2D simulation of the deformation of pH-sensitive hydrogel by novel strong-form meshless random differential quadrature method

Abstract

The objective of presented work is to simulate the response of 2D hydrogel when subjected to the varying pH of buffer solution and initial fixed-charge concentration inside the hydrogel. The novelty of the work is that this is the first attempt to perform the 2D simulation of pHresponsive hydrogel by novel strong-form meshless method, such as random differential quadrature (RDQ) method. The analytical equations, derived for the hydrogel deformation in the x and y directions, are numerically verified by the square shaped hydrogel disc. The jumps in the distributions of ionic concentrations and electrical potential, across the interface between solution and hydrogel, are effectively captured by the RDQ method. A novel approach is proposed to correctly impose natural boundary conditions for non-uniform boundary. The effects of solution pH and initial fixed-charge concentration on the hydrogel swelling are also successfully investigated.Keywords Random differential quadrature methods · 2D simulation of hydrogel · Meshless method · Differential quadrature method

A review on swelling theories of pH-sensitive hydrogels

“…Finite element simulation of hydrogel swelling has been expedited with the development of monophasic swelling theories (Kang et al, 2008; Suthar et al, 2010a, 2010b, 2013; Wallmersperger et al, 2011a; Yi et al, 2017; Yulianti et al, 2011). Various finite-element-based methods have been proposed in the literature, such as in-house codes (Bouklas et al, 2015; Lai and Li, 2010; Li and Mulay, 2011), implementation through user-defined subroutines of ABAQUS (e.g. including user-defined hyperelastic material (Ding et al, 2013; He et al, 2012; Hong et al, 2009; Marcombe et al, 2010; Zalachas et al, 2013), user-defined element (Chester et al, 2015), and user-defined heat transfer with the analogy between the mass and heat transfer phenomena), and implementation using COMSOL platform (Caccavo and Lamberti, 2017; Lucantonio et al, 2013; Wang et al, 2018).…”

“…Besides the finite element method, meshless methods are also used for simulation of hydrogels behavior (Wang et al, 2006). However, there is a wide variety of approaches for meshless methods which has been used in the modeling of hydrogels including the improved complex variable element-free Galerkin (Li et al, 2014), strong-form meshless random differential quadrature method (Li and Mulay, 2011), finite cloud method (De and Aluru, 2004; De et al, 2002), and Hermite-Cloud method (Chen et al, 2005; Lam et al, 2006; Li, 2009; Li and Lai, 2010, 2011; Li and Yew, 2010; Li et al, 2003, 2004a, 2004b, 2005a, 2005b, 2006, 2007a, 2007b, 2007c, 2007d, 2008, 2011, 2014; Ng et al, 2007).…”

Solute Transport In Two Layered Porous Media (Separated Diagonally) Using Suitable DQM Scheme

“…Further developments achieved by Shu et al [7] based on Polynomial-based differential quadrature, (PDQ) (Shu and Richards [8]; Shu et al [9] ), Fourier expansion-based differential quadrature (FDQ) ( Shu and Xue [10]; Shu and Chew [11]) and RBF-DQ based on Radial Basis Function, (Shu et al [12], [13]). Now DQM has been applied successfully in many fields such as fluid dynamics (Shu et al [14], [15]; Tsai et al [16]), solid mechanics (Wang et al [17]), chemical engineering (Civan,[18]; Li and Mulay [19]), vibration and buckling (Mahmoud et al [20]; Danesh et al [21]), Geotechnics (Chen et al [22]), mass transfer (Char et al [23]). In groundwater fields, Kaya and Arisoy [24] used DQM to solve three one-dimensional aquifer flow equation problems including a confined aquifer flow with time dependent boundary conditions, a composite confined aquifer and an unconfined aquifer with seepage.…”

Simulation of Stimuli-Responsive Polymer Networks

“…The strip is fixated at one end electric field, leads to a bending of the non which can be used for sensors and actuators in biological and other aqueous environments reproduced and analyzed in detail in various numerical studies [ Equations (6)- (9) are typically solved with finite element methods. Alternatively, meshless methods have been used [39,40,50,[53][54][55][56], which are conceptually more complex but avoid the definition and adaptation of a mesh grid during the simulation. In finite element and meshless methods, boundary conditions have to be defined on the hydrogel surface with a flow velocity , is added to the right side of Equation obeys the Poisson equation:…”