A porous media is a collection of particles of different shapes and sizes. Particles can be deformed such that they rarely contact at a point, but on extended surfaces. As a consequence of these contacts between particles, the resulting voids can present a large number of cusp-like sections resulting in a low-angle intersection of solid surfaces. Depending on the angle at which surfaces interact and on the contact angle between a liquid and the solid surface, a meniscus will rise on a wedge in a similar way a liquid meniscus rises inside a capillary. If the sum of the half-angle of the wedge and the contact angle is less than π/2, there is no possible equilibrium shape and a liquid filament will rise to fill the entire length of the wedge. It was found that filaments have an active role in the enhanced diffusion process between carbon dioxide and liquid hydrocarbons. The presence of filament not only increases the mass transfer area but also plays an important role in the convective mixing process that occurs inside the pore.