The generation of identical droplets of controllable size in the micrometer range is a problem of much interest owing to the numerous technological applications of such droplets. This work reports an investigation of the regime of periodic emission of droplets from an electrified oscillating meniscus of a liquid of low viscosity and high electrical conductivity attached to the end of a capillary tube, which may be used to produce droplets more than ten times smaller than the diameter of the tube. To attain this periodic microdripping regime, termed axial spray mode II by Juraschek and Röllgen [R. Juraschek and F. W. Röllgen, Int. J. Mass Spectrom. 177, 1 (1998)], liquid is continuously supplied through the tube at a given constant flow rate, while a dc voltage is applied between the tube and a nearby counter electrode. The resulting electric field induces a stress at the surface of the liquid that stretches the meniscus until, in certain ranges of voltage and flow rate, it develops a ligament that eventually detaches, forming a single droplet, in a process that repeats itself periodically. While it is being stretched, the ligament develops a conical tip that emits ultrafine droplets, but the total mass emitted is practically contained in the main droplet. In the parametrical domain studied, we find that the process depends on two main dimensionless parameters, the flow rate nondimensionalized with the diameter of the tube and the capillary time, $q$, and the electric Bond number $B_E$, which is a nondimensional measure of the square of the applied voltage. The meniscus oscillation frequency made nondimensional with the capillary time, $f$, is of order unity for very small flow rates and tends to decrease as the inverse of the square root of $q$ for larger values of this parameter. The product of the meniscus mean volume times the oscillation frequency is nearly constant. The characteristic length and width of the liquid ligament immediately before its detachment approximately scale as powers of the flow rate and depend only weakly on the applied voltage. The diameter of the main droplets nondimensionalized with the diameter of the tube satisfies $d_d\approx {(6/\pi )}^{1/3}{(q/f)}^{1/3}$, from mass conservation, while the electric charge of these droplets is about $1/4$ of the Rayleigh charge. At the minimum flow rate compatible with the periodic regimen, the dimensionless diameter of the droplets is smaller than one-tenth, which presents a way to use electrohydrodynamic atomization to generate droplets of highly conducting liquids in the micron-size range, in marked contrast with the cone-jet electrospray whose typical droplet size is in the nanometric regime for these liquids. In contrast with other microdripping regimes where the mass is emitted upon the periodic formation of a narrow capillary jet, the present regime gives one single droplet per oscillation, except for the almost massless fine aerosol emitted in the form of an electrospray.

Optimization of flow fields in redox flow batteries can increase performance and efficiency, while reducing cost. Therefore, there is a need to establish a fundamental understanding on the connection between flow fields, electrolyte flow management and electrode properties. In this work, the flow distribution and pressure drop characteristics of interdigitated flow fields with constant and tapered cross-sections are examined numerically and experimentally. Two simplified 2D along-the-channel models are used: (1) a CFD model, which includes the channels and the porous electrode, with Darcy’s viscous resistance as a momentum sink term in the latter; and (2) a semi-analytical model, which uses Darcy’s law to describe the 2D flow in the electrode and lubrication theory to describe the 1D Poiseuille flow in the channels, with the 2D and 1D sub-models coupled at the channel/electrode interfaces. The predictions of the models are compared between them and with experimental data. The results show that the most influential parameter is $\gamma$ , defined as the ratio between the pressure drop along the channel due to viscous stresses and the pressure drop across the electrode due to Darcy’s viscous resistance. The effect of $Re$ in the channel depends on the order of magnitude of $\gamma$ , being negligible in conventional cells with slender channels that use electrodes with permeabilities in the order of ${10}^{-12}{\mathrm{m}}^2$ and that are operated with moderate flow rates. Under these conditions, tapered channels can enhance mass transport and facilitate the removal of bubbles (from secondary reactions) because of the higher velocities achieved in the channel, while being pumping losses similar to those of constant cross-section flow fields. This agrees with experimental data measured in a single cell operated with aqueous vanadium-based electrolytes.

Next-generation redox flow batteries will benefit from the progress of macroscopic continuum models that enable the optimization of new architectures without the need of expensive fabrication and experimentation. Despite previous attempts, there is still need for robust and thoroughly validated models. Here, a steady-state two-dimensional unit-cell model of an all-vanadium redox flow battery is presented. The model integrates state-of-the-art descriptions of the fundamental physical phenomena, along with new features such as local mass transfer coefficients for each active species, precise sulfuric acid dissociation kinetics, and experimental data of the electrochemical parameters and electrolyte properties. The model is validated at different states of charge and flow rates using polarization, conductivity and open circuit voltage measurements. Then, the contribution of operating conditions on battery performance is studied by analyzing its separate effect on the various phenomena that affect cell performance, such as local pore mass transfer limitations, parasitic hydrogen evolution reactions, crossover and self-discharge fluxes. The resulting model is a reliable tool that can be used to assess the relevance of these coupled phenomena that take place simultaneously within the reaction cell. This important information is critical to optimize cell components, reactor design and to select optimal operating conditions.