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41	Mathematical modelling of primary alkaline batteries Johansen, Jonathan Frederick January 2007 (has links) Three mathematical models, two of primary alkaline battery cathode discharge, and one of primary alkaline battery discharge, are developed, presented, solved and investigated in this thesis. The primary aim of this work is to improve our understanding of the complex, interrelated and nonlinear processes that occur within primary alkaline batteries during discharge. We use perturbation techniques and Laplace transforms to analyse and simplify an existing model of primary alkaline battery cathode under galvanostatic discharge. The process highlights key phenomena, and removes those phenomena that have very little effect on discharge from the model. We find that electrolyte variation within Electrolytic Manganese Dioxide (EMD) particles is negligible, but proton diffusion within EMD crystals is important. The simplification process results in a significant reduction in the number of model equations, and greatly decreases the computational overhead of the numerical simulation software. In addition, the model results based on this simplified framework compare well with available experimental data. The second model of the primary alkaline battery cathode discharge simulates step potential electrochemical spectroscopy discharges, and is used to improve our understanding of the multi-reaction nature of the reduction of EMD. We find that a single-reaction framework is able to simulate multi-reaction behaviour through the use of a nonlinear ion-ion interaction term. The third model simulates the full primary alkaline battery system, and accounts for the precipitation of zinc oxide within the separator (and other regions), and subsequent internal short circuit through this phase. It was found that an internal short circuit is created at the beginning of discharge, and this self-discharge may be exacerbated by discharging the cell intermittently. We find that using a thicker separator paper is a very effective way of minimising self-discharge behaviour. The equations describing the three models are solved numerically in MATLABR, using three pieces of numerical simulation software. They provide a flexible and powerful set of primary alkaline battery discharge prediction tools, that leverage the simplified model framework, allowing them to be easily run on a desktop PC. advection anode asymptotic analysis BET surface area binary electrolyte boundary condition Butler-Volmer equation cathode closed circuit voltage concentration polarisation control volume current path discretisation diffusion electrochemical reaction electrode electrolytic manganese dioxide EMD crystals EMD particles exchange current density geometric surface area initial condition linearisation macrohomogeneous porous electrode theory mathematical model Nernst equation ohmic losses open circuit voltage ordinary differential equation overpotential partial differential equation perturbation techniques potassium hydroxide potassium zincate precipitation reaction primary battery separator paper simulation ternary electrolyte theoretical capacity utilisation zinc zinc oxide

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Mathematical modelling of primary alkaline batteries