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Comparison of four boundary conditions for the fluid-hydrogel interface

Zelai Xu1, Jiaqi Zhang2, Yuan-Nan Young3, Pengtao Yue4, and James J. Feng1,5

  • 1Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z3
  • 2School of Mathematical and Statistical Sciences, Clemson University, Clemson, South Carolina 29634, USA
  • 3Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA
  • 4Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061, USA
  • 5Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z2

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Phys. Rev. Fluids 7, 093301 – Published 21 September, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.093301

Abstract

In adopting a poroelastic model for a hydrogel, one views its constituent fluid and solid phases as interpenetrating continua, thereby erasing the pore-scale geometry. This gives rise to the need for additional boundary conditions (BCs) at the interface between a hydrogel and a clear fluid to supplement the momentum equations for the fluid and solid phases in the hydrogel. Using a thermodynamic argument on energy dissipation, we propose three sets of BCs for the gel-fluid interface that link the normal and tangential velocity jumps across the interface to the normal and tangential stresses on either side of the interface. Using several flow problems—one-dimensional compression, two-layer Couette and Poiseuille shear flows, and deformation of a gel particle by a planar extension flow—as tests, we compare the predictions of these three BCs with that of a previously proposed BC. Some differences are stark and reveal flaws in certain BCs. Others are subtler and will require quantitative experimental data for validation. Based on these results, we recommend one set of BCs over the other three for computing the flow and deformation of hydrogels in contact with a clear fluid. In addition, we suggest benchmark experiments to validate the BCs and our recommendation.

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Phys. Rev. Fluids 7, 093301– Published 21 September, 2022
  • Received 9 December 2021
  • Accepted 13 September 2022
Article part of CHORUS
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