In this
article we obtain rigorously the homogenization limit for a
fluid-structure-reactive flow system. It consists of cell tissue and
intercellular liquid, transporting solutes. The cell tissue is assumed
to be linearly elastic and deforming with a viscous nonstationary flow.
The elastic moduli of the tissue change with cumulative concentration
value. In the limit, when the scale parameter goes to zero, we obtain
the quasi-static Biot system, coupled with the upscaled reactive flow.
Effective Biot's coefficients depend on the reactant concentration. In
addition to the weak two-scale convergence results, we prove convergence
of the elastic and viscous energies. This then implies a strong
two-scale convergence result for the fluid-structure variables. Next we
establish the regularity of the solutions for the upscaled equations. To
the best of our knowledge, ours is the only known study of the
regularity of solutions to the quasi-static Biot system. The regularity
is used to prove the uniqueness for the upscaled model.

Read More: https://epubs.siam.org/doi/abs/10.1137/100808393

Read More: https://epubs.siam.org/doi/abs/10.1137/100808393

In this
article we obtain rigorously the homogenization limit for a
fluid-structure-reactive flow system. It consists of cell tissue and
intercellular liquid, transporting solutes. The cell tissue is assumed
to be linearly elastic and deforming with a viscous nonstationary flow.
The elastic moduli of the tissue change with cumulative concentration
value. In the limit, when the scale parameter goes to zero, we obtain
the quasi-static Biot system, coupled with the upscaled reactive flow.
Effective Biot's coefficients depend on the reactant concentration. In
addition to the weak two-scale convergence results, we prove convergence
of the elastic and viscous energies. This then implies a strong
two-scale convergence result for the fluid-structure variables. Next we
establish the regularity of the solutions for the upscaled equations. To
the best of our knowledge, ours is the only known study of the
regularity of solutions to the quasi-static Biot system. The regularity
is used to prove the uniqueness for the upscaled model.

Read More: https://epubs.siam.org/doi/abs/10.1137/100808393

},
author = {Jäger, Willi and Mikelic, Andro and Neuss-Radu, Maria},
faupublication = {no},
journal = {SIAM Journal on Mathematical Analysis},
pages = {1390–1435},
peerreviewed = {Yes},
title = {{Homogenization} limit of a model system for interaction of flow, chemical reactions, and mechanics in cell tissues},
volume = {43},
year = {2011}
}
Read More: https://epubs.siam.org/doi/abs/10.1137/100808393