Tolman length of simple droplet: Theoretical study and molecular dynamics simulation
Shu-Wen Cui(崔树稳)1,2, Jiu-An Wei(魏久安)3, Qiang Li(李强)1, Wei-Wei Liu(刘伟伟)1, Ping Qian(钱萍)4,†, and Xiao Song Wang(王小松)5
1 Department of Physics and Information Engineering, Cangzhou Normal University, Cangzhou 061001, China; 2 State Key Laboratory of Nonlinear Mechanics (LNM) and Key Laboratory of Microgravity, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China; 3 Silfex, a Division of Lam Research, 950 South Franklin Street, Eaton, Ohio 45320, USA; 4 Department of Physics, University of Science and Technology Beijing, Beijing 100083, China; 5 Institute of Mechanics and Power Engineering, Henan Polytechnic University, Jiaozuo 454003, China
Abstract In 1949, Tolman found the relation between the surface tension and Tolman length, which determines the dimensional effect of the surface tension. Tolman length is the difference between the equimolar surface and the surface of tension. In recent years, the magnitude, expression, and sign of the Tolman length remain an open question. An incompressible and homogeneous liquid droplet model is proposed and the approximate expression and sign for Tolman length are derived in this paper. We obtain the relation between Tolman length and the radius of the surface of tension (R s) and found that they increase with the R s decreasing. The Tolman length of plane surface tends to zero. Taking argon for example, molecular dynamics simulation is carried out by using the Lennard-Jones (LJ) potential between atoms at a temperature of 90 K. Five simulated systems are used, with numbers of argon atoms being 10140, 10935, 11760, 13500, and 15360, respectively. By methods of theoretical study and molecular dynamics simulation, we find that the calculated value of Tolman length is more than zero, and it decreases as the size is increased among the whole size range. The value of surface tension increases with the radius of the surface of tension increasing, which is consistent with Tolman's theory. These conclusions are significant for studying the size dependence of the surface tension.
Fund: Project supported by the National Key Research and Development Program of China (Grant No. 2016YFB0700500), the Scientific Research and Innovation Team of Cangzhou Normal University, China (Grant No. cxtdl1907), the Key Scientific Study Program of Hebei Provincial Higher Education Institution, China (Grant No. ZD2020410), the Cangzhou Natural Science Foundation, China (Grant No. 197000001), and the General Scientific Research Fund Project of Cangzhou Normal University, China (Grant No. xnjjl1906).
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