Götz, Thomas; Pinnau, René Nanoscale Poiseuille flow of charged particles. (English) Zbl 1122.35110 J. Math. Anal. Appl. 332, No. 1, 551-563 (2007). 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 Keywords:Poisson-Nernst-Planck system; Navier-Stokes equations; convection; diffusion; hydrodynamic transport of charged particles; electrodiffusion; semiconductor; porous medium PDFBibTeX XMLCite \textit{T. Götz} and \textit{R. Pinnau}, J. Math. Anal. Appl. 332, No. 1, 551--563 (2007; Zbl 1122.35110) Full Text: DOI References: [1] Abramowitz, M.; Stegun, I. A., Handbook of Mathematical Functions (1972), Dover · Zbl 0515.33001 [2] Barcilon, V.; Chen, D.-P.; Eisenberg, R. S.; Jerome, J. W., Qualitative properties of steady-state Poisson-Nernst-Planck systems: Perturbation and simulation study, SIAM J. Appl. Math., 57, 3, 631-648 (1997) · Zbl 0874.34018 [3] Cimatti, G.; Fragalà, I., Invariant regions for the Nernst-Planck equations, Ann. Mat. Pura Appl., 175, 4, 93-118 (1998) · Zbl 0954.35152 [4] Gardner, C. L.; Nonner, W.; Eisenberg, R. S., Electrodiffusion model simulation of ionic channels: 1d simulation, J. Comp. Electronics, 3, 25-31 (2004) [5] Henry, J.; Louro, B., Asymptotic analysis of reaction-diffusion-electromigration systems, Asymptotic Anal., 10, 3, 279-302 (1995) · Zbl 0845.34035 [6] Jerome, J. W., Analytical approaches to charge transport in a moving medium, TTSP, 31, 4-6, 333-366 (2002) · Zbl 1032.35166 [7] Kerkhoven, Th., On the one-dimensional current driven semiconductor equations, SIAM J. Appl. Math., 51, 3, 748-774 (1991) · Zbl 0732.35099 [8] Pivonka, P.; Smith, D., Investigation of nanoscale electrohydrodynamic transport phenomena in charged porous materials, Internat. J. Numer. Methods Engrg., 63, 1975-1990 (2005) · Zbl 1103.76378 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.