Mpemba effect - WikiHQ

thumb|[[Erasto Mpemba, namesake of the phenomenon ]]

The Mpemba effect is the observation that very hot liquids or colloids (such as ice cream) can freeze more quickly than colder ones, for similar volumes and surrounding conditions. Physicists remain divided on the effect's reproducibility, precise definition, and underlying mechanisms. It is named after Erasto Mpemba, a Tanzanian teenager who studied it scientifically in the 1960s for the first time, along with Denis Osborne.

The Mpemba effect was initially observed in only ice cream and water, and later in other colloids. It has been studied extensively in water, with mixed results, and some experiments finding no reproducible effect. It has also been studied in magnetic alloys, nanomechanical systems, and quantum systems.

Definition

The definition of the Mpemba effect used in theoretical studies varies, Monwhea Jeng proposed this definition for the effect in water: "There exists a set of initial parameters, and a pair of temperatures, such that given two bodies of water identical in these parameters, and differing only in initial uniform temperatures, the hot one will freeze sooner." Even this definition does not specify whether "freezing" refers to the point at which a visible surface layer of ice has formed, or the point at which the liquid is completely frozen. In water, this would be when the liquid has completely frozen.

Mpemba's observation

The effect is named after Tanzanian student Erasto Mpemba, who described it in 1963 in Form 3 of Magamba Secondary School, Tanganyika; when freezing a hot ice cream mixture in a cookery class, he noticed that it froze before a cold mixture. He later became a student at Mkwawa Secondary (formerly High) School in Iringa. The headmaster invited Dr. Denis Osborne from the University College in Dar es Salaam to give a lecture on physics. After the lecture, Mpemba asked him, "If you take two similar containers with equal volumes of water, one at and the other at , and put them into a freezer, the one that started at freezes first. Why?" Osborne thought the student was mistaken at first, but, intrigued by the question, he experimented on the issue back at his workplace, and was amused to see he was able to confirm Mpemba's finding. Osborne and Mpemba later published the results together in 1969, while Mpemba was studying at the College of African Wildlife Management.

Mpemba and Osborne described placing samples of water in beakers in the icebox of a domestic refrigerator on a sheet of polystyrene foam. They showed the time for freezing to start was longest with an initial temperature of and that it was much less at around . They ruled out loss of liquid volume by evaporation and the effect of dissolved air as significant factors. In their setup, most heat loss was found to be from the liquid surface. Aristotle's explanation involved antiperistasis: "...the supposed increase in the intensity of a quality as a result of being surrounded by its contrary quality."

Francis Bacon noted that "slightly tepid water freezes more easily than that which is utterly cold." René Descartes wrote in his Discourse on the Method, relating the phenomenon to his vortex theory: "One can see by experience that water that has been kept on a fire for a long time freezes faster than other, the reason being that those of its particles that are least able to stop bending evaporate while the water is being heated."

Scottish scientist Joseph Black in 1775 investigated a special case of the phenomenon by comparing previously boiled with unboiled water. He found that the previously boiled water froze more quickly, even when evaporation was controlled for. He discussed the influence of stirring on the results of the experiment, noting that stirring the unboiled water led to it freezing at the same time as the previously boiled water, and also noted that stirring the very cold unboiled water led to immediate freezing. Joseph Black then discussed Daniel Gabriel Fahrenheit's description of supercooling of water, arguing that the previously boiled water could not be as readily supercooled.

Modern experimental work

Studies of the effect in water

Modern studies using freezers with well-understood properties have observed the Mpemba effect where water supercools before freezing. Water that starts out cooler tends to reach a lower supercooled temperature before freezing. Some studies measure the time it takes for a sample to begin to freeze (the start of recalescence, the moment where the heat of freezing first starts to be released) the time it takes to completely freeze, or the difference: the time from the onset of recalescence to the completion of freezing. Some also measure the time it takes for a sample to reach the freezing point of the fluid, before any freezing has begun.

