2020/08/28 by Gelu Paşa, Paşa}, Gelu
Engineering · Physics and Astronomy · #34B09 #34D20 #35C09 #35J20 #76S05 #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Lattice Boltzmann Simulation Studies #Mathematical Physics (math-ph) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2008.12561
openalex publication_date 2020/08/28 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
An useful approximation for the displacement of two immiscible fluids in a porous medium is the Hele-Shaw model. We consider several liquids with different constant viscosities, inserted between the displacing fluids. The linear stability analysis of this model leads us to an ill-posed problem. The growth rates (in time) of the perturbations exist iff some compatibility conditions on the interfaces are verified. We prove that these conditions cannot be fulfilled.