Scaling Behavior of stochastic fluid flow in porous media: Langevin equation

Transport phenomena of fluids in porous media occur in a variety of mediums with different properties. These phenomena are governed by a behavior of scaling law as a function of the different universal components. Hence, we study numerically the fluid transport phenomena in a porous medium under the effect of a static pressing force. Our numerical investigation is developed using the Langevin dynamics based on the competition between the stochastic and the dissipation processes. We study both average flow distance and average flow velocity. The results show that the time evolution of these two magnitudes exhibits exponential profiles with two different regimes, and they evince a decreasing behavior versus fluid viscosity, but an increasing behavior with both static pressure and medium porosity. Scaling law of the mean flow velocity is checked for different control parameters: static pressure, friction coefficient, and medium porosity. We have concluded that the exponent values β ≈ 0.5 ± 0.01 and α ≈ 1 ± 0.01 are independent of these control parameters, which proves their universal character and their consistency with other experimental outcomes.