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Langevin Dynamics Study of the Mean Flow Rate-Energy Stochastic Fluid Intrusion Process in Porous Media

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Fluid transport phenomena in porous media exhibit different properties with scaling law behavior according to different universal components, which describe the corresponding universal classes exactly. A numerical study of the fluid intrusion process in a porous medium under the effect of a static pressing force is introduced. Investigations are developed by using Langevin dynamic based on the competition between the stochastic and the dissipation processes. The mean flow rate is studied with an energetic study, then the temporal profiles are shown. The results show that the time evolution of these two magnitudes exhibits exponential profiles with two different regimes; transient and permanent, characterized by their cross-over time. They also exhibit a decreasing behavior versus the friction coefficient, but an increasing behavior versus both the static pressure and the medium porosity. Scaling laws with universal exponents of the mean flow rate are checked for different parameters, namely the static pressure and the friction coefficient. The system mean energy follows a scaling law with universal exponents, independently of the parameters (static pressure, friction coefficient, medium porosity, and system size), which proves their universal character.
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Porous Media; Langevin Dynamics; Mean Flow Rate; Scaling Law; Average Kinetic Energy; Average Potential Energy

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