Influence of capillary pressure gradient on connectivity of flow through a porous medium

We study the nonlinear development of perturbations of the phase transition surface in the Hele-Shaw cell and a porous medium with a change of capillary pressure gradient along the interface. A bounded water-saturated region surrounded by humid air is explored. Capillary pressure at the interface causes deformation and movement of the water-saturated region. An approximate analytical solution using the method of characteristics is derived and compared with numerical simulation results. It is shown that the evolution of the deforming region can lead to its breakup into disconnected parts. Numerical experiments also show that the deformation of closely spaced separate regions can lead to their fusion. Such the reconfiguration of the interfaces can cause significant changes in the flow properties. Fragmentation during the motion and evaporation of groundwater leads to the formation of isolated inclusions of the substance carried by the water flow.