Polymer phase porous membrane model

Within the alternative approach, the film is considered a porous medium [54, 94,114,119,121,122,127-129,148], Physically, it represents a porous membrane that includes a matrix formed by the conducting polymer and pores filled with an electrolyte. Mathematically, in this approach the film is modeled as a macroscop-ically homogeneous two-phase system consisting of an electronically conducting sohd phase and an ionically conducting electrolyte phase. Considering a planar geometry, each layer perpendicular to the electrode smface contains these two phases, and it can therefore be described at any point by two potentials that depend on the time and the spatial coordinates. 

Some of these studies focused on the analysis of equilibrium-limited reactions, namely those in which the conditions of the respective conversion could be enhanced relatively to the value obtained in a conventional reactor, the so-called thermodynamic equilibrium conversion.i i The developed models considered generic equilibrium-limited reactions carried on in membrane reactors with perfectly mixed or plug-flow pattems. In all these studies, the main assumptions considered consisted in isothermal and steady-state operation, Fickian transport across a non-porous membrane with a homogeneously distributed nanosized catalyst with constant diffusion coefficients, Henry s law for describing the equilibrium condition at the interfaces membrane/gas, and equality of local concentrations at the interface polymer phase/catalyst surface. 

There are different ways to depict membrane operation based on proton transport in it. The oversimplified scenario is to consider the polymer as an inert porous container for the water domains, which form the active phase for proton transport. In this scenario, proton transport is primarily treated as a phenomenon in bulk water [1,8,90], perturbed to some degree by the presence of the charged pore walls, whose influence becomes increasingly important the narrower are the aqueous channels. At the moleciflar scale, transport of excess protons in liquid water is extensively studied. Expanding on this view of molecular mechanisms, straightforward geometric approaches, familiar from the theory of rigid porous media or composites [ 104,105], coifld be applied to relate the water distribution in membranes to its macroscopic transport properties. Relevant correlations between pore size distributions, pore space connectivity, pore space evolution upon water uptake and proton conductivities in PEMs were studied in [22,107]. Random network models and simpler models of the porous structure were employed. 

The simplest model used to explain and predict gas permeation through non-porous polymers is the solution-diffusion model. In this model it is assumed that the gas at the high-pressure side of the membrane dissolves in the polymer and diffuses down a concentration gradient to the low pressure side, where the gas is desorbed. It is further assumed that sorption and desorption at the interfaces is fast compared to the diffusion rate in the polymer. The gas phase on the high- and low-pressure side is in equilibrium with the polymer interface. The combination of Henry s law (solubility) and Picks law (diffusion) leads to... 

Key words polymer electrolyte membrane fuel cell, PEMFC, two-phase transport, porous media, pore network model, lattice Boltemarm model, direct numerical simulation, macroscopic upscaling. 

The accumulation and distribution of licpiid water in the polymer electrolyte membrane fuel cell (PEMFC) is highly dependent on the porous gas diffusion layer (GDL). The accmnulation of liquid water is often simply reduced to a relationship between liquid water saturation and capillary pressure however, recent experimental studies have provided valuable insights in how the microstmcture of the GDL as well as the dynamic behavior of the liquid play important roles in how water will be distributed in a PEMFC. Due to the importance of the GDL microstmcture, there have been recent efforts to provide predictive modeling of two-phase transport in PEMFCs including pore network modehng and lattice Boltzmann modeling, which are both discussed in detail in this chapter. Furthermore, a discussion is provided on how pore-scale infonnation is used to coimect microstmcture, transport and performance for macroscale upscaling. 

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