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A multicomponent flow model in deformable porous media
Author(s) -
Detmann Bettina,
Krejčí Pavel
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5482
Subject(s) - porous medium , degenerate energy levels , capillary action , mathematics , formalism (music) , mechanics , fluid mechanics , continuum mechanics , fluid dynamics , porosity , classical mechanics , physics , thermodynamics , geology , geotechnical engineering , art , musical , quantum mechanics , visual arts
We propose a model for multicomponent flow of immiscible fluids in a deformable porous medium accounting for capillary hysteresis. Oil, water, and air in the soil pores offer a typical example of a real situation occurring in practice. We state the problem within the formalism of continuum mechanics as a slow diffusion process in Lagrange coordinates. The balance laws for volumes, masses, and momentum lead to a degenerate parabolic PDE system. In the special case of a rigid solid matrix material and three fluid components, we prove under further technical assumptions that the system is mathematically well posed in a small neighborhood of an equilibrium.