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simplifying assumptions are needed that reduce the amount of unknown parameters. Probably the most important of these assumptions is that the system be isothermal. While this does limit the scope of the model, it is not expected to affect the quality of the results. For small (coin) cells, the temperature can be controlled very effectively by putting them in an isothermal temperature chamber, so that the assumption T = const. is justified. Especially for the rather low rates used, thermal gradients in the cell are negligible. Other important simplifying assumptions include the lack of convection in the liquid electrolyte and constant 100 % activity of dissolved species which will be discussed below. electrode y void Figure 4.2: Sketch of the computational domain of the 1D model. Current collectors and cell casing are not part of the modeling domain. Discretization is performed in y-direction. Each CV represents the entire cross section of the cell, potentially including void space inside the casing. Before describing the phenomena and governing equations in detail, nomenclature and naming conventions need to be introduced. Except for the more precise indices, notation in this work follows Ref. [59]; a full list of the symbols used can be found in Tab. A.1. In each control volume (CV), several interfaces (denoted by index m) may exist, at which chemical species (index n) present in the adjacent phases (index p) take part in reactions (index q). Note that the same interfaces, species, phases, and reactions are by design present in each CV within one layer of the cell (cathode, separator, anode) but may differ from layer to layer. That said, the amount of a phase, the concentration of a species or the active surface area of an interface may still be zero in some CVs. Unless otherwise noted, all quantities are considered functions of space (y) and time (t), e.g. εn ≡ εn(y,t). The entire set of equations, boundary conditions, and parameters discussed below can also be found in Tabs. 4.1 and A.5–A.7. 4.2.2 Transport There are numerous models of transport in the liquid electrolyte [144, 202–209]. Most models published to date cannot be easily adapted to the Li/S system, however, be- cause they assume explicitly or by the formulation of the governing equations that 72 Positive electrode Separator Negative ElectrodePDF Image | Lithium-Sulfur Battery: Design, Characterization, and Physically-based Modeling
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