A bi-porous layer flow-field features a secondary porous layer of smaller permeability attached to a bi-polar plate to remove excessive liquid water from the main flow-field by capillary-induced liquid water re-distributions, therefore enhances liquid water management of a proton exchange membrane fuel cell (PEMFC). In this work, we present a two-dimensional two-phase model to elucidate the underlying physics of liquid water re-distribution inside a bi-porous layer flow-field. We reveal that liquid water re-distribution can improve liquid water management in the flow-field and gas diffusion layer, leading up to significant enhancement in oxygen diffusion to the catalyst layer. However, if permeability of the secondary porous layer is too low and the permeability ratio exceeds a threshold, the secondary porous layer may suffer from flooding. This causes liquid water build-up in the main flow-field and GDL, which leads poor oxygen diffusion to the catalyst layer and hence operational instability. The threshold permeability ratio is analytically derived, and flow behaviors at conditions above and below the threshold permeability ratio are explored numerically and analytically. We suggest choosing a permeability ratio below the threshold permeability ratio to avoid flooding in the secondary porous layer and to fully utilize the benefits of liquid water re-distributions.