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The paper deals with the homogenization of deformable porous media saturatedby two-component electrolytes. The model relevant to the microscopic scaledescribes steady states of the medium while reflecting essential physicalphenomena, namely electrochemical interactions in a dilute Newtonian solventunder assumptions of a small external electrostatic field and slow flow. Thehomogenization is applied to a linearized micromodel, whereby the thermodynamicequilibrium represents the reference state. Due to the dimensional analysis,scaling of the viscosity and electric permitivity is introduced, so that thelimit model retains the characteristic length associated with the pore size andthe electric double layer thickness. The homogenized model consists of twoweakly coupled parts: the flow of the electrolyte can be solved in terms of aglobal pressure and streaming potentials of the two ions, independently of thenthe solid phase deformations which is computed afterwards for the fluid stressacting on pore walls. The two-scale model has been implemented in the SfePyfinite element software. The numerical results show dependence of thehomogenized coefficients on the microstructure porosity. By virtue of thecorrector result of the homogenization, microscopic responses in a localrepresentative cell can be reconstructed from the macroscopic solutions.

Homogenization based two-scale modelling of ionic transport in fluid saturated deformable porous media