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Involutive formulation and simulation for electroneutral microfluids. (English) Zbl 1267.76132
Summary: We study a microfluidic flow model where the movement of several charged species is coupled with electric field and the motion of ambient fluid. The main numerical difficulty in this model is the net charge neutrality assumption which makes the system essentially overdetermined. Hence we propose to use the involutive and the associated augmented form of the system in numerical computations. Numerical experiments on electrophoresis and stacking show that the completed system significantly improves electroneutrality constraint conservation and recovers analytical results while a direct implementation of the initial model fails.

MSC:
76W05 Magnetohydrodynamics and electrohydrodynamics
35K55 Nonlinear parabolic equations
58J10 Differential complexes
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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