Moving charged particles in lattice Boltzmann-based electrokinetics

Kuron, Michael; Rempfer, Georg; Schornbaum, Florian; Bauer, Martin; Godenschwager, Christian; Holm, Christian; Graaf, Joost de

doi:10.1063/1.4968596

Cited by 30 publications

(42 citation statements)

References 75 publications

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“…To ensure charge conservation in electrophoresis simulations, appropriate moving BCs for the solute fluxes are introduced. This method is verified in [41] by electrophoresis simulations of up to eight particles.…”

Section: Related Workmentioning

confidence: 90%

“…With our approach we aim for simulations of millions of charged particles as in [31]. For these large numbers of particles the dynamics of an electrical double layer as in [41] is computationally too expensive, even on modern supercomputers. This paper is structured as follows: The physical background of fluid-particle interactions and electrophoresis are described in Sec.…”

Section: Objectives and Outlinementioning

confidence: 99%

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A scalable multiphysics algorithm for massively parallel direct numerical simulations of electrophoretic motion

Bartuschat¹,

Rüde²

2018

Journal of Computational Science

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In this article we introduce a novel coupled algorithm for massively parallel direct numerical simulations of electrophoresis in microfluidic flows. This multiphysics algorithm employs an Eulerian description of fluid and ions, combined with a Lagrangian representation of moving charged particles. The fixed grid facilitates efficient solvers and the employed lattice Boltzmann method can efficiently handle complex geometries. Validation experiments with more than 70 000 time steps are presented, together with scaling experiments with over 4 · 10 6 particles and 1.96 · 10 11 grid cells for both hydrodynamics and electric potential. We achieve excellent performance and scaling on up to 65 536 cores of a current supercomputer.At the finest level of resolution, fluid, ions, and particles are simulated by Lagrangian approaches. These explicit solvent methods [37] typically apply coarse-grained molecular dynamics (MD) models to describe the motion of fluid molecules and incorporate Brownian motion [38]. The mesoscale dissipative particle dynamics method is applied in [39] to simulate electrophoresis of a polyelectrolyte in a nanochannel. Another explicit solvent method is presented in [40] for simulating DNA electrophoresis, modeling DNA as a polymer. In both methods the polymer is represented by bead-spring chains with beads represented by a truncated Lennard-Jones potential and connected by elastic spring potentials. Explicit solvent models, however, are computationally very expensive, especially for large numbers of fluid molecules due to pairwise interactions [40]. Moreover, the resolution of solvent, macromolecules, and ions on the same scale limits the maximal problem sizes that can be simulated [41]. Also the mapping of measurable properties from colloidal suspensions to these particle-based methods is problematic [37]. The high computational effort is significantly reduced in implicit particle-based methods that incorporate hydrodynamic interactions into the inter-particle forces. Such methods are applied in [37] and [42] to simulate electrophoretic deposition under consideration of Brownian motion and van der Waals forces. Nevertheless, these methods are restricted to few particle shapes and hydrodynamic interactions in Stokes flow.Euler-Lagrange methods constitute the intermediate level of resolution. These approaches employ Eulerian methods to simulate the fluid phase, whereas the motion of individual particles is described by Newtonian mechanics. For simulations of particles in steady-state motion, the resolved particles can be modeled as fixed while the moving fluid is modeled by an Eulerian approach. In [43] the finite volume method is applied to simulate electrophoresis of up to two stagnant toroids in a moving fluid, employing the Hückel approximation for a fixed ζ-potential and different electrical double layer thicknesses. The steady-state electrophoretic motion of particles with low surface potentials under a weak applied electric field in a charged cylindrical pore is simulated in [44] for a single c...

