| Abstract: |
| We study a diffusive interface model for ion active transport through free boundaries. By an energy-variation approach, we derive a phase-field system that couples the order parameter, species concentrations, electrostatic potential, and incompressible flow, and establish an energy dissipation law. A sharp interface limit analysis is carried out to connect the diffuse-interface model with the corresponding free-boundary formulation. Based on the thermodynamically consistent structure, we design an unconditionally energy stable scheme. Numerical tests in one and two dimensions validate the model and demonstrate key features of active transport, with additional comparisons to results reported in the literature. The proposed framework provides a consistent modeling and simulation tool for ion transport with restricted diffusion across membranes. |
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