Zinc-air flow batteries are a promising energy storage technology. Their performance depends on their porous cathodes where the oxygen reduction reaction (ORR) occurs. A key feature of the cathode is the invasion of electrolyte, creating the so-called triple phase boundary between air, electrolyte and catalyst, which is shown in this work to be an overly simplified picture. In this study a mathematical framework based on pore network modeling (PNM) was developed to better understand the interplay between electrode structure, transport of species and electrolyte invasion. The results suggest that increasing electrolyte volume provides highly branched invasion pattern and enhances performance up to a saturation of 0.7 , whereas further invasion reduces air-liquid interfacial area and lowers the performance. Interestingly, at lower saturations (<0.3) the liquid structure is so excessively branched that hydroxide ions are unable to diffuse to the anode at a sufficient rate, resulting in supersaturation, which is a degradation problem. The pore size distribution of the catalyst layer also affects the performance with wider pore size distributions generally performing better. This work represents the first 3D PNM of a zinc-air cathode that includes all the key physics and transport mechanisms, enabling prediction of the structure-performance relationship of porous cathodes.