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The negative differential thermal resistance (NDTR) effect refers to a phenomenon that may take place in a heat transport system where the heat current counterintuitively decreases as the temperature difference between heat baths increases. Understanding and controlling the NDTR properties of out-of-equilibrium systems and using them to design new functional thermal devices are the major challenges of modern science and technology, which has important theoretical significance and application prospects. Up to now, the various lattice models representing solid materials have been taken to study the NDTR properties, but the fluid models have not received enough attention. It has recently been shown that in one-dimensional hard-point gas models representing fluids, there is a mechanism for NDTR induced by heat baths. The mechanism for NDTR in such a system depends on the simple fact that decreasing the temperature of the cold bath can weaken the motion of particles and decrease the collision rate between particles and the hot bath, thus impeding thermal exchange between the cold and hot baths. In this paper, we study how this mechanism works in more general two-dimensional gas models described by multi-particle collision dynamics. The gas models we consider are in a finite rectangular region of two-dimensional space with each end in contact with a heat bath. Based on the analytical results and numerical simulations, we show that the mechanism underlying NDTR induced by heat baths is also in effect for two-dimensional gas models and is applicable for describing systems with small sizes and weak interactions. Our result, together with that previously obtained in one-dimensional gas models, provides strong evidence that gas systems can exhibit NDTR by decreasing the temperature of the heat bath, which sheds new light on the exploring direction for developing various fluidic thermal control devices.
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Keywords:
- gas model /
- negative differential thermal resistance /
- transport /
- multi-particle collision
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图 1 由多粒子碰撞动力学描述的与热库耦合的二维气体模型示意图
Figure 1. Schematic drawing of the two-dimensional gas model described by the multi-particle collision dynamics. The system is coupled at its left- and right-hand ends to two thermal baths of fixed temperature
$T_{\rm{L}}$ and$T_{\rm{R}}$ . The$ x $ coordinate goes along the channel and$ y $ is perpendicular to it
图 2 不同时间间隔
$ \tau $ 下, 热流$ J $ 与温差$ \Delta T $ 的函数关系. 红色曲线为(12)式给出的解析结果, 符号数据点是系统尺寸$ L = 64 $ 时的数值结果. 黑色点虚线是出现负微分热阻现象的参考线Figure 2. The heat current
$ J $ as a function of temperature difference$ \Delta T $ for various time interval$ \tau $ . The red curve is the analytical result given by Eq. (12). The symbols are for the numerical results and obtained for$ L = 64 $ , and the black dashed line is drawn for reference
图 3 不同系统尺寸L下, 热流
$ J $ 与温差$ \Delta T $ 的函数关系. 这里时间间隔$ \tau = 1.0 $ Figure 3. The heat current
$ J $ as a function of temperature difference$ \Delta T $ for various system size L. Here we set$ \tau = 1.0 $ -
[1] Li N B, Ren J, Wang L, Zhang G, Hänggi P, Li B W 2012 Rev. Mod. Phys. 84 1045
Google Scholar
[2] Lepri S 2016 Thermal Transport in Low Dimensions: From Statistical Physics to Nanoscale Heat Transfer (Berlin: Springer)
