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Nanoscale Poiseuille flow of charged particles. (English) Zbl 1122.35110

Summary: We consider the convection-diffusion process of charged particles in a fluid which is described by the Navier-Stokes equations. Assuming a Hagen-Poiseuille flow profile, a one-dimensional model is derived. For stationary cases, the positivity of the concentrations is proven. Unique equilibrium solutions are shown to exist for a certain range of Dirichlet boundary data. Based on the one-dimensional model and its analytical solution, numerical simulations are presented for several test cases.

MSC:

35Q35 PDEs in connection with fluid mechanics
78A35 Motion of charged particles
82D37 Statistical mechanics of semiconductors
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