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Multi-Scale Modeling and Simulation of Transport Processes in an Elastically Deformable Perforated Medium.

Jonas Knoch1,2, Markus Gahn1, Maria Neuss-Radu1,2

  • 1IWR, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany.

Transport in Porous Media
|January 11, 2023
PubMed
Summary

This study presents an effective model for transport in elastic media with periodic perforations, considering deformations like those in lung tissue. The model reveals how cyclic deformations influence diffusion processes.

Keywords:
Diffusive transportEvolving microstructureFinite-element methodsPerforated elastic mediumTwo-scale expansion

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Area of Science:

  • Multiphysics modeling
  • Computational mechanics
  • Transport phenomena

Background:

  • Transport processes in elastic media are crucial for understanding biological tissues like lungs.
  • Cyclic deformations, such as those during respiration, significantly impact these transport phenomena.
  • Existing models may not fully capture the interplay between domain deformation and diffusion.

Purpose of the Study:

  • To derive an effective model for transport processes in periodically perforated elastic media.
  • To incorporate the effects of cyclic elastic deformations, exemplified by respiratory movements in lung tissue.
  • To analyze the influence of deformation on diffusion through an upscaled, nonlinearly coupled model.

Main Methods:

  • Coupling of domain deformation and diffusion using a mixed Lagrangian/Eulerian formulation.
  • Transformation of the diffusion problem to a fixed domain.
  • Application of two-scale asymptotic expansion to derive the upscaled model.
  • Implementation and validation of the effective model using an application-inspired problem.

Main Results:

  • Derivation of a nonlinearly coupled effective model with effective coefficients.
  • Numerical investigation and interpretation of solutions for cell problems and macroscopic equations.
  • Qualitative determination of deformation effects on the transport process via simulations.

Conclusions:

  • The derived effective model accurately captures transport in deformable, perforated elastic media.
  • Cyclic deformations play a significant role in modulating diffusion processes.
  • The study provides a validated computational framework for analyzing such coupled phenomena.