Abstract
Ionized hydrogels, as osmoelastic media, swell enormously (1000 times its original volume in unionized water) due to the osmotic pressure difference caused by the presence of the negatively charged ion groups attached to the solid matrix (polymer chains). The coupling between the extremely large deformations (induced by swelling) and fluid permeation is a field of application that regular poroelasticity formulations cannot handle. In this work, we present a mixed hybrid finite element (MHFE) computational framework featuring a three-field (deformation-chemical potential-flux) formulation. This formulation guarantees that mass conservation is preserved both locally and globally. The impact of such a property on the swelling simulations is demonstrated by four numerical examples in 2D. This paper focuses on the implementation aspects of the MHFE model and shows that it stays robust and accurate for a volume increase of more than 3000%.
Highlights
Hydrogels are water-swollen and cross-linked polymeric networks, produced by the simple reaction of one or more monomers
As it is argued that MHFEM possesses local mass conservation property, which should lead to more accurate calculation of flux, we plot the flux vectors and corresponding streamlines originating from the bottom edge for both methods at a given moment Fig. 7) in order to trace back the deformation differences presented above
We have developed a mixed hybrid finite element (MHFE) model under the theoretical framework of mixture theory for the simulation of swelling ionized hydrogels in two dimensions
Summary
Hydrogels are water-swollen and cross-linked polymeric networks, produced by the simple reaction of one or more monomers. Considering a SAPs gel particle facing a gush of urine which can be approximated by the physiological salt solution, i.e. a solution of Na+ and Cl− of concentration 0.154 mol/L, chemical potential responds much faster to the local ions concentration change than solvent permeating into the gel This claim is justified by the following calculation. MHFEM (Mixed Hybrid Finite Element Method), which approximates flux as an independent variable using Raviart–Thomas element and resolves the resulting indefinite coefficient matrix by means of hybridization procedure, possesses local mass conservation property and has proven to be effective in solving Darcy type equations [22,23]. Motived by the success of MHFEM in solving Darcy’s type equations and Biot consolidation problems, we apply MHFEM in swelling simulations in order to achieve more reliable and satisfactory results. By means of numerical examples in two dimensions, we demonstrate that MHFEM is a robust and accurate method for swelling simulations involving large deformations
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call