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]

The presence of nanoparticles in a diblock copolymer leads to changes in the morphology and properties of the matrix and can produce highly organized hybrid materials. The resulting material properties depend not only on the polymer composition but also on the size, shape, and surface properties of the colloids. The dynamics of this kind of systems using a hybrid mesoscopic approach has been studied in this work. A continuum description for the polymer is used, while colloids are individually resolved. The method allows for a variable preference of the colloids, which can have different sizes, to the different components the block copolymer is made of. The impact that the nanoparticle preference for either, both, or none of the blocks has on the collective properties of nanoparticle–block copolymer composites can be analyzed. Several experimental results are reproduced covering colloid‐induced phase transition, particles' placement within the matrix, and the role of incompatibilities between colloids and monomers.

We use Lattice-Boltzmann and analytical calculations to investigate transient hydrodynamic finite size effects induced by the use of periodic boundary conditions in simulations at the molecular, mesoscopic or continuum levels of description. We analyze the transient response to a local perturbation in the fluid and obtain via linear response theory the local velocity correlation function. This new approach is validated by comparing the finite size effects on the steady-state velocity with the known results for the diffusion coefficient. We next investigate the full time-dependence of the local velocity auto-correlation function. We find at long times a cross-over between the expected t −3/2 hydrodynamic tail and an oscillatory exponential decay, and study the scaling with the system size of the cross-over time, exponential rate and amplitude, and oscillation frequency. We interpret these results from the analytic solution of the compressible Navier-Stokes equation for the slowest modes, which are set by the system size. The present work not only provides a comprehensive analysis of hydrodynamic finite size effects in bulk fluids, but also establishes the Lattice-Boltzmann method as a suitable tool to investigate such effects in general.It is by now well established that hydrodynamic finite size effects arise in simulations due to the use of periodic boundary conditions (PBC). These effects can be understood as the result of spurious hydrodynamic interactions between particles and their periodic images. Following Dünweg and Kremer [1], Yeh and Hummer [2] proposed a complete analysis of the finite size effect on the diffusion coefficient of fluid particles in a cubic box based on the mobility tensor T: . More recently, the extension to anisotropic boxes was also investigated [8,9] and interpreted in terms of the same hydrodynamic arguments [10,11]. The distortion of the flow field due to the finite size of the system (and the associated use of PBC) does not only affect the diffusion coefficient D of particles, but in principle all dynamical properties. In particular, hydrodynamic flows in an unbounded fluid result in long-time tails of correlations functions, e.g. as t −3/2 for the velocity autocorrelation function (VACF) in three dimensions [12,13]. Such long time tails have been reported in molecular simulations for the VACF since the pioneering work of Ref. 14 (see e.g.[15]) as well as in purely hydrodynamic lattice simulations for the VACF or other correlation functions [16][17][18][19]. Such slow hydrodynamic modes also manifest themselves in the non-Markovian dynamics of solutes, which includes a deterministic component of the force exerted by the suspending fluid, well described for colloidal spheres by the Basset-Boussinesq force [20,21]. Simulations displaying such a hydrodynamic memory, either on a coarse-grained [22] or molecular [23] scale, may therefore suffer from artefacts associated with the use of PBC, at least on long time scales. This was already recognized by Alder and Wainwright in their semi...

We extend the Moment Propagation method to capture the combined effects of adsorption/desorption of charged tracers, their migration under local and applied electric fields, as well as their advection by the local velocity of the fluid. This is achieved by combining previous developments for the separate description of these phenomena, in particular taking advantage of the Lattice Boltzmann Electrokinetics method to capture electrokinetic effects in the underlying fluid. We validate the method on the case of dispersion by an electro-osmotic flow in a slit-pore with charged walls and counterions in the absence of added salt. We compute the velocity auto-correlation function of charged and neutral tracers, from which we extract their average mobility and dispersion coefficient. Analytical results for the former allow to validate the algorithm, while the latter illustrates an example of property which can be provided by the Moment Propagation method when no analytical results are available. For both properties, we discuss the combined effects of the surface charge, of the tracer valency and of the adsorption/desorption rates.