Scaling laws for concentration-gradient-driven electrolyte transport through a 2D membrane

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The files in this repository are associated with the following paper: H.C.M. Baldock, D.M. Huang, Phys. Fluids 37, 022032 (2025), https://doi.org/10.1063/5.0251773

All files are .txt files containing the fluxes calculated inside of the pore (along z=0) from Finite-Element method calculations of concentration-gradient-driven flow and electric-field-driven flow in Comsol 4.3a. Columns with "Velocity field, z component (m^3/s)" and "Electric current (A)" indicate the solution flux (in m³/s) and the negative electric current (in A), respectively. The first instances of "Total flux, z component (mol/s)", "Diffusive flux, z component (mol/s)", "Convective flux, z component (mol/s)" and "Electrophretic flux, z component (mol/s)" are the ion flux, the diffusive ion flux, the convective ion flux and electrophoretic ion flux of the positively-charged ion (all in mol/s), respectively, while their second instances are those of the negatively-charged ion.

Fluxes obtained from simulations of concentration-gradient-driven flow and electric-field-driven flow are indicated in the file name by "-dc-" and "-dV-" respectively. The concentration difference (in mmol/L) or the potential difference (in V) is given in the second column. "a[X]" indicates a fixed pore radius of [X] nm, "c[X]" indicates a fixed average ion concentration (cL/2 + cH/2) of [X] mmol/L and "sig[X]" indicates a fixed surface charge density of –[X] mC/m² over the parameter sweep. The pore radius and surface charge density is changed over the parameter sweep for files with names containing "-a-" and "-sig-", respectively, while all other parameters are fixed. The pore radius (in m) and the surface charge density (in C/m²) is given in the second column.

All simulations were of electrolyte flow in a 2D membrane using the diffusivity constants and ion valences of potassium chloride (KCl) and the viscosity and dielectric constant of water (H20) at an ambient temperature. The length of pore (L) was set to 0.2 nm in all simulations ("L0.2"). All file names contain "-mesh9-res4-P2+P1-c3-V2", which corresponds to the mesh configurations, reservoir sizes and discretizations of the Stokes equations, ion concentrations and electric potential as described in the section "Finite-Element Method simulations" in the Supplementary Material of "Scaling laws for concentration-gradient-driven electrolyte transport through a 2D membrane".