A hybrid Lattice-Boltzmann model for hydro-electrochemical modeling and sensitivity analysis of crystallization potential in nanoporous media. Part I: simulation model

This is the first in a two paper series investigating the process of hydro-electrochemical crystallization in nano-scale porous media at the supersaturation stage. In Part I, the synchronous numerical model for integrated hydro-electro-chemo-dynamics simulation, and sensitivity analysis of nano-scale crystallization potential, is developed within the Lat-tice-Boltzmann framework using the open-source software library OpenLB. The present work makes use of a reactive Navier-Stokes-Poisson-Nernst-Planck (RNSPNPE) Equation system for three types of ions in the moving carrier fluid and in the presence of a dynamic electric field. We propose a time-adaptive splitting approach to decouple the system, using Lattice-Boltzmann method (LBM) for the discretization of the equations. We apply an algorithmic differentiation approach for calculation of the parameters’ sensitivities. The complete solver is validated with analytical solutions, on the basis of a first-order convergence criterion. The sensitivity approach is validated by comparison to predictions achieved from a sensitivity analysis performed with finite difference method, enabling a meaningful analysis of crystallization potential on
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the nanopore level. The work integrates the RNSPNPE system into a framework specifically designed for the supersaturation process investigations of the crystallizing species within nanoporous geometries. This work proposes a model that couples fluid flow, electric potential, and ion transport in a reactive setting. A novel aspect of this work lies in the seamless integration of sensitivity analysis algorithms into the Lattice-Boltzmann physicochemical solver, extending the LBM beyond its conventional role as a fluid-flow solver and employing it as a tool for sensitivity analysis. This solver can be applied to other nanoscopic and microscopic chemical electro-hydrodynamics processes as well.