Modeling the oscillating actuation

To estimate time dependent deflection, and frequency of IPMC selfoscillation in HCHO solution with different concentrations, a physical finite element (FE) model was developed. Some of the advantages of the FE model over the equivalent beam model that was introduced in Chapter 2 are the physics-based governing equations of the fundamental actuation mechanisms of IPMC. This allows the model to be extended to different geometries both in 2D and in 3D. Furthermore, it is convenient to couple the differential equations describing the electrochemical processes into a finite element bending model of IPMC. 

The physical domains shown in Fig. 3.21 were considered in the FE model. Most of the simulations were carried out for an IPMC strip, 2-4 cm long, 200 /Ltm thick polymer, including 10 pm thick Pt diffusion region on each side, coated with 2 pm thick platinum, in a cantilever configuration. 

The Nernst-Planck and Poisson equations were used to describe the underlying physical processes (see Section 2.5.2 Eq. (2.38) (2.41).). 

Values of the simulation constants are shown in Table 3.1. Equations (2.38)-(2.41) are described only for pure Nafion and Pt diffusion domain (see Fig. 3.21) as there is no ionic diffusion nor migration in the thin Pt coating. 

To relate the force in Eq. (2.41) to the physical bending of an IPMC sheet, a set of continuum mechanics equations were introduced. These equations are described in the Comsol Multiphysics structural mechanics 

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