5.6. exec/immersedIons – Brownian ions in a fluctuating fluid

Purpose

Simulates charged (or neutral) Brownian particles immersed in a fluctuating Stokes fluid, with electrostatics, short-range interactions, walls and external fields. Typical uses are ionic conductivity, electro-osmosis, diffusion and structure factors of electrolytes.

Libraries and build

src_particles, src_hydro, src_gmres, src_electrostatic, src_geometry, src_immersed-boundary (base kernels), src_analysis, src_rng, src_common; built with USE_PARTICLES = TRUE, USE_FFT = TRUE, DIM = 3.

Algorithm

Each time step:

  1. computes short-range (Lennard-Jones) forces and the P3M short-range correction (when sr_tog != 0 or es_tog = 3);

  2. spreads charges to the grid and solves the Poisson equation (es_tog = 1 or 3), or computes pairwise Coulomb forces (es_tog = 2);

  3. spreads particle forces to the fluid with the chosen kernel;

  4. solves the fluctuating Stokes equations (fluid_tog = 1);

  5. moves the ions with the interpolated fluid velocity plus their dry Brownian motion (move_tog);

  6. accumulates statistics, distributions, structure factors and output.

Wet and dry diffusion

The kernel width sets each ion’s hydrodynamic (“wet”) radius: about 0.91, 1.255 and 1.481 grid spacings for pkernel_fluid = 3, 4 and 6. For exponential-of-semicircle kernels (eskernel_fluid), the radius is tabulated in wetRad_wN.dat files. The total diffusion coefficient comes from Stokes–Einstein if diameter > 0, and from diff otherwise. The remainder after subtracting the wet part is applied as dry diffusion. all_dry = 1 makes all diffusion dry and requires fluid_tog = 0.

Key parameters

Parameter

Meaning

fluid_tog

0 no fluid, 1 Stokes (2, low Mach, is not supported).

es_tog

0 off, 1 Poisson, 2 pairwise Coulomb (serial only), 3 P3M.

move_tog

Total particle move: 0 off, 1 single step, 2 midpoint.

dry_move_tog

Dry particle move: 0 off, 1 on, 2 on without the dry stochastic drift correction.

sr_tog, eepsilon, sigma, rmin, rmax

Short-range Lennard-Jones interactions between particles (*_wall variants for walls).

wall_mob

Dry mobility correction near walls: 0 none, 1 infinite plane, 2 alternative model.

pkernel_fluid, pkernel_es, eskernel_fluid, eskernel_beta

Kernels for fluid coupling and charge spreading.

qval, permittivity, images

Charges, permittivity, and the number of periodic images for pairwise Coulomb interactions.

eamp, efreq, ephase

Amplitude, frequency and phase of an external electric field.

bc_es_lo/hi, potential_lo/hi

Potential boundary conditions: -1 periodic, 1 Dirichlet, 2 Neumann.

particle_count, particle_n0, particle_neff

Number or number density of ions per species.

particle_placement

1 reads x y z pinned for each particle from particles.dat; any other value places particles randomly.

msd_int, msd_len, radialdist_int, cartdist_int

Mean-square displacement and pair-distribution diagnostics.
Example inputs

inputs_template documents every option. regression_inputs/ contains conductivity, electro-osmosis and boundary-condition tests. paper_inputs/ and paper_inputs_2/ reproduce published results; the README maps them to their cases. inputs_gpu is set up for GPU runs.

Output

Fluid plotfiles plt* (and stagx/y/z*), particle and charge plotfiles cplt*, eplt* and parplt*, and structure factors plt_SF_charge and plt_SF_vel. Particle diagnostics are written as text files, e.g. msdEst_<i>, radialDistribution*, cartesianDistribution*, currentEst and bulkFlowEst. plot_ascii = 1 adds ASCII copies of mean fields.