We use direct numerical simulations of the Poisson-Nernst-Planck equations to study the charging kinetics of porous electrodes and to evaluate the predictive capabilities of effective circuit models, both linear and nonlinear. The classic transmission line theory of de Levie holds for general electrode morphologies, but only at low applied potentials. Charging dynamics are slowed appreciably at high potentials, yet not as significantly as predicted by the nonlinear transmission line model of Biesheuvel and Bazant. We identify surface conduction as a mechanism which can effectively "short circuit" the highresistance electrolyte in the bulk of the pores, thus accelerating the charging dynamics and boosting power densities. Notably, the boost in power density holds only for electrode morphologies with continuous conducting surfaces in the charging direction.
We employ optimal control theory to design an event-based, minimum energy, desynchronizing control stimulus for a network of pathologically synchronized, heterogeneously coupled neurons. This works by optimally driving the neurons to their phaseless sets, switching the control off, and letting the phases of the neurons randomize under intrinsic background noise. An event-based minimum energy input may be clinically desirable for deep brain stimulation treatment of neurological diseases, like Parkinson's disease. The event-based nature of the input results in its administration only when it is necessary, which, in general, amounts to fewer applications, and hence, less charge transfer to and from the tissue. The minimum energy nature of the input may also help prolong battery life for implanted stimulus generators. For the example considered, it is shown that the proposed control causes a considerable amount of randomization in the timing of each neuron's next spike, leading to desynchronization for the network.
We present scalable algorithms for the level-set method on dynamic-adaptive Quadtree and Octree Cartesian grids. The algorithms are fully parallelized and implemented using the MPI standard and the open-source p4est library. We solve the level set equation with a semi-Lagrangian method which, similar to its serial implementation, is free of any time-step restrictions. This is achieved by introducing a scalable global interpolation scheme on adaptive tree-based grids. Moreover, we present a simple parallel reinitialization scheme using the pseudo-time transient formulation. Both parallel algorithms scale on the Stampede supercomputer, where we are currently using up to 4096 CPU cores, the limit of our current account. Finally, a relevant application of the algorithms is presented in modeling a crystallization phenomenon by solving a Stefan problem, illustrating a level of detail that would be impossible to achieve without a parallel adaptive strategy. We believe that the algorithms presented in this article will be of interest and useful to researchers working with the level-set framework and modeling multi-scale physics in general.
We present a theory of the interfacial stability of two immiscible electrolytes under the coupled action of pressure gradients and electric fields in a Hele-Shaw cell or porous medium. Mathematically, our theory describes a phenomenon of "vector Laplacian growth," in which the interface moves in response to the gradient of a vector-valued potential function through a generalized mobility tensor. Physically, we extend the classical Saffman-Taylor problem to electrolytes by incorporating electrokinetic (EK) phenomena. A surprising prediction is that viscous fingering can be controlled by varying the injection ratio of electric current to flow rate. Beyond a critical injection ratio, stability depends only upon the relative direction of flow and current, regardless of the viscosity ratio. Possible applications include porous materials processing, electrically enhanced oil recovery, and EK remediation of contaminated soils.
Viscous fingering is a widely observed phenomenon, in which finger-like instabilities occur at the interface of two fluids, whenever a less viscous phase displaces a more viscous phase. This instability is notoriously difficult to control, especially for given viscosity ratio and geometry. Here we demonstrate experimentally the active control of viscous fingering of two given liquids, for given geometry and flow rate in a Hele-Shaw cell. The control is realized by taking advantage of electro-osmotic flows along the surfaces confining the fluid, via applying an external electric field. Depending on the direction of electric field, the induced secondary electro-osmotic flows either assist or oppose the hydraulic flow, effectively reducing or increasing the flow resistance, leading to the control of interface stability. The mechanism of apparent “electrokinetic thinning/thickening” is proposed to explain the experimental observations. Theoretical predictions of linear stability are confirmed experimentally for a broad range of immiscible electrolyte displacements.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.