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Flow through time-evolving porous media
Publication . Matias, André F. V.; Araújo, Nuno A. M.; Coelho, Rodrigo C. V.
In several problems of interest, a fluid flows through a porous medium modifying its structure.
The dynamics of this fluid-structure interaction is a problem of practical interest that encompasses
several fundamental questions in Soft Matter Physics related to complex flows, instabilities,
and solute transport. In this thesis, we extended the theories for fluid flow in porous
media to account for different phenomena such as swelling, erosion, and deposition. We also
extend the continuum descriptions of the fluid flow in porous media and of the dispersion and
dissolution of solute. We start by considering changes in the medium due to swelling and erosion
and extend existing pore scale lattice Boltzmann models to include both. We analyze their
competition and identify a transition between regimes where either swelling or erosion dominate.
Next, we propose a continuum description for erosion and deposition that couples the
velocity and porosity fields. The proposed model, based on the capillary model, is validated
using pore scale simulations. The simulation of media with mild spatial inequalities in porosity,
and erosion resistance is now possible. These inequalities over time get amplified, leading to
the formation of main streamlines. We show that, even for uniform erosion resistance, a weak
disorder in porosity suffices to trigger permanent channelization. The same is observed with
uneven erosion resistance. We finish with a continuum equation to model solute transport and
dissolution, parametrized by the P´eclet number and the rate of mass transfer between the solid
and the fluid. We study the time dependence of the extracted mass for different values of the
parameter space. The continuum description is validated by combining extraction experiments
with coffee and computational fluid dynamics. An analytical solution is derived for the limit of
slow mass transfer, which is corroborated by numerical simulations
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Fundação para a Ciência e a Tecnologia
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SFRH/BD/143955/2019