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Electric field driven drift and diffusion of ions in two materials - flux continuity
Posted 14.12.2020, 05:45 GMT-5 Semiconductor Devices, Electrochemistry, Equation-Based Modeling 0 Replies
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Dear All, I am trying to simulate the E field driven drift - diffusion of ions within two different materials (a liquid and a solid, but for now it does not matter), separating two parallel plate electrodes.
I am solving for the concentration of a negative and positive charge carrier species, and for Poisson equation of E field (the set of equations is known as planck-nernst-poisson or electro hydrodynamic modelling of ions), using the mathematical modules Stabilized convection-diffusion and Electrostatic: the space charge in the electrostatic module is obtained from the drift-diff. equations, whereas the E field in the drift-diff. equations is computed by the electrostatic module.
I have implemented the equations so far, and I validated the implementation with results from literature, in presence of a single material. The implementation with a single material works well.
The problems arise when I include a second material having different mobility.
Since I expect concentration boundary layers, and several order of magnitude difference between the concentration of species in different materials, I want to use different scaling constant. Therefore, I defined separate physics for the positive and negative species, for the solid and the liquid material (four physics in total).
I am forcing the conservative flux (the only present in my formulation) at the interface, paying attention to the direction of the normal versors.
After some problems (divercence), I tried to simplify the model by: - decoupling poisson equations from drift/diffusion: only one way coupling to get the electric field from the poisson eq. for the drift term in the drift-diff. equations - solving the drift diffusion of only the positive species, without any nonlinear term (since the concentration is not used anywhere else I can break the electroneutral assumption). The boundary conditions are: known concentration at the cathode(+) and zero diffusive flux at the anode(-).
The problem persists when there is a discontinuity in either the E field or in the mobility. I am attaching the model, I am really looking forward to some suggestions as I am really struggling on this problem since several weeks. Kindest regards Andrea
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