Dynamics of active paths during two-phase flow through the capillary fiber bundle model

We investigate the dynamics of active paths during a two-phase flow of immiscible fluids under an external pressure drop ΔP. We demonstrate that this dynamics of new path opening plays a crucial role in understanding the nonlinear rheology for the one-dimensional capillary fiber bundle model in the limit where the capillary forces are comparable with the viscous forces. The contribution of gradual path-opening dynamics is controlled by tuning maximum value of the capillary thresholds (P_{M}) around which one observes the following situation: flow through existing paths plus new path opening for ΔP<P_{M} and flow through existing paths only beyond P_{M}. The nonlinear rheology is expressed in terms of the Q-ΔP, with continuously varying P_{M}, showing two different nonlinear behavior around P_{M} where one can be explained from the information of the other. P_{M} is also the point around which the kinetic energy of the system is rearranged and expressed through a variation in participation number (π). π in the Fourier space shows a signature of red noise through inverse square decay of power spectrum indicating toward equipartition of energy as well as the underlying self organized criticality.