Hydrodynamic dispersion and mixing under two-phase flow can be found in many natural, industrial, and engineering processes such as the modified salinity water flooding (MSWF). In MSWF the injected water displaces the formation brine and will interact with the crude oil and rock to improve the oil recovery. We show throughout numerical simulations that access of the injection water to the available pore space is not homogeneous, even in homogeneous porous media, and it is controlled by the saturation topology and pore-scale velocity field. Under the steady-state two-phase flow in a homogeneous porous medium, the velocity field has a bimodal distribution. The bimodal distribution of pore-scale velocity dictates two different transport time scales spatially distributed over the stagnant and flowing regions at a given saturation topology. These distinctly different transport time scales lead to a non-Fickian transport, which cannot be captured using the conventional advection-dispersion equation. Using the volume-of-fluid method implemented in the OpenFOAM (ver. 4.0), we simulated pore-scale two-phase flow and the hydrodynamic transport at different saturations. We have investigated the impact of stagnant saturation and the tortuosity of flow pathways on the dispersion coefficient and the mass exchange rate - as the two major parameters controlling transport and mixing - under steady-state two-phase flow. At the Darcy scale, different theories such as the mobile-immobile (MIM) theory have been proposed to capture the non-Fickian transport and mixing in two-phase flow through porous media. Based on the simulation results, we assess the validity of the assumptions employed in MIM to define the stagnant saturation and mass exchange rate coefficient. The results of this research provide fresh insights into the potential impact of saturation topology on mixing between the modified salinity water and the formation brine under steady-state flow conditions, which has not been investigated and reported in the literature. (C) 2018 Published by Elsevier Ltd.