A Computational Framework for the Swelling Dynamics of Mucin-Like Polyelectrolyte Gels

40 Pages Posted: 20 Jun 2022

See all articles by Jian Du

Jian Du

Florida Institute of Technology

Bindi M. Nagda

Florida Institute of Technology

Owen L. Lewis

affiliation not provided to SSRN

Daniel B. Szyld

Temple University

Aaron Fogelson

University of Utah

Abstract

Gastric mucus is a polyelectrolyte gel that serves as the primary defense of the stomach lining against acid and digestive enzymes. Experiments show that a mucus gel may swell explosively within a short time period, and that this is accompanied by a massive transport of monovalent cations from the extracellular environment into the densely packed mucus in exchange for divalent calcium that had crosslinked the negatively-charged mucus fibers. We propose a 2D computational method for simulating mucus swelling with a two-fluid model. The model includes electro-diffusive transport of ionic species, the coupled motion of the glycoprotein network and hydrating fluid, and chemical interactions between the network and dissolved ions. Each ionic species in the solvent phase is subject to a Nernst–Planck type equation. Together with the electro-neutrality constraint, these equations constitute a system of non-linear parabolic PDEs subject to an algebraic constraint. The discretized system is solved by a Schur complement reduction scheme. Numerical results indicate that the method is very efficient, robust and accurate, even for problems which exhibit large spatial gradients in the concentration of ions. Computational investigation of swelling dynamics is presented and the physical significance of the simulation results is discussed.

Keywords: Saddle point problem, GMRES, preconditioning, Nernst-Planck, Electro-diffusion, Two-phase Mixture Models, Polymer solution, Polyelectrolyte gels

Suggested Citation

Du, Jian and Nagda, Bindi M. and Lewis, Owen L. and Szyld, Daniel B. and Fogelson, Aaron, A Computational Framework for the Swelling Dynamics of Mucin-Like Polyelectrolyte Gels. Available at SSRN: https://ssrn.com/abstract=4141232 or http://dx.doi.org/10.2139/ssrn.4141232

Jian Du

Florida Institute of Technology ( email )

150 West University Blvd.
Melbourne, FL 32901-6975
United States

Bindi M. Nagda

Florida Institute of Technology ( email )

150 West University Blvd.
Melbourne, FL 32901-6975
United States

Owen L. Lewis

affiliation not provided to SSRN ( email )

No Address Available

Daniel B. Szyld

Temple University ( email )

Philadelphia, PA 19122
United States

Aaron Fogelson (Contact Author)

University of Utah ( email )

1645 E. Campus Center
Salt Lake City, UT 84112
United States

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