# Lattice Boltzmann Electrokinetics simulation of nanocapacitors

## TL;DR

This paper introduces a Lattice Boltzmann Electrokinetics method to simulate nanocapacitors, accurately modeling ion and solvent dynamics near metallic surfaces, validated against analytical models, and capable of handling complex electrochemical systems.

## Contribution

The paper presents a novel boundary condition implementation for Lattice Boltzmann simulations of electrokinetics with metallic surfaces, enabling accurate modeling of nanocapacitors and related systems.

## Key findings

- Validated the method against analytical models for nanocapacitors.
- Demonstrated the method's ability to simulate steady-state and dynamic electrokinetic phenomena.
- Showcased potential applications in complex nanofluidic and electrochemical systems.

## Abstract

We propose a method to model metallic surfaces in Lattice Boltzmann Electrokinetics simulations (LBE), a lattice-based 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 time-dependent 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 time-dependent 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.