Two-phase porous media flow is important in many applications from drug delivery to groundwater diffusion and oil recovery and is of particular interest to biomedical diagnostic test developers using cellulose and nitrocellulose membranes with limited fluid sample volumes. This work presents a new two-phase porous media flow model based on the incompressible Navier-Stokes equation. The model aims to address the limitations of existing methods by incorporating a partial saturation distribution in porous media to account for limited fluid volumes. The basic parameters of the model are the pore size distribution and the contact angle. To validate the model, we solved five analytical solutions and compared them to corresponding experimental data. The experimentally measured penetration length data agreed with the model predictions, demonstrating model accuracy. Our findings suggest that this new two-phase porous media flow model can provide a valuable tool for researchers developing fluidic assays in paper and other porous media.