In low-permeability rock, fluid and mineral transport occur in pores and fracture apertures at the scale of micrometers and below. At this scale, the presence of surface charge, and a resultant electrical double layer, may considerably alter transport properties. However, due to the inherent nonlinearity of the governing equations, numerical and theoretical studies of the coupling between electric double layers and flow have mostly been limited to two-dimensional or axisymmetric geometries. Here, we present comprehensive three-dimensional simulations of electrohydrodynamic flow in an idealized fracture geometry consisting of a sinusoidally undulated bottom surface and a flat top surface. We investigate the effects of varying the amplitude and the Debye length (relative to the fracture aperture) and quantify their impact on flow channeling. The results indicate that channeling can be significantly increased in the plane of flow. Local flow in the narrow regions can be slowed down by up to 5% compared to the same geometry without charge, for the highest amplitude considered. This indicates that electrohydrodynamics may have consequences for transport phenomena and surface growth in geophysical systems.
Bernaise (Binary Electrohydrodynamic Solver) is a flexible high-level finite element solver of two-phase electrohydrodynamic flow in complex geometries. Two-phase flow with electrolytes is relevant across a broad range of systems and scales, from 'lab-on-a-chip' devices for medical diagnostics to enhanced oil recovery at the reservoir scale. For the strongly coupled multi-physics problem, we employ a recently developed thermodynamically consistent model which combines a generalized Nernst-Planck equation for ion transport, the Poisson equation for electrostatics, the Cahn-Hilliard equation for the phase field (describing the interface separating the phases), and the Navier-Stokes equations for fluid flow. As an efficient alternative to solving the coupled system of partial differential equations in a monolithic manner, we present a linear, decoupled numerical scheme which sequentially solves the three sets of equations. The scheme is validated by comparison to limiting cases where analytical solutions are available, benchmark cases, and by the method of manufactured solution. The solver operates on unstructured meshes and is therefore well suited to handle arbitrarily shaped domains and problem set-ups where, e.g., very different resolutions are required in different parts of the domain. Bernaise is implemented in Python via the FEniCS framework, which effectively utilizes MPI and domain decomposition, and should therefore be suitable for large-scale/high-performance computing. Further, new solvers and problem set-ups can be specified and added with ease to the Bernaise framework by experienced Python users. * linga@nbi.dk arXiv:1805.11642v1 [physics.comp-ph] 29 May 2018 Two-phase flow with electrolytes is encountered in many natural and industrial settings. Although Lippmann already in the 19th century [1, 2] made the observation that an applied electric field changes the wetting behaviour of electrolyte solutions, the phenomenon of electrowetting has remained elusive. Recent decades have seen an increased theoretical and experimental interest in understanding the basic mechanisms of electrokinetic or electrohydrodynamic flow [3,4]. Progress in micro-and nanofluidics [5,6] has enabled the use electrowetting to control small amounts of fluid with very high precision (see e.g. the comprehensive reviews by Mugele and coworkers [2,7] and Nelson and Kim [8] and references therein). This yields potential applications in, e.g., "lab-on-chip" biomedical devices or microelectromechanical systems [9][10][11], membranes for harnessing blue energy [12], energy storage in fluid capacitors, and electronic displays [13][14][15][16].It is known that electrohydrodynamic phenomena affects transport properties and energy dissipation in geological systems, as a fluid moving in a fluid-saturated porous medium sets up an electric field that counteracts the fluid motion [17][18][19]. Electrowetting may also be an important factor in enhanced oil recovery [20,21]. Here, the injection of water of a particular salinity, or "smart water" ...
Transport of electrolytic solutions under influence of electric fields occurs in phenomena ranging from biology to geophysics. Here, we present a continuum model for single-phase electrohydrodynamic flow, which can be derived from fundamental thermodynamic principles. This results in a generalized Navier-Stokes-Poisson-Nernst-Planck system, where fluid properties such as density and permittivity depend on the ion concentration fields. We propose strategies for constructing numerical schemes for this set of equations, where the electrochemical and the hydrodynamic subproblems are decoupled at each time step. We provide time discretizations of the model that suffice to satisfy the same energy dissipation law as the continuous model. In particular, we propose both linear and non-linear discretizations of the electrochemical subproblem, along with a projection scheme for the fluid flow. The efficiency of the approach is demonstrated by numerical simulations using several of the proposed schemes.have often aimed for the steady-state solution to the governing equations [15,24]. To this end, commercial multi-physics software packages (e.g. Comsol) are available, and have long been successfully applied to simulate a variety microfluidic systems. With regard to the transient development of streaming potential, detailed simulations have often been limited to two-dimensional or axisymmetric geometries such as finitelength symmetric channels [25,26]. In studies of electroconvection near permselective membranes [27], both finite element [28] and (pseudo-) spectral methods [29][30][31] have proven efficient. Recently, a spectral method was also applied in a study of the interaction between electrokinetics and turbulent drag [32]. In simulations of electrokinetic flow, the electrolyte solutions are usually assumed to be dilute enough for density, viscosity and permittivity to be independent of the local ion concentrations. The ion mobilities are usually taken to be proportional to the concentrations.For the separate subproblems comprising the NSPNP problem, there exists many efficient numerical methods. For the Poisson-Nernst-Planck (PNP) problem, efficient approaches have been demonstrated for semi-conductors [33] and biological ion channels [34], where e.g. dispersion and size effects of ions can be included. For transient simulation of the Navier-Stokes equations, projection methods that date back to Chorin [35,36] (see also Guermond, Minev, and Shen [37]), have imparted speedup compared to solving the monolithic problem, since it effectively decouples the computation of velocity and pressure (although at the cost of some reduced accuracy). For the full NSPNP problem, however, less is certain, but it seems clear that succesful numerical schemes should aim to decouple, at least, the fluid mechanical subproblem from the electrochemical subproblem, and thus take advantage of the progress made in numerically resolving each of these, although a direct combination does not necessarily yield a successful scheme.In the field of diff...
The wetting properties of immiscible two-phase systems are crucial in applications ranging from laboratory-on-a-chip devices to field-scale oil recovery. It has long been known that effective wetting properties can be altered by the application of an electric field; a phenomenon coined as electrowetting. Here, we consider theoretically and numerically a single droplet sitting on an (insulated) conductor, i.e., within a capacitor. The droplet consists of a pure phase without solutes, while the surrounding fluid contains a symmetric monovalent electrolyte, and the interface between them is impermeable. Using nonlinear Poisson-Boltzmann theory, we present a theoretical prediction of the dependency of the apparent contact angle on the applied electric potential. We then present well-resolved dynamic simulations of electrowetting using a phase-field model, where the entire two-phase electrokinetic problem, including the electric double layers (EDLs), is resolved. The simulations show that, while the contact angle on scales smaller than the EDL is unaffected by the application of an electric field, an apparent contact angle forms on scales beyond the EDL. This contact angle relaxes in time towards a saturated apparent contact angle. The dependency of the contact angle upon applied electric potential is in good agreement with the theoretical prediction. The only phenomenological parameter in the prediction is shown to depend on the permeability ratio between the two phases. Based on the resulting unified description, we obtain an effective expression of the contact angle which can be used in more macroscopic numerical simulations, i.e. where the electrokinetic problem is not fully resolved.
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.