Gravity-Induced Modulation of Negative Differential Thermal Resistance in Fluids

Abstract

We investigate how gravity influences negative differential thermal resistance (NDTR) in fluids modeled by multiparticle collision dynamics. In the integrable case, we derive the heat flux formula for the system exhibiting the NDTR effect, and show that by introducing a gravity along the direction of the thermodynamic force, the temperature difference required for the occurrence of NDTR can be greatly reduced. Meanwhile, we also demonstrate that the heat-bath-induced NDTR mechanism -- originally found to be applicable only to weakly interacting systems -- can now operate in systems with stronger interactions due to the presence of gravity, and further remains robust even in mixed fluids. These results provide new insights into heat transport and establish a theoretical foundation for designing fluidic thermal devices that harness the NDTR effect under gravity.

Figures (8)

• Figure 1: Schematic illustration of the 2D fluid model composed of interacting point particles, based on multiparticle collision dynamics. The dashed-line cells indicate the spatial partitioning used to model collision events. A gravitational field is applied in the $y$-direction, and the system is coupled to the upper and lower heat baths maintained at fixed temperatures $T_U$ and $T_L$, respectively (see the main text for further details).
• Figure 2: In the integrable case, (a) heat flux $J$ and (b) collision frequency $f$ as functions of the temperature difference $\Delta T$; (c) particle number density $\rho(h)/\rho_0$ and (d) temperature $T(h)$ as functions of height $h$ at $\Delta T = 0$, for different values of $g$. Here, $\rho_0$ is the particle number density at zero gravitational potential energy. In (a) and (b): solid curves in different colors show the analytical results from Eq. (\ref{['J0']}) and Eq. (\ref{['f']}), respectively; for reference, the dot-dashed line indicates the critical temperature difference $(\Delta T)_{\mathrm{cr}} = 0.75$ for $g = 0$, while the dashed line connects the corresponding $(\Delta T)_{\mathrm{cr}}$ values for different $g$, where NDTR emerges. In (c), the solid lines represent the Boltzmann distribution $\rho(h)=\rho_0e^{-mgh/k_BT}$.
• Figure 3: Results are shown for varying interaction time scales $\tau$: heat flux $J$ as a function of temperature difference $\Delta T$ for (a) $g=0$ and (d) $g=0.2$; particle number density $\rho(h)$ as a function of height $h$ at $\Delta T = 0.75$ for (b) $g=0$ and (e) $g=0.2$; temperature profile $T(h)$ as a function of height $h$ at $\Delta T = 0.75$ for (c) $g=0$ and (f) $g=0.2$ . In (a) and (d), the red curve shows Eq. (\ref{['J0']}), and the dot-dashed line marks the critical temperature difference $(\Delta T)_{\mathrm{cr}}$ in the noninteracting limit ($\tau = \infty$). Semi-log plot in the inset of (e) reveals exponential density decay with height.
• Figure 4: $J$ as a function of $\Delta T$ for binary fluid systems: (a) varying $p$ at fixed $M=12$; (b) varying $M$ at fixed $p=0.5$. For reference, the dot-dashed line in (a) and (b) indicates the critical temperature difference $(\Delta T)_{\mathrm{cr}}$ for the onset of NDTR. Parameters: $g=0.01$, $\tau=1$.
• Figure 5: Schematic of the 2D multiparticle collision fluid model with gravity counter to the thermodynamic force.