Abstract
A simple rational model is proposed for discharge of batteries with aqueous electrolytes, based on Nernst equation. Details of electrode kinetics are not taken into account. Only a few overall parameters of the battery are considered. A simple algorithm, with variable time step-length Δt, is presented, for proposed model. The model is first applied to Daniel cell, in order to clarify concepts and principles of battery operation. It is found that initial pinching, in time-history curve of voltage E-t, is due to initial under-concentration of product ion. Then, model is applied to a lead-acid battery. In absence of an ion product, and in order to construct nominator of Nernst ratio, such an ion, with coefficient tending to zero, is assumed, thus yielding unity in nominator. Time-history curves of voltage, for various values of internal resistance, are compared with corresponding published experimental curves. Temperature effect on voltage-time curve is examined. Proposed model can be extended to other types of batteries, which can be considered as having aqueous electrolytes, too.
Highlights
IntroductionA simple rational model is proposed, based on Nernst equation [2] [3] [4]
Proposed model can be extended to other types of batteries, which can be considered as having aqueous electrolytes, too
Proposed model is first applied to Daniel cell [8], in order to clarify concepts and principles of battery operation
Summary
A simple rational model is proposed, based on Nernst equation [2] [3] [4]. Overall parameters of battery are considered: voltage, capacity, current, concentrations of aqueous ions in reactants and products, internal resistance, volume, temperature, number of electrons involved in chemical reaction. A simple algorithm, with variable time step-length Δt, is presented, for proposed model. When exhausting of battery capacity is approached and denominator of Nernst ratio tends to become negative, Δt is halved and algorithm step is repeated, as many times are needed for denominator to remain positive. It is found that initial pinching of voltage-time curve E-t is due to initial under-concentration of product ion. Time-history curves of voltage E-t of lead-acid battery, for various values of internal resistance, are compared with corresponding published experimental curves [10] and found in satisfactory approximation with them. In future research, proposed model can be extended to other types of batteries, which can be considered as having aqueous electrolytes, too, e.g. redox flow cells [11], vanadium batteries [12], lithium-ion batteries [13], fuel cells [14]
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