A computational framework for the swelling dynamics of mucin-like polyelectrolyte gels

Gastric mucus is a polyelectrolyte gel that serves as the primary defense of the stomach lining against acid and digestive enzymes. Mucus is released from granules in specialized cells where it is stored at very high concentration. Experiments show that such a dense 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. The new method is combined with our previously-published numerical methods for solving the coupled momentum equations of the solvent and network, extended to account for the chemical forces determined from the distribution of ions between solvent and network and in space. The computational effectiveness of the new methods is demonstrated through accuracy and efficiency metrics and through investigation of some of the factors that influence swelling dynamics.