We theoretically study the electrokinetic problem of a pressure-induced liquid flow through a narrow long channel with charged walls, going beyond the classical Helmholtz-Schmolukowski picture by considering the surprisingly strong combined effect of (i) Stern-layer conductance and (ii) dynamic charge-regulating rather than fixed surface charges. We find that the water flow induces, apart from the well-known streaming potential, also a strongly heterogeneous surface charge and zeta potential on chemically homogeneous channel walls. Moreover, we identify a novel steady state with a nontrivial 3D electric flux with 2D surface charges acting as sources and sinks. For a pulsed pressure drop our findings also provide a first-principles explanation for ill-understood experiments on the effect of flow on interfacial chemistry [D. Lis et al., Science 344, 1138 (2014)SCIEAS0036-807510.1126/science.1253793].

We theoretically study the electrokinetic transport properties of nano-uidic devices under the in uence of a pressure, voltage or salinity gradient. On a microscopic level the behaviour of the device is quanti ed by the Onsager matrix L, a generalised conductivity matrix relating the local driving forces and the induced volume, charge and salt ux. Extending L from a local to a global linear-response relation is trivial for homogeneous electrokinetic systems, but in this manuscript we derive a generalised conductivity matrix G from L that applies also to heterogeneous electrokinetic systems. is extension is especially important in the case of an imposed salinity gradient, which gives necessarily rise to heterogeneous devices. Within this formalism we can also incorporate a heterogeneous surface charge due to, for instance, a charge regulating boundary condition, which we show to have a signi cant impact on the resulting uxes. e predictions of the Poisson-Nernst-Planck-Stokes theory show good agreement with exact solutions of the governing equations determined using the Finite Element Method under a wide variety of parameters. Having established the validity of the theory, it provides an accessible method to analyse electrokinetic systems in general without the need of extensive numerical methods. As an example, we analyse a Reverse Electrodialysis "blue energy" system, and analyse how the many parameters that characterise such a system a ect the generated electrical power and e ciency. arXiv:1911.13156v1 [cond-mat.soft]

We present analytical solutions for the electrokinetics at a charged surface with both non-zero Sternlayer conductance and nite chemical reaction rates. We have recently studied the same system numerically [Werkhoven et al., Phys. Rev. Le . 120, 264502 (2018)], and have shown that an applied pressure drop across the surface leads to a non-trivial, laterally heterogeneous surface charge distribution at steady state. In this work, we linearise the governing electrokinetic equations to nd closed expressions for the surface charge pro le and the generated streaming electric eld. e main results of our calculations are the identi cation of three important length and time scales that govern the charge distribution, and consequently the classi cation of electrokinetic systems into three distinct regimes. e three governing time scales can be associated to (i) the chemical reaction, (ii) di usion in the Stern layer, and (iii) conduction in the Stern layer, where the dominating (smallest) time scale characterises the regime. In the reaction-dominated regime we nd a constant surface charge with an edge e ect, and recover the Helmholtz-Smoluchowski equation. In the other two regimes, we nd that the surface charge heterogeneity extends over the entire surface, either linearly (di usion-dominated regime) or nonlinearly (conduction-dominated regime). arXiv:1809.03287v1 [cond-mat.soft]

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We theoretically study a vibrating pair of parallel electrodes bridged by a (deformed) liquid droplet, which is a recently developed microfluidic device to harvest vibrational energy. The device can operate with various liquids, including liquid metals, electrolytes, as well as ionic liquids. We numerically solve the Young-Laplace equation for all droplet shapes during a vibration period, from which the time-dependent capacitance follows that serves as input for an equivalent circuit model. We first investigate two existing energy harvesters (with a constant and a vanishing bias potential), for which we explain an open issue related to their optimal electrode separations, which is as small as possible or as large as possible in the two cases, respectively. Then we propose a new engine with a time-dependent bias voltage, with which the harvested work and the power can be increased by orders of magnitude at low vibration frequencies and by factors 2-5 at high frequencies, where frequencies are to be compared to the inverse RC-time of the circuit.Small-amplitude oscillations are ubiquitous. Not only devices like fans, laundry machines and speakers vibrate, pretty much everything around us does. Converting these mechanical vibrations into electric energy could provide a valuable alternative to batteries in portable electronic devices which require only modest amounts of electric power [1]. Moreover, powering remote sensors with vibrations could relieve the requirement of connection to the electricity grid. Unfortunately, engines based on induction [2] or piezo electricity [3] are not well suited for these small-scale applications since their power performance rarely surpasses the 0.1W range [4]. In search of a promising alternative, variable-capacitance engines have received considerable interest in recent years [5,6].Variable-capacitance engines operate by cyclically (dis)charging electrodes at alternating high (low) capacitance. Net electric energy is harvested during a cycle because the charging stroke occurs at a lower potential than the discharging stroke. The change in capacitance can be caused by a mechanical stimulus as in the case of vibrational-energy harvesters, but also by a change in the properties of the dielectric or electrolyte material. Examples of the latter include electrolyte-filled nanoporous supercapacitors where variable capacitance is achieved by changing electrolyte concentration (in capacitive mixing) [7,8], or temperature (in capacitive thermal energy extraction) [9], or combinations thereof [10,11].Variable-capacitance engines driven by mechanical energy typically consist of air-filled parallel-plate capacitors connected to a battery, where the capacitance is modified either by varying the plate separation or the lateral plate overlap [12]. A key new development in these engines was recently realized by Krupenkin and Taylor [4] who suggested to inject an array of small liquid droplets (Mercury and Galinstan) between the electrodes. Charge on the capacitor's plates is now balanced by the...