Bernaise: A Flexible Framework for Simulating Two-Phase Electrohydrodynamic Flows in Complex Domains

Abstract

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" ...

Transient electrohydrodynamic flow with concentration-dependent fluid properties: Modelling and energy-stable numerical schemes

“…which bears striking similarity with its continuous counterpart, Eq. (61). In particular, it can be verified that the terms that differ between ∂ − τ F k and ∂ t F are of order O(τ).…”

“…In this section we proceed to show and compare the effectiveness of these schemes. The schemes have been implemented and simulations are carried out within the Bernaise framework, developed by the authors [61]. Bernaise is a flexible simulation environment for two-phase electrohydrodynamic flow [62], which is built on top of the Dolfin [63] interface to Python within the finite element framework Fenics [64].…”

“…Note the test cases considered herein are found as four separate scrips, that is, problem modules (see[61]), in the latest version of Bernaise. Respectively, the problem modules are single_taylorgreen, single_cell, single_reaction, and single_porous.…”

Controlling wetting with electrolytic solutions: Phase-field simulations of a droplet-conductor system

“…For the time integration of the discretized equations, we use the same linear operator splitting scheme as presented in Ref. [34]. With regard to spatial discretization, we use P 2 finite elements for the velocity field, and P 1 elements for the remaining fields.…”

“…This phase-field model combines the Nernst-Planck equation for chemical transport, the Poisson equation for electrostatics, the Cahn-Hilliard equation for the description of the interface, and the Navier-Stokes equations for fluid flow. Using a recently introduced solver [34] for this model, we simulate electrowetting dynamically. We demonstrate explicitly that the contact angle is only apparent on scales beyond the Debye length, whereas the microscopic contact angle remains unaffected.…”