Deconstructing Temperature Gradients across Fluid Interfaces: The Structural Origin of the Thermal Resistance of Liquid-Vapor Interfaces

The interfacial thermal resistance determines condensation-evaporation processes and thermal transport across material-fluid interfaces. Despite its importance in transport processes, the interfacial structure responsible for the thermal resistance is still unknown. By combining nonequilibrium molecular dynamics simulations and interfacial analyses that remove the interfacial thermal fluctuations we show that the thermal resistance of liquid-vapor interfaces is connected to a low density fluid layer that is adsorbed at the liquid surface. This thermal resistance layer (TRL) defines the boundary where the thermal transport mechanism changes from that of gases (ballistic) to that characteristic of dense liquids, dominated by frequent particle collisions involving very short mean free paths. We show that the thermal conductance is proportional to the number of atoms adsorbed in the TRL, and hence we explain the structural origin of the thermal resistance in liquid-vapor interfaces.

Figure 1

Schematic diagram showing the periodic simulation cell containing a liquid-vapor interface. The liquid phase is in the center of the box. The spheres represent the atoms. Kinetic energy is extracted in the center of the liquid phase (blue highlighted region) and added in the center of the gas phase (red highlighted regions) at a constant rate. The arrows indicate the direction of the resultant energy flux. It should be noted that the actual simulation cells used in the simulations are significantly more elongated in the $z$ direction than in this snapshot.

Figure 2

Top-left panels: Intrinsic temperature profiles [$\tilde{T}(z)$, red line] and intrinsic density profiles [$\tilde{\rho }(z)$, black line] for systems at different average temperatures, systems I (top), II (middle), and III (bottom). Top-right panels: Absolute values of the gradient of the intrinsic temperature profiles [$|\nabla \tilde{T}(z)|$, red line] and intrinsic density profiles [$\tilde{\rho }(z)$, black line] shifted and scaled to highlight the adsorbed layer for systems I (top), II (middle), and III (bottom). The numerical derivative of the temperature profile is calculated from data averaged over a $0.2\sigma$ window with the derivative further smoothed over a window of the same size. The labels 1, 2, 3 refer to the fluid layers represented in the bottom panel. Bottom-central panel: Representative surface configuration for system III. Atoms at the IS are represented in cyan. The atoms colored in blue represent the first layer in the vapor phase, and the yellow atoms the first liquid layer.

Figure 3

Thermal conductance $G_K$ against adsorption $\mathrm{\Gamma }$. The red line is a guide for the eye. The inset plot illustrates the calculation of the adsorption from Eq. (5) for system II. The shaded region is subtracted from the integral over the intrinsic density profile.