With nonconducting substrates, streaming potential in sufficiently broad (vs Debye screening length) capillaries is well known to be a linear function of applied pressure (and coordinate along the capillary). This study for the first time explores streaming potential with ideally polarizable electron-conducting substrates and shows it to be a nonlinear function of both coordinate and applied pressure. Experimental manifestations can be primarily expected for streaming potentials arising along thin porous electron-conducting films experiencing solvent evaporation from the film side surface. Model predictions are in good qualitative agreement with literature experimental data.