  The paper deals with the homogenization of deformable porous media saturated
by two-component electrolytes. The model relevant to the microscopic scale
describes steady states of the medium while reflecting essential physical
phenomena, namely electrochemical interactions in a dilute Newtonian solvent
under assumptions of a small external electrostatic field and slow flow. The
homogenization is applied to a linearized micromodel, whereby the thermodynamic
equilibrium represents the reference state. Due to the dimensional analysis,
scaling of the viscosity and electric permitivity is introduced, so that the
limit model retains the characteristic length associated with the pore size and
the electric double layer thickness. The homogenized model consists of two
weakly coupled parts: the flow of the electrolyte can be solved in terms of a
global pressure and streaming potentials of the two ions, independently of then
the solid phase deformations which is computed afterwards for the fluid stress
acting on pore walls. The two-scale model has been implemented in the SfePy
finite element software. The numerical results show dependence of the
homogenized coefficients on the microstructure porosity. By virtue of the
corrector result of the homogenization, microscopic responses in a local
representative cell can be reconstructed from the macroscopic solutions.
