Mpemba effect in inertial suspensions

Takada, Satoshi; Hayakawa, Hisao; Santos, Andrés

doi:10.48550/arxiv.2011.00812

Cited by 1 publication

(3 citation statements)

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“…Because of the non-linearity of the evolution equation of the temperature, a crossover is still possible. This curious effect is the so-called mixed Mpemba effect (MME) [11]. Moreover, Fig.…”

Section: Resultsmentioning

confidence: 97%

“…For this reason, from an analytical point of view, simple models have been usually considered to gain some insight into the problem. This is particularly the case of kinetic-theory-based models employed to describe the emergence of Mpembalike effect (and its inverse counterpart, namely when the two initial temperatures are below the asymptotic one) in granular [8][9][10][11]-i.e. with inelastic collisions-and molecular gases [12,14].…”

Section: Introductionmentioning

confidence: 99%

“…The main goal of the present work is to extend the results obtained in [14] to those situations where the temperature presents a non-monotonic relaxation. Following the definition of Takada et al [11], an anomalous Mpemba-like effect will appear when at least one of the two samples whose temperature curves cross presents nonmonotonic relaxation. Namely, when the temperature difference |T (t) − T ex |-of at least one of the samplesincreases at the early stages of the evolution but, at a given time, T (t) reaches the equilibrium value T ex .…”

Section: Introductionmentioning

confidence: 99%

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Non-monotonic Mpemba effect in binary molecular suspensions

González,

Garzó

2020

Preprint

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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.

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Section: Resultsmentioning

confidence: 97%