[3] Benenti G, Lepri S, Livi R 2020 Front. Phys. 8 292
Google Scholar
[4] Zhang Z W, Ouyang Y L, Cheng Y, Chen J, Li N B, Zhang G 2020 Phys. Rep. 860 1
Google Scholar
[5] Yang S, Wang J, Dai G L, Yang F B, Huang J P 2021 Phys. Rep. 908 1
Google Scholar
[6] 赵鸿, 王矫, 张勇, 贺达海, 符维成 2021 中国科学: 物理学 力学 天文学 51 030012
Google Scholar
Zhao H, Wang J, Zhang Y, He D H, Fu W C 2021 Sci Sin-Phys. Mech. Astron. 51 030012
Google Scholar
[7] 吴祥水, 汤雯婷, 徐象繁 2020 物理学报 69 196602
Google Scholar
Wu X S, Tang W T, Xu X F 2020 Acta Phys. Sin. 69 196602
Google Scholar
[8] Li B W, Wang L, Casati G 2004 Phys. Rev. Lett. 93 184301
Google Scholar
[9] Li B W, Wang L, Casati G 2006 Appl. Phys. Lett. 88 143501
Google Scholar
[10] Chang C, Okawa D, Majumdar A, Zettl A 2006 Science 314 1121
Google Scholar
[11] Wang L, Li B W 2007 Phys. Rev. Lett. 99 177208
Google Scholar
[12] Wang L, Li B W 2008 Phys. Rev. Lett. 101 267203
Google Scholar
[13] Wu J P, Wang L, Li B W 2012 Phys. Rev. E 85 061112
Google Scholar
[14] Yang N, Li N B, Wang L, Li B W 2007 Phys. Rev. B 76 020301(R
Google Scholar
[15] Pereira E 2010 Phys. Rev. E 82 040101(R
[16] He D H, Buyukdagli S, Hu B B 2009 Phys. Rev. B 80 104302
Google Scholar
[17] He D H, Ai B Q, Chan H K 2010 Phys. Rev. E 81 041131
Google Scholar
[18] Zhong W R 2010 Phys. Rev. E 81 061131
Google Scholar
[19] Zhong W R, Zhang M P, Ai B Q, Hu B B 2011 Phys. Rev. E 84 031130
Google Scholar
[20] Zhong W R, Yang P, Ai B Q, Shao Z G, Hu B B 2009 Phys. Rev. E 79 050103(R
Google Scholar
[21] Zhao Z G, Yang L, Chan H K, Hu B B 2009 Phys. Rev. E 79 061119
Google Scholar
[22] Segal D, Yang L, Chan H K, Hu B B 2006 Phys. Rev. B 73 205415
Google Scholar
[23] Lo W C, Wang L, Li B W 2008 J. Phys. Soc. Jpn. 77 054402
Google Scholar
[24] Chan H K, He D H, Hu B B 2014 Phys. Rev. E 89 052126
[25] Fu W C, Jin T, He D H, Qu S X 2014 Physica A 433 211
[26] Mendonca M, Pereira E 2015 Phys. Lett. A 379 1983
Google Scholar
[27] Ruan Q L, Wang L 2020 Phys. Rev. Res. 2 023087
Google Scholar
[28] Yang Y, Ma D K, Zhao Y S, Zhang L F 2020 J. Appl. Phys. 127 195301
Google Scholar
[29] Luo R X 2019 Phys. Rev. E 99 032138
Google Scholar
[30] Gompper G, Ihle T, Kroll D M, Winkler R G 2009 Multi-Particle Collision Dynamics: A Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids (Berlin: Springer)
[31] Cintio D P, Livi R, Lepri S, Ciraolo G 2017 Phys. Rev. E 95 043203
Google Scholar
[32] Luo R X, Benenti G, Casati G, Wang J 2020 Phys. Rev. Research 2 022009(R
Google Scholar
[33] Lebowitz J L, Spohn H 1978 J. Stat. Phys. 19 633
Google Scholar
[34] Tehver T, Toigo F, Koplik J, Banavar J R 1998 Phys. Rev. E 57 17(R
Google Scholar
[35] Luo R X 2020 Phys. Rev. E 102 052104
Google Scholar
[36] Luo R X, Huang L S, Lepri S 2021 Phys. Rev. E 103 L050102
Google Scholar
[37] Squires T M, Quake S R 2005 Rev. Mod. Phys. 77 977
Google Scholar
[38] Schoch R B, Han J, Renaud P 2008 Rev. Mod. Phys. 80 839
Google Scholar
[39] Li L, Mo J, Li Z 2015 Phys. Rev. Lett. 115 134503
Google Scholar
[40] Hu B B, Yang L, Zhang Y 2006 Phys. Rev. Lett. 97 124302
Google Scholar
[41] 王军, 李京颍, 郑志刚 2010 物理学报 59 476
Google Scholar
Wang J, Li J Y, Zheng Z G 2010 Acta Phys. Sin. 59 476
Google Scholar
[42] Wang J, Zheng Z G 2010 Phys. Rev. E 81 011114
Google Scholar
[43] Brantut J P, Grenier C, Meineke J, Stadler D, Krinner S, Kollath C, Esslinger T, Georges A 2013 Science 342 713
Google Scholar
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