Non-monotonic Mpemba effect in binary molecular suspensions

TL;DR

This paper demonstrates a non-monotonic Mpemba-like effect in a binary molecular mixture immersed in a viscous gas, where temperature relaxation exhibits crossover behavior due to component-specific energy exchange with the bath.

Contribution

It introduces the first theoretical and simulation analysis of a non-monotonic Mpemba effect in molecular mixtures influenced by viscous drag and stochastic forces.

Findings

The non-monotonic Mpemba effect arises from coupling between temperature and partial temperatures.

Analytical results from Enskog kinetic theory agree well with Monte Carlo simulations.

The effect includes inverse and mixed Mpemba phenomena depending on system parameters.

Abstract

The Mpemba effect is a phenomenon in which an initially hotter sample cools sooner. In this paper, we show the emergence of a non-monotonic 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 non-monotonic 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.