Measuring heat flux beyond Fourier's law

A perspective on the microscopic pressure (stress) tensor: History, current understanding, and future challenges

The pressure tensor (equivalent to the negative stress tensor) at both microscopic and macroscopic levels is fundamental to many aspects of engineering and science, including fluid dynamics, solid mechanics, biophysics, and thermodynamics. In this Perspective, we review methods to calculate the microscopic pressure tensor. Connections between different pressure forms for equilibrium and nonequilibrium systems are established. We also point out several challenges in the field, including the historical controversies over the definition of the microscopic pressure tensor; the difficulties with many-body and long-range potentials; the insufficiency of software and computational tools; and the lack of experimental routes to probe the pressure tensor at the nanoscale. Possible future directions are suggested.

Thermal transport mechanism at a solid-liquid interface based on the heat flux detected at a subatomic spatial resolution

Heat flux is a fundamental quantity in thermal science and engineering and is essential for understanding thermal transport phenomena. In this study, the heat flux in a solid-liquid interfacial region is obtained in a three-dimensional (3D) space at a subatomic spatial resolution based on classical molecular dynamics, yielding a 3D structure of the heat flux between the solid and liquid layers in contact. The results using the Lennard-Jones potential reveal the directional qualities of the heat flux, which are significantly dependent on the subatomic stresses in the structures of condensed phase systems. The heat flux and stress at the subatomic scale are related to the macroscopic transport quantities, which can be obtained using distribution functions; the stress and energy flux properties at the subatomic scale are comprehensively investigated using a single-interaction-based stress and energy flux to determine the origin of the thermal transport mechanism at the solid-liquid interface. The findings reveal that the density of states due to the stress caused by a single interaction exhibits a bandlike behavior. The net energy transport comprises positive and negative energy transport inside and outside the band. In addition, this is related to the intrinsic transport property of the atoms and molecules at the solid-liquid interface at the subatomic scale. The difference between the energy transport rates when a solid atom in the vicinity of the interface is near to or far from the liquid phase is the origin of the energy transport mechanism at the solid-liquid interface. 3D analysis of the heat flux and stress is carried out by varying the interaction strengths between the liquid molecules and solid atoms at the solid-liquid interface. This reveals that the directional quality of transport quantities is high at strong interaction strengths, thus indicating enhanced thermal transport. Furthermore, the influence of the temperature gradient in the system suggests that the energy transport imbalance between inside and outside the stress band in a high-stress field at the subatomic scale induces the net thermal transport across the interface in the nonequilibrium state.

Room temperature second sound in cumulene

Second sound is known as the thermal transport regime occurring in a wave-like fashion, usually identified in a limited number of materials only at cryogenic temperatures. Here we show that second sound in a μm-long carbon chain (cumulene) might occur even at room temperature. To this aim, we calibrate a many-body force field on the first principles calculated phonon dispersion relations of cumulene and, through molecular dynamics, we mimic laser-induced transient thermal grating experiments. We provide evidence that by tuning temperature as well as the space modulation of its initial profile we can reversibly drive the system from a wave-like to a diffusive-like thermal transport. By following three different theoretical methodologies (molecular dynamics, the Maxwell-Cattaneo-Vernotte equation, and heat transport microscopic theory) we estimate for cumulene a second sound velocity in the range of 2.4-3.2 km s-1.

Hydrodynamics across a fluctuating interface

Understanding what happens inside the rippling and dancing surface of a liquid remains one of the great challenges of fluid dynamics. Using molecular dynamics, we can pick apart the interface structure and understand surface tension. In this work, we derive an exact mechanical formulation of hydrodynamics for a liquid-vapor interface using a control volume, which moves with the surface. This mathematical framework provides the local definition of hydrodynamic fluxes at any point on the surface. These are represented not only by the flux of molecules and intermolecular interactions acting across the surface but also as a result of the instantaneous local curvature and movement of the surface itself. By explicitly including the surface dynamics in the equations of motion, we demonstrate an exact balance between kinetic and configurational pressure normal to the surface. The hydrodynamic analysis makes no assumptions regarding the probability distribution function, so it is valid for any system arbitrarily far from thermodynamic equilibrium. The presented equations provide a theoretical basis for the study of time-evolving interface phenomena, such as bubble nucleation, droplet dynamics, and liquid-vapor instabilities.