In search of a Mpemba effect protocol: Some hot water does cool and freeze faster than cold

Abstract

Zimmerman [Chem.Eng.Sci. 238: 116618, 2021] developed a theory for additional convection of latent heat by microbubbles from regions of hot water to regions of cold water, a modified heat transport equation that incorporates this convective effect, and a scaling analysis that gives a rough prediction for how this additional heat transfer is proportional to the phase fraction of microbubbles. This theory is supported by arguing that Mpemba and Osborne (1969) had such microbubbles dispersed, resulting in a strong correlation between the dissolved gas solubility at saturation, dependent on the sole controlled variable – the initial temperature of the freezing experiment – and the inferred heat transfer coefficient. The argument was made that the source of the microbubbles was exogeneous due to vigorous boiling. In this paper, a range of systematic errors and uncertainties concerning the Mpemba effect is explored. The two largest uncontrolled variables are the level of vigorous boiling and the level of dissolved gases in tap water. Using the same approach for estimation of the heat transfer coefficients, the experiments of Bregovic (2012) which had no boiling are analyzed. The resulting heat transfer coefficients are shown to pass the accepted Mpemba line criteria for the occurrence of a Mpemba effect. Employing the scaling analysis for additional heat transfer shows reasonable agreement with the hypothesis that source of microbubbles in Bregovic’s experiments is endogeneous: the saturation-nucleation mechanism for spontaneous growth of microbubbles in supersaturated water. The parallel analysis applied to the experiments of Mpemba and Osborne show consistency with predictions of endogenous microbubble generation, too.