Mpemba effect in inertial suspensions

TL;DR

This paper investigates the Mpemba effect in inertial suspensions under shear, revealing normal and anomalous types, supported by kinetic theory and simulations, and also confirms the inverse Mpemba effect with mixed heating and cooling behaviors.

Contribution

It introduces a kinetic theory model for the Mpemba effect in inertial suspensions, identifying two classes and confirming the inverse effect through simulations.

Findings

Normal Mpemba effect observed due to initial viscous heating differences.

Anomalous Mpemba effect where a slower cooling state overtakes a colder state.

Existence of inverse Mpemba effect with mixed heating and cooling during relaxation.

Abstract

The Mpemba effect (a counterintuitive thermal relaxation process where an initially hotter system may cool down to the steady state sooner than an initially colder system) is studied in terms of a model of inertial suspensions under shear. The relaxation to a common steady state of a suspension initially prepared in a quasi-equilibrium state is compared with that of a suspension initially prepared in a nonequilibrium sheared state. Two classes of Mpemba effect are identified, the normal and the anomalous one. The former is generic, in the sense that the kinetic temperature starting from a cold nonequilibrium sheared state is overtaken by the one starting from a hot quasi-equilibrium state, due to the absence of initial viscous heating in the latter, resulting in a faster initial cooling. The anomalous Mpemba effect is opposite to the normal one since, despite the initial slower cooling of the nonequilibrium sheared state, it can eventually overtake an initially colder quasi-equilibrium state. The theoretical results based on kinetic theory agree with those obtained from event-driven simulations for inelastic hard spheres. It is also confirmed the existence of the inverse Mpemba effect, which is a peculiar heating process, in these suspensions. More particularly, we find the existence of a mixed process in which both heating and cooling can be observed during relaxation.