Resonant Nanopumps: ac Gate Voltages in Conical Nanopores Induce Directed Electrolyte Flow

Inducing transport in electrolyte-filled nanopores with dc fields has led to influential applications ranging from nanosensors to DNA sequencing. Here we use the Poisson-Nernst-Planck and Navier-Stokes equations to show that unbiased ac fields can induce comparable directional flows in gated conical nanopores. This flow exclusively occurs at intermediate driving frequencies and hinges on the resonance of two competing timescales, representing space charge development at the ends and in the interior of the pore. We summarize the physics of resonant nanopumping in an analytical model that reproduces the results of numerical simulations. Our findings provide a generic route toward real-time controllable flow patterns, which might find applications in controlling the translocation of small molecules or nanocolloids.

Figure 1

Resonant nanopumping. (a) Schematic illustration of the conical nanopore connecting two reservoirs (indicated by gray disks), the flow field (arrows), and the charge density [colors, ranging from low (yellow) to high (purple) charge density]. (b)–(d) Applying an unbiased ac gate potential $\zeta$ with a frequency $\omega$ (c) to the pore wall leads to a flow $Q$ that oscillates with $2\omega$ and is biased toward the wide end of the pore (b). The magnitude of the mean flow $\overline{Q}$ strongly depends on $\omega$, with a distinct resonant behavior (d).

Figure 2

Net charge density ${\rho }_v$ and electric field vectors $\mathit{E}$ within the nanopore for slow, resonant, and fast driving with $\zeta ={\zeta }_0\sin (\omega t)$. The scales ${\rho }_v^{*}$ are 250, 80, and $20{\mathrm{kC}\text{m}}^{-3}$, respectively, $\mathit{E}$ is scaled for optimized visualization. Splits show instantaneous fields at different phase angles $\varphi =\omega t$.

Figure 3

Net charge density ${\rho }_v$ with electric field vectors $\mathit{E}$ (left-hand split) and pressure $P$ (right-hand split) right after the gate potential step and after the short and long timescales. An axial pressure gradient quickly develops in response to electric body forces acting at the corners. For long times, equilibrium EDLs form, and the wall-normal electric body force and the pressure gradient cancel.

Figure 4

(a) Step response of the system. (b) Mean flow rate $\overline{Q}$ over ac driving frequency for the analytical model and simulations; symbols denote time-domain simulations of governing equations. (a),(b) ${\zeta }_0=10\mathrm{mV}$. (c) Scatter plots comparing analytical and simulation results over a large domain of the parameter space for step responses, using the maximum flow rate $Q_{\max }$ and time of maximum flow rate $t_{\max }$ (inset), with shaded factor-two error areas and ${\tilde{c}}_0=c_0/3.653\mathrm{mM}$.