Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.mce.biophys.msu.ru/archive/doc97210/eng.pdf Дата изменения: Mon Oct 1 23:20:30 2012 Дата индексирования: Mon Oct 1 23:20:30 2012 Кодировка:

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

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:

c 1 c zF u c (t , r ) = D r r + RT c(t , r ) r ; r (t ,0) = 0; c (t , R) = C*; t r r 1 u F u r r = - c(t , r ); r (t ,0) = 0; u (t , R) = U * . r r 0
Here c(t,r) is the Li+ ion concentration, and u(t,r) is the model possesses the unique steady state solution c=C(r), ~ 2C ~2 2 C (r ) = ~ 2 2 ; U (r ) = U + ln (1 - Cr ) ; = (1 - Cr )

(1)

electric potential. We prove that this u=U(r): zF zF , = , = . RT 0 4 (2)

~~ The constants C , U are the roots of certain quadratic equations; for each equation only one of its roots is eligible. We study numerically the behavior of time-dependent solutions to (1) with various initial conditions and 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.