Simplified mathematical model for effects of freezing on the low-temperature performance of the lead-acid battery

Discharge periods of lead-acid batteries are significantly reduced at subzero centigrade temperatures. The reduction is more than what can be expected due to decreased rates of various processes caused by a lowering of temperature and occurs despite the fact that active materials are available for discharge. It is proposed that the major cause for this is the freezing of the electrolyte. The concentration of acid decreases during battery discharge with a consequent increase in the freezing temperature. A battery freezes when the discharge temperature falls below the freezing temperature. A mathematical model is developed for conditions where charge-transfer reaction is the rate-limiting step, and Tafel kinetics are applicable. It is argued that freezing begins from the midplanes of electrodes and proceeds toward the reservoir in-between. Ionic conduction stops when one of the electrodes freezes fully and the time taken to reach that point, namely the discharge period, is calculated. The predictions of the model compare well to observations made at low current density (C/5) and at -20 and -40°C. At higher current densities, however, diffusional resistances become important and a more complicated moving boundary problem needs to be solved to predict the discharge periods