Temporal Evolution of Flow in Pore-Networks: From Homogenization to Instability

Kavli Affiliate: Ariel Amir

| First 5 Authors: Ahmad Zareei, Deng Pan, Ariel Amir, ,

| Summary:

We study the dynamics of flow-networks in porous media using a pore-network
model. First, we consider a class of erosion dynamics assuming a constitutive
law depending on flow rate, local velocities, or shear stress at the walls. We
show that depending on the erosion law, the flow may become uniform and
homogenized or become unstable and develop channels. By defining an order
parameter capturing these different behaviors we show that a phase transition
occurs depending on the erosion dynamics. Using a simple model, we identify
quantitative criteria to distinguish these regimes and correctly predict the
fate of the network, and discuss the experimental relevance of our result.

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