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Electroconvective instability of self-similar equilibria | | E. Demekhin
; S. Polyanskikh
; Yury Shtemler
; | | Date: |
25 Jan 2010 | | Abstract: | Stability of electro-hydrodynamic processes between ion-exchange membranes is
investigated. Solutions of the equilibrium problem which represents the balance
between diffusion and electro-migration are commonly described in an
one-dimensional (1D) steady-state approximation. In the present work a novel
class of the 1D unsteady self-similar equilibrium solution is developed
asymptotically in small Debye length, epsilon, and large distance between
membranes (both made dimensionless with the diffusion-layer thickness). First,
the 1D unsteady family of self-similar equilibrium solutions is developed.
Then, a linear stability of the self-similar solutions slowly varied with time
is investigated in the limit of small epsilonand the marginal stability curves
are obtained. Method of matched asymptotics is applied provided that only the
outer solution is considered, ignoring the inner solutions. The success of the
analysis is provided by transforming the equations to the divergent type (nabla
G=0) with the patching conditions applied to the outer values of the functions,
which constitute the expression G. The interface instability of the boundary of
space charge region is found to be the main reason of instability of 1D
equilibrium solution}. The self-similar solution and marginal stability curves
are in a fair agreement with those obtained by direct numerical simulations of
the entire problem at intermediately large times for which the dimensionless
distance between membranes is large. | | Source: | arXiv, 1001.4502 | | Services: | Forum | Review | PDF | Favorites | |
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