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Channel formation and branching is widely seen in physical systems where movement of fluid through a porous structure causes the spatiotemporal evolution of the medium in response to the flow, in turn causing flow pathways to evolve. We provide a simple theoretical framework that embodies this feedback mechanism in a multi-phase model for flow through a fragile porous medium with a dynamic permeability. Numerical simulations of the model show the emergence of branched networks whose topology is determined by the geometry of external flow forcing. This allows us to delineate the conditions under which splitting and/or coalescing branched network formation is favored, with potential implications for both understanding and controlling branching in soft frangible media.
We report forced radial imbibition of water in a porous medium in a Hele-Shaw cell. Washburns law is confirmed in our experiment. Radial imbibition follows scaling dynamics and shows anomalous roughening dynamics when the front invades the porous med
We develop a 3D porous medium model for sap flow within a tree stem, which consists of a nonlinear parabolic partial differential equation with a suitable transpiration source term. Using an asymptotic analysis, we derive approximate series solutions
Hypothesis Control of capillary flow through porous media has broad practical implications. However, achieving accurate and reliable control of such processes by tuning the pore size or by modification of interface wettability remains challenging. He
Flows through porous media can carry suspended and dissolved materials. These sediments may deposit inside the pore-space and alter its geometry. In turn, the changing pore structure modifies the preferential flow paths, resulting in a strong couplin
Extremely small amounts of surface-active contaminants are known to drastically modify the hydrodynamic response of the water-air interface. Surfactant concentrations as low as a few thousand molecules per square micron are sufficient to eventually i