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Section: Related Workmentioning

confidence: 90%

Section: Objectives and Outlinementioning

confidence: 99%

A scalable multiphysics algorithm for massively parallel direct numerical simulations of electrophoretic motion

Bartuschat¹,

Rüde²

2018

Journal of Computational Science

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“…Particles interact between themselves via a Hertz potential when in contact, as also via a lubrication force [21,22]. Finally, particle-ion interactions are resolved using a partial-volume discretization that reduces discretization errors, as recently proposed by Kuron et al [24]. Overall this presents the first description of a model capable of handling the electrokinetics of both binary fluid mixtures and moving particles.…”

Section: Introductionmentioning

confidence: 90%

“…For the boundary conditions of the ion fluxes with the colloids we follow an equivalent procedure as proposed by Kuron et al [24]. As in general an electrical double layer is formed around the colloids, where ion concentrations are considerably larger than in the bulk, the displacement of charges due to the creation and removal of solid sites leads to sudden electric field variations, which result in large fluctuations of the particles' velocities.…”

Section: E Colloidal Dynamicsmentioning

confidence: 99%

Mesoscopic electrohydrodynamic simulations of binary colloidal suspensions

Rivas

Frijters

Pagonabarraga

et al. 2018

The Journal of Chemical Physics

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A model is presented for the solution of electrokinetic phenomena of colloidal suspensions in fluid mixtures. We solve the discrete Boltzmann equation with a Bhatnagar-Gross-Krook collision operator using the lattice Boltzmann method to simulate binary fluid flows. Solvent-solvent and solvent-solute interactions are implemented using a pseudopotential model. The Nernst-Planck equation, describing the kinetics of dissolved ion species, is solved using a finite difference discretization based on the link-flux method. The colloids are resolved on the lattice and coupled to the hydrodynamics and electrokinetics through appropriate boundary conditions. We present the first full integration of these three elements. The model is validated by comparing with known analytic solutions of ionic distributions at fluid interfaces, dielectric droplet deformations, and the electrophoretic mobility of colloidal suspensions. Its possibilities are explored by considering various physical systems, such as breakup of charged and neutral droplets and colloidal dynamics at either planar or spherical fluid interfaces.

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“…This point of view has a number of advantages, such as strictly enforcing charge conservation in particular at solid-liquid boundaries, and offering a statistical interpretation which can be exploited to compute other properties such as velocity auto-correlation functions via moment propagation 47 . This hybrid LB/link-flux method, called Lattice Boltzmann Electrokinetics (LBE), has been successfully used to investigate the dynamics of charged colloids [48][49][50][51][52] , charged porous media and ions in oil-water mixtures 53 or binary colloidal suspensions 54 . In these systems, electrostatic boundary conditions at solid-liquid interfaces correspond to constant charge (Neumann, i.e.…”

Section: Introductionmentioning

confidence: 99%

Lattice Boltzmann electrokinetics simulation of nanocapacitors

Asta

Palaia

Trizac

et al. 2019

The Journal of Chemical Physics

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We propose a method to model metallic surfaces in Lattice Boltzmann Electrokinetics simulations (LBE), a latticebased algorithm rooted in kinetic theory which captures the coupled solvent and ion dynamics in electrolyte solutions. This is achieved by a simple rule to impose electrostatic boundary conditions, in a consistent way with the location of the hydrodynamic interface for stick boundary conditions. The proposed method also provides the local charge induced on the electrode by the instantaneous distribution of ions under voltage. We validate it in the low voltage regime by comparison with analytical results in two model nanocapacitors: parallel plate and coaxial electrodes. We examine the steady-state ionic concentrations and electric potential profiles (and corresponding capacitance), the timedependent response of the charge on the electrodes, as well as the steady-state electro-osmotic profiles in the presence of an additional, tangential electric field. The LBE method further provides the time-dependence of these quantities, as illustrated on the electro-osmotic response. While we do not consider this case in the present work, which focuses on the validation of the method, the latter readily applies to large voltages between the electrodes, as well as to timedependent voltages. This work opens the way to the LBE simulation of more complex systems involving electrodes and metallic surfaces, such as sensing devices based on nanofluidic channels and nanotubes, or porous electrodes. arXiv:1907.04732v1 [physics.comp-ph]

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Moving charged particles in lattice Boltzmann-based electrokinetics

Cited by 30 publications

References 75 publications

A scalable multiphysics algorithm for massively parallel direct numerical simulations of electrophoretic motion

A scalable multiphysics algorithm for massively parallel direct numerical simulations of electrophoretic motion

Mesoscopic electrohydrodynamic simulations of binary colloidal suspensions

Lattice Boltzmann electrokinetics simulation of nanocapacitors

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