*2.7. Water Transport*

In this model, the estimation of the flow of water *jw* from anode to cathode is divided in three categories: osmotic *j*osmo and diffusive *j*diff flow as well as hydraulic permeation *j*hyd. A positive value means an increase in water concentration:

$$j\_{w\_{\text{anclov}}} = j\_{\text{diff}} + j\_{\text{hyd}} - j\_{\text{osmao}} \tag{20}$$

$$j\_{w\_{\text{cathode}}} = j\_{\text{gen}} + j\_{\text{osm}} - j\_{\text{diff}} - j\_{\text{hyd}}.\tag{21}$$

Three major simplifications are applied to reduce the complexity of water transport mechanisms. First, only the flow through the membrane is considered, whilst transport through the porous media of catalyst and gas diffusion layers is neglected. Second, it is assumed that liquid water is only present once the gas mixture is saturated. Finally, liquid and vapor phases are not directly considered. Instead,

the chosen equations for diffusive and hydraulic flow are adjusted by several functions (Figure 2) created with the MATLAB curve fitting application and experimental data from Adachi et al. [24]. As a result, three cases are described in the following sections: vapor–vapor (VVP), liquid–vapor (LVP) and liquid–liquid permeation (LLP).

**Figure 2.** Estimated Water flux through the membrane at 70 ◦C (Equations (24)–(32), adjusted with data from Adachi et al. [24]); VVP: cathode 96%, anode 38% RH; LVP: cathode liquid volume fraction 100% (flooded), anode 38% RH; LLP: cathode and anode flooded, Δ*p* 1 [bar] note: only a few data points were available to develop each function, which leads to some numerical inaccuracies.
