| Abstract: |
| We present a phase field model to describe the charged droplets suspended in a viscous fluid with ion transport across the membrane. Our model incorporates spatial variations in electric permittivity and diffusion constants, as well as interfacial capacitance. An ion pump is added to describe the ion active transport to maintain the ion difference between the inner and outer regions. We perform a detailed asymptotic analysis to demonstrate the convergence of the diffusive interface model to the sharp interface model as the interface thickness approaches zero. A series of numerical experiments are conducted to validate the asymptotic analysis and demonstrate the model`s effectiveness. Our numerical results show the pump with phase field method is effective in maintaining the ion difference across the interface. Besides, the motions of multiple droplets have been investigated in the numerical tests. The numerical solutions confirm our model is a reasonable model and easy to develop a series of models to consider the interface problems. |
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