Conference publications

Abstracts

XVIII conference

Centrally Symmetric Steady States in a Model of Electrodiffusion

Savenkova N.P., Kuzmin R.N.¹, Maximov D.S.¹, Shobukhov A.V.

Lomonosov Moscow State University, Faculty of Comput. Mathem. and Cybernetics, Russia 119991, Moscow, Leninskiye Gory, MSU, 2-nd Educ.Build., room 728, phone: +7 (495) 939-52-55, e-mail: shobukhov@cs.msu.su

¹Lomonosov Moscow State University, Faculty of Physics, Russia 119991, Moscow, Leninskiye Gory, MSU, House 1, Build.2

2 pp. (accepted)

We consider a mathematical model of electrodiffusion in a centrally symmetric case [1]-[2]. This model describes in particular the transport of the Li+ ions inside the graphite spherical particles in the porous negative electrodes [3] due to diffusion and migration:

(1)

Here c(t,r) is the Li+ ion concentration, and u(t,r) is the electric potential. We prove that this model possesses the unique steady state solution c=C(r), u=U(r):

(2)

The constants are the roots of certain quadratic equations with positive discriminant; for each equation only one of its roots proves to be eligible. We study numerically the behavior of time-dependent solutions to (1) with various initial conditions using a finite-volume symmetric difference scheme of second order of accuracy. We demonstrate that the spatially non-uniform steady state (2) is the stable attractor for the time-dependent solutions to (1) regardless of the initial distributions of ion concentration and electric potential.

References.

1. Rubinstein I. Electro-Diffusion of Ions, SIAM, Studies in Appl. Math., v.11, 1990.

2. Biler P., Nadzieja T. Math. Methods in the Applied Sciences, v.20, is.9, 1997. pp.767-782.

3. Frumin L.L., Zilberstein G.V. Journ. Electrochem. Soc., v.144, n.10, 1997. pp.3458-3462.

• view as PDF (in English) (PDF)
• view as PDF (in Russian) (PDF)