Yield stress of foam flow in porous media: The effect of bubble trapping

Foam behaves as a yield-stress fluid as it flows in a porous medium. Quasi-static analysis suggests that the yield stress arises from the non-smooth motion of foam films, denoted as lamellae, in pores. In order to study the effect of trapped lamellae on the motion of a moving lamella and consequently on the yield stress of foam, we conduct numerical simulations in the quasi-static limit. We propose a new method utilizing the surface energy minimization algorithm, which explicitly considers the connectivity of pores in a porous medium. We consider two different shapes of pore and vary the number of nearby trapped lamellae to investigate the effects of bubble trapping on the non-smooth and the smooth motion of a single lamella passing through a pore, respectively. We find that the trapped lamellae lead to the increased volume-averaged pressure drop and thus the increased yield stress. Notably, the motion of a lamella through a pore with rounded corners in the pore body becomes non-smooth, due to the presence of trapped lamellae. The results contribute to a better understanding of the yield stress of foam in porous media.