In 1995, David Auerbach studied glass beakers placed into a liquid cooling bath, where the water supercooled to before freezing. In some cases water which started off hotter began freezing first. Considerable random variation was observed in the time required for spontaneous freezing to start, and Auerbach observed the Mpemba effect more frequently when the ambient temperature was between . James Brownridge later studied a variety of initial conditions and containers, measuring the time to the onset of recalescence, and found that while hot samples sometimes froze first this was also affected by properties of the container holding the liquid.

Writing for New Scientist, Mick O'Hare recommended starting the experiment with containers at , respectively, to maximize the effect.

In 2021, John Bechhoefer described a way to reliably reproduce the effect. In 2024, Argelia Ortega, et al. studied the freezing of small () drops in a Peltier cell with a thermographic camera, and found that hot drops consistently froze faster than cold ones, with a more pronounced difference for larger drops. In particular, hot drops finished freezing sooner after the onset of recalescence, and experienced less of a temperature spike during the freezing process.

Criticisms of experiments with water

Some researchers have criticized studies of the Mpemba effect for not accounting for dissolved solids and gases, and other confounding factors. Even among experiments that agree on a definition and observe the Mpemba effect for some experimental setups, they often do not observe it for all setups and starting conditions.

Studies of the effect in colloids and other systems

Classical systems

The original classroom observations of the Mpemba effect were of fresh ice cream, a colloid, freezing in a freezer.

A generalized version of the Mpemba effect is "when a hotter system equilibrates faster than a colder one when both are quenched to the same low temperature." This has been modeled theoretically for simple systems such as single particles under Brownian motion. In 2020 the strong Mpemba effect was demonstrated experimentally by Avinash Kumar and John Boechhoefer in a single-particle colloidal system.

Quantum systems

Since 2020, quantum researchers have studied Mpemba effects in quantum systems as an example of how initial conditions of a system affects its thermal evolution. In 2024, a team in John Goold's lab at Trinity College described their quantum-mechanical analysis of an abstract problem wherein "an initially hot system is quenched into a cold bath and reaches equilibrium faster than an initially cooler system." and Chatterjee, et al. found the Mpemba effect occurs naturally during the cooling of nuclear spin states.

Theoretical explanations

While the definition of the Mpemba effect used in theoretical studies varies, Antonio Lasanta and co-authors also predicted the direct and inverse Mpemba effects for a granular gas in a far-from-equilibrium initial state. Lasanta's paper also suggested that a very generic mechanism leading to both Mpemba effects is due to a particle velocity distribution function that significantly deviates from the Maxwell–Boltzmann distribution. In 2017, Yunwen Tao and co-authors suggested that the vast diversity and peculiar occurrence of different hydrogen bonds could contribute to the effect. They argued that the number of strong hydrogen bonds increases as temperature is elevated, and that the existence of the small strongly bonded clusters facilitates in turn the nucleation of hexagonal ice when warm water is rapidly cooled down. The authors used vibrational spectroscopy and modelling with density functional theory-optimized water clusters.

Dissolved gases: Cold water can contain more dissolved gases than hot water, which may somehow change the properties of the water with respect to convection currents.
Convection, accelerating heat transfers: Reduction of water density below tends to suppress the convection currents that cool the lower part of the liquid mass; the lower density of hot water would reduce this effect, perhaps sustaining the more rapid initial cooling. Higher convection in the warmer water may also spread ice crystals around faster. Colder temperature may freeze more readily from the top, reducing further heat loss by radiation and air convection; while warmer water freezes from the bottom and sides because of water convection. Some experiments account for this factor.
Distribution function: Strong deviations from the Maxwell–Boltzmann distribution can result in a Mpemba effect in gases and granular fluids.

References

Notes

Bibliography

Auerbach attributes the Mpemba effect to differences in the behaviour of supercooled formerly hot water and formerly cold water.
An extensive study of freezing experiments.

External links

A possible explanation of the Mpemba Effect
An analysis of the Mpemba effect London South Bank University
– History and analysis of the Mpemba effect
An historical interview with Erasto B. Mpemba, Dr Denis G. Osborne and Ray deSouza
High school experiment description, with link to experimental results
in the University of California Usenet Physics FAQ
Mpemba Competition - Royal Society of Chemistry