Efficiency of lithium-ion batteries largely relies on the performance of battery separator membrane as it controls the mobility and concentration of Li-ions between the anode and cathode electrodes. Recent advances in electrochemical strain microscopy (ESM) prompted the study of Li diffusion and transport at the nanoscale via electromechanical strain developed under an application of inhomogeneous electric field applied via the sharp ESM tip. In this work, we observed unexpectedly high electromechanical strain developed in polymer membranes based on porous poly(vinylidene fluoride) (PVDF) and poly(vinylidene fluoride-co-chlorotrifluoroethylene) (PVDF-CTFE) and, using it, could study a dynamics of electroosmotic flow of electrolyte inside the pores. We show that, independently of the separator membrane, electric field-induced deformation observed by ESM on wetted membrane surfaces can reach up to 10 nm under a moderate bias of 1 V (i.e., more than an order of magnitude higher than that in best piezoceramics). Such a high strain is explained by the electroosmotic flow in a porous media composed of PVDF. It is shown that the strain-based ESM method can be used to extract valuable information such as average pore size, porosity, elasticity of membrane in electrolyte solvent, and membrane-electrolyte affinity expressed in terms of zeta potential. Besides, such systems can, in principle, serve as actuators even in the absence of apparent piezoelectricity in amorphous PVDF.