On the equilibrium of the PoissonNernstPlanckBikermann model equipping with the steric and correlation effects
Abstract
The PoissonNernstPlanckBikermann (PNPB) model, in which the ions and water molecules are treated as different species with nonuniform sizes and valences with interstitial voids, can describe the steric and correlation effects in ionic solution neglected by the PoissonNernstPlanck and PoissonBoltzmann theories with point charge assumption. In the PNPB model, the electric potential is governed by the fourthorder PoissonBikermann (4PBik) equation instead of the Poisson equation so that it can describe the correlation effect. What's more, the steric potential is included in the ionic and water fluxes as well as the equilibrium Fermilike distributions which characterizes the steric effect quantitatively. In this work, after doing a nondimensionalization step, we analyze the selfadjointness and the kernel of the fourthorder operator of the 4PBik equation. Also, we show the positivity of the void volume function and the convexity of the free energy. Following these properties, the wellposedness of the PNPB model in equilibrium is given. Furthermore, because the PNPB model has an energy dissipated structure, we adopt a finite volume scheme which preserves the energy dissipated property at the semidiscrete level. After that, various numerical investigations are given to show the parameter dependence of the steric effect to the steady state.
 Publication:

arXiv eprints
 Pub Date:
 January 2022
 arXiv:
 arXiv:2201.01423
 Bibcode:
 2022arXiv220101423L
 Keywords:

 Mathematical Physics;
 35Q92
 EPrint:
 30 pages