Electrohydraulic Power Conversion in Planar Nanochannels

We explore mechanisms for flow generation in water-filled nanochannels, employing the coupling between translational and rotational momentum. Using a generalized Navier-Stokes equation that includes dipolar polarization and relaxation, we show that static electric fields do not induce fluid flow in the planar geometry, while rotating electric fields efficiently convert electric into hydraulic power on the nanoscale. We also perform extensive molecular dynamics simulations of water in nanochannels and find that erroneous force truncation can give rise to spurious flow effects for static electric fields.

Figure 1

(a) Sketch of the geometry. Snapshots of the simulation box of the oil (b) and diamond (c) systems.

Figure 2

Rescaled flow profiles ${\overline{u}}_1\kappa /\Theta$ as a function of rescaled position $x_3/h$ for vanishing spin slip length $s=0$ in channels of rescaled height $\kappa h=3$ (top) and $\kappa h=30$ (bottom) for symmetric hydrophilic (left, $b_{-}=b_{+}=0$), symmetric hydrophobic (middle, $b_{-}=b_{+}\to \infty$), and asymmetric channels (right, $b_{-}=0$ and $b_{+}\to \infty$). Solid lines show the perturbative predictions of Eqs. (13, 14), while broken lines show numerical solutions of Eqs. (5, 6) using $E_3^{\mu }(x_3)$ from simulations as an input.

Figure 3

(a) Lennard-Jones force between two water molecules for the two different truncation schemes using $r_c=0.8\mathrm{nm}$ compared to the uncut Lennard-Jones force (dashed line). Simulation results for the water-diamond system using a simple cutoff at $r_c=0.8\mathrm{nm}$ and a static field of $E_1^0=0.4\mathrm{V}·{\mathrm{nm}}^{-1}$: (b) velocity $u_1$ and (c) spin ${\omega }_2$ (solid line) and vorticity ${\nabla }_3{u}_1$ (dashed line). $\zeta$-potential $\zeta =-\eta u_1/(\epsilon {\epsilon }_0{E}_1^0)$ versus $r_c$ for both truncation schemes and a system consisting of (d) diamond slabs and (e) oil slabs.