Mpemba-like effect in driven binary mixtures

Abstract

The Mpemba effect occurs when two samples at different initial temperatures evolve in such a way that the temperatures cross each other during the relaxation towards equilibrium. In this paper we show the emergence of a Mpemba-like effect in a molecular binary mixture in contact with a thermal reservoir (bath). The interaction between the gaseous particles of the mixture and the thermal reservoir is modeled via a viscous drag force plus a stochastic Langevin-like term. The presence of the external bath couples the time evolution of the total and partial temperatures of each component allowing the appearance of the Mpemba phenomenon, even when the initial temperature differences are of the same order of the temperatures themselves. Analytical results are obtained by considering multitemperature Maxwellian approximations for the velocity distribution functions of each component. The theoretical analysis is carried out for initial states close to and far away (large Mpemba-like effect) from equilibrium. The former situation allows us to develop a simple theory where the time evolution equation for the temperature is linearized around its asymptotic equilibrium solution. This linear theory provides an expression for the crossover time. We also provide a qualitative description of the large Mpemba effect. Our theoretical results agree very well with computer simulations obtained by numerically solving the Enskog kinetic equation by means of the direct simulation Monte Carlo method and by performing molecular dynamics simulations. Finally, preliminary results for driven granular mixtures also show the occurrence of a Mpemba-like effect for inelastic collisions.

16 pages; 7 figures; the title has been changed; a new section devoted to granular mixtures has been added; to be published in Physics of Fluids

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• Anomalous thermal relaxation of Langevin particles in a piecewise-constant potential
• Mpemba effect in a Langevin system: population statistics, metastability and other exact results
• Strong non-exponential relaxation and memory effects in a fluid with non-linear drag
• Mpemba meets Newton: Exploring the Mpemba and Kovacs effects in the time-delayed cooling law
• Time-dependent homogeneous states of binary granular suspensions
• Diffusion of intruders in granular suspensions: Enskog theory and random walk interpretation
• Kinetic Theory and Memory Effects of Homogeneous Inelastic Granular Gases under Nonlinear Drag
• Mpemba effect in the relaxation of an active Brownian particle in a trap without metastable states
• The Mpemba effect in the Descartes protocol: A time-delayed Newton's law of cooling approach
• Anomalous thermal relaxation in warm ion plasmas
• Mpemba-like effect protocol for granular gases of inelastic and rough hard disks
• Kinetic glass transition in granular gases and non-linear molecular fluids
• Thermal versus entropic Mpemba effect in molecular gases with nonlinear drag