Non-monotonic Mpemba effect in binary molecular suspensions

Abstract

The Mpemba effect is a phenomenon in which an initially hotter sample cools sooner. In this paper, we show the emergence of a anomalous Mpemba-like effect in a molecular binary mixture immersed in a viscous gas. Namely, a crossover in the temperature evolution when at least one of the samples presents non-monotonic relaxation. The influence of the bath on the dynamics of the particles is modeled via a viscous drag force plus a stochastic Langevin-like term. Each component of the mixture interchanges energy with the bath depending on the mechanical properties of its particles. This discrimination causes the coupling between the time evolution of temperature with that of the partial temperatures of each component. The anomalous Mpemba effect-and its inverse and mixed counterparts-stems from this coupling. In order to obtain analytical results, the velocity distribution functions of each component are approximated by considering multitemperature Maxwellian distributions. The theoretical results derived from the Enskog kinetic theory show an excellent agreement with direct simulation Monte Carlo (DMSC) data.

Mpemba effect in driven granular Maxwell gases

“…Analysis of model-based systems also shows the existence of the Mpemba effect in spin systems [17][18][19][20], three state Markovian systems [21], spin glasses [22], molecular gases in contact with a thermal reservoir [23][24][25] and granular systems [26][27][28][29][30]. For the case of spin systems [17][18][19][20] and three state Markovian systems [21], the initial probability distributions describing the hot and the cold systems correspond to their equilibrium (Boltzmann) distribution and then they are evolved to the equilibrium of the final cold temperature following the Markovian dynamics.…”

“…For the case of molecular gas of single species, in contact with a thermal bath [23], the Mpemba effect is due to the coupling of mean kinetic energy with the excess kurtosis of the velocity distribution function in the presence of non-linear viscous drag. On the other hand, for binary mixture of molecular gases [24,25] in contact with a background fluid, the Mpemba effect is due to the coupling of mean kinetic energies of the individual components of the binary gas. In both cases for molecular gases, the Mpemba effect is illustrated only for non-stationary initial states.…”