Revisiting the Mpemba Effect … in Reverse

A while back, I told you about the Mpemba effect, a physics effect demonstrated by a Tanzanian high school student in 1963, Erasto Mpemba, whereby hot water freezes faster than cold water. This is a ‘modern’ (after the 1960s) physics law made in Africa, by an African high schooler, and named after an African (history is full of cases of ‘intellectual’ misnaming i.e. naming the work of an African or others after a European). 

Flag of Tanzania

More recently, scientists John Bechhoefer at Simon Fraser University in Canada, and colleagues, have experimentally demonstrated the Mpemba effect in reverse, also called inverse Mpemba effect, where they observed that under specific conditions a cold particle will heat up faster than a warmer counterpart. The team used optical tweezers to create a tilted double-well potential that confined a colloidal particle, and then measured the particle’s response as a function of its initial temperature. The new measurements indicate the inverse Mpemba effect is much weaker than the conventional, forward effect. The work also experimentally corroborates some of the predicted mechanisms behind both the forward and the inverse effects. The findings were published in the Proceedings of the National Academy of Sciences in January. Excerpts below are from Physics Today; check out the full article which also goes into detail about Erasto Mpemba, and explains the effect in depth. Enjoy!

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Map of Tanzania

In 1963, a 13-year-old Tanzanian student named Erasto Mpemba and his secondary school classmates were tasked with making ice cream. There was limited room in the freezers, and he found himself falling behind other students. His classmates were boiling milk for the treat, then letting the mixture cool before placing it in the freezer. To stay on track, Mpemba put his hot concoction straight into the freezer. Checking on the dessert some time later, he found it perfectly frozen, while his classmates’ remained liquid.

The idea of water freezing faster when it starts at a higher temperature was christened the Mpemba effect after he published the finding in 1969 with physicist Denis Osborne. …

Ice cream
Ice cream

… a decade ago, computational chemists simulated water molecules and observed the Mpemba effect despite the absence of the supposedly necessary mechanisms. Recently, researchers have also observed the effect in other liquids and magnetic alloys, which indicates that causes specific to water, like hydrogen bonds, cannot fully explain the effect. Further complicating the investigation of the Mpemba effect is that many water-based experiments involve a phase transition between liquid and ice, which is dependent on conditions like the container and environment; that makes measurements hard to obtain and extremely difficult to reproduce.

… Bechhoefer and his team used a simple and unambiguous definition to measure the inverse Mpemba effect: the time it takes a system that starts at one equilibrium temperature to reach another, higher temperature. By using a single colloidal particle, they avoided the unnecessary complications of phase transitions in water and other systems.

In their experiment, optical tweezers create a force and thus a potential in which the particle moves. The potential is a tilted double well, … . The particle can settle into two different local minima, the left or the right valley. The potential qualitatively mimics the states of supercooled water: One local minimum has a slightly higher free energy, representing liquid (left), and the other, representing solid ice (right), has a lower free energy because that state is favored.

… To get the same quality of results observed for the forward Mpemba effect, the team had to perform five times the number of trials—5000 rather than 1000—and they believe they know why. In the forward effect, particles fall quickly into one of the two potential wells. The fraction in the left and the fraction in the right, in general, differ from the fractions that should probabilistically be in each well in equilibrium, after the system has settled to its final temperature. That difference leads to a second, slower step, in which particles hop the barrier into the other well until the correct fractions are attained. If the barrier is tall, the process can be slow and create a sharp separation in time between the initial drop into the well and the hopping. When the Mpemba effect is working at its strongest, the hopping is minimal and the relaxation time to the final equilibrium temperature is short.

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