Slow invasion of a fluid from multiple inlet sources in a thin porous layer: influence of trapping and wettability.

We study numerically the process of quasistatic invasion of a fluid in thin porous layers from multiple inlet injection sources focusing on the effect of trapping or mixed wettability, that is, when hydrophobic and hydrophilic pores coexist in the system. Two flow scenarios are considered. In the first one, referred to as the sequential scenario, the injection bonds at the inlet are activated one after the other. In the second one, referred to as the kinetic scenario, the injection bonds at the inlet are activated simultaneously. In contrast with the case of purely hydrophobic systems with no trapping, studied in a previous work, it is shown that the invasion pattern and the breakthrough point statistics at the end of the displacement depend on the flow scenario when trapping or mixed wettability effects are taken into account. The transport properties of the defending phase are also studied and it is shown that a one-to-one relationship between the overall diffusive conductance and the mean saturation cannot be expected in a thin system. In contrast with thick systems, the diffusive conductance also depends on the thickness when the system is thin. After consideration of various generic aspects characterizing thin porous systems, the main results are briefly discussed in relation with the water management problem in proton exchange membrane fuel cells.