Formulation of the Gel Lattice Spring Model gLSM

To study the dynamic behavior of the BZ gels, we numerically integrate Equations 3.1 - 3.3 in three dimensions using our recently developed gel lattice spring model (gLSM) [18, 19]. This method combines a finite element approach for the spatial discretization of the elastodynamic equations and a finite difference approximation for the reaction and diffusion terms. We briefly describe the 3D formulation of the gLSM below for more details of the model, we refer the reader to Ref [18]. 

Each element is labeled by the vector m = (i,j, k), and the element nodes are numbered by the index n = 1 — 8 and characterized by the coordinates r (m) [18]. Within each element m, the concentrations of the dissolved reagent, u(m), the oxidized metal-ion catalyst, u(m), and the volume fraction of polymer, (m), are taken to be spatially uniform. The value of p m) is related to the volume of the element, V(m), as (j (m) = /S 4 olV m). Within each element, we define a local 

We assume that the dynamics of the polymer network is purely relaxational hence, we find the velocity of node n of the element m is proportional to the force acting on this node, F (m), that is, [18,19] 

The total force acting on each node contains contributions from the elastic and osmotic properties of the system. We have shown [18] that the total force acting on node n of the element m consists of two contributions, F (m) = Fi, (m) + F2, (m). The first term, Fi (m), describes the neo-Hookean elasticity contribution to the energy of the system and can be expressed as a combination of the linear springlike forces [18]  

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