Mathematical model of fluid front dynamics driven by porous media pumps

Air-permeable porous media host air within their pores. Upon removal from the material's interior, these porous media have the tendency to reabsorb air from the surrounding, acting as a suction pump. Therefore, the technique used to convert porous media into a pump consists of degassing the material to remove the air inside. The suction property when recovering the air can be used to move a liquid through a microfluidic channel. Porous media pumps are very accurate devices to move liquids in a completely controlled way. By studying the dynamics of the liquid front moved by these pumps, it is possible to extract characteristic properties of both the fluid and the porous material. In this article, we have developed a theoretical mathematical model that precisely characterizes the dynamics of a liquid moved by a degassed porous media pump through a microchannel by comparing it with experimental data. We have seen the differences between sealing the external surface of the pump so that it cannot absorb air from the outside, both mathematically and experimentally. We have observed that, in all cases, the theory fits satisfactorily with the experiments, corroborating the validity of the model. The creation of microfluidic pumps using porous media can be a very useful tool in various fields due to its long operating time and small size and the fact that it operates without any external power source.