in a previous figure, was determined from equilibrium molecular dynamics simulations).