A Thermo-Poro-Viscoelastic Model for the Behavior of Polymeric Porous Separators

Abstract

Porous separator membranes play an important role in the long-term performance of lithium battery cells. They provide a barrier between two electrodes and enable migration of lithium ions through the pores, where lithium ions migrate through the electrolyte via diffusion-migration and reach the electrode materials. During the discharge process, the intercalation of Li ions into active materials in the electrode leads to swelling of active particles, expansion of the electrode, mechanical stresses, and compression of the separator membrane. Moreover, the extreme thermal condition lessens the performance of the separator by closing the pores through a melting process. To assess the performance of the separator under mechanical and thermal conditions, we present a thermo-poro-viscoelastic model for polymeric porous separators. We study the thermo-mechanical behavior of fully saturated porous separators through the thermo-poromechanics formulations. Two-phase mixture with solid and fluid phases is considered. Governing and balance equations are presented for the solid-fluid mixture, where the displacement of the solid skeleton, temperature and fluid pore pressure are considered as unknowns with a quasi-static loading condition. The stress-strain behavior of the polymeric separator membrane is described by a viscoelastic constitutive law in the form of convolution integral, where the thermal effects are considered through the thermal strain. The flow of the fluid through the porous medium is described by the Darcy’s law. The constitutive equation for the Darcy fluid velocity is described by the permeability of the fluid. To present more realistic physical phenomena, the hydraulic conductivity is described as a function of the porosity in the solid phase. Numerical simulations are performed to study the performance of the separator in a saturated porous medium.