Harvesting vibrational energy with liquid-bridged electrodes: thermodynamics in mechanically and electrically driven RC-circuits

Abstract

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...

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