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On numerical schemes for phase‐field models for electrowetting with electrolyte solutions
Author(s) -
Metzger Stefan
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510346
Subject(s) - electrokinetic phenomena , electrowetting , cahn–hilliard equation , field (mathematics) , momentum (technical analysis) , energy–momentum relation , electrolyte , physics , phase (matter) , classical mechanics , flow (mathematics) , mechanics , mathematical analysis , mathematics , chemistry , voltage , quantum mechanics , differential equation , finance , electrode , pure mathematics , economics
We present an energy‐stable, decoupled discrete scheme for a recent model (see [1]) supposed to describe electrokinetic phenomena in two‐phase flow with general mass densities. This model couples momentum and Cahn–Hilliard type phase‐field equations with Nernst–Planck equations for ion density evolution and an elliptic transmission problem for the electrostatic potential. The transport velocities in our scheme are based on the old velocity field updated via a discrete time integration of the force densities. This allows to split the equations into three blocks which can be treated sequentially: The phase‐field equation, the equations for ion transport and electrostatic potential, and the Navier–Stokes type equations. By establishing a discrete counterpart of the continuous energy estimate, we are able to prove the stability of the scheme. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)