Tolman length of simple droplet: Theoretical study and molecular dynamics simulation

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 Rs 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.

Relation between Tolman length and isothermal compressibility for simple liquids

The Tolman length δ 0 of a liquid with a plane surface has attracted increasing theoretical attention in recent years,but the expression of Tolman length in terms of observable quantities is still not very clear.In 2001,Bartell gave a simple expression of Tolman length δ 0 in terms of isothermal compressibility.However,this expression predicts that Tolman length is always negative,which is contrary to the results of molecular dynamics simulations（MDS） for simple liquids.In this paper,this contradiction is analyzed and the reason for the discrepancy in the sign is found.In addition,we introduce a new expression of Tolman length in terms of isothermal compressibility for simple fluids not near the critical points under some weak restrictions.The Tolman length of simple liquids calculated by using this formula is consistent with that obtained using MDS regarding the sign.

Thermodynamic theory of the Tolman's length

There still exists controversy on the sign and magnitude of the Tolman＇s length and the Tolman＇s gap. Further experimental, computational and theoretical investigations on them are needed to solve this problem. In 2006, Blokhuis and Kuipers obtained a rigorous relationship between the Tolman＇s length and other thermodynamic quantities for the single-component liquid-vapour system. In the present paper, we derive two general relationships between the Tolman＇s length and other thermodynamic quantities for the single-component liquid vapour system. The relationship derived by Blokhuis and Kuipers and an earlier result turn out to be two special cases of our results.

气泡Tolman长度的热力学分析

以气泡作为研究对象,采用热力学推导的方法,建立了气泡Tolman长度的表达形式,并与有关文献中液滴Tolman长度和等温压缩系数关系式进行比较,指出气泡Tolman长度与气相等温压缩系数以及气液两相密度比值有关。另外,讨论了纳米气泡表面张力的取值情况。

纳米液滴Tolman长度的分子动力学计算

给出球状液滴表面张力和等摩尔面和张力面的计算公式,用分子动力学模拟了温度T*=0.65不同粒子数的球状液滴,计算了Tolman长度δ;计算同一温度下平液面的表面张力,利用Tolman方程计算δ。结果都显示δ取正值,随液滴半径增加而减小。

用改进的重正化群理论计算缔合流体的临界表面性质

针对通常的统计缔合流体(SAFT)状态方程结合全局重正化群理论不能正确预测缔合流体的临界非对称性的问题,提出用微扰链-统计缔合流体(PC-SAFT)方程结合改进的全局重正化群方法描述缔合流体的临界热力学性质。通过改写原始重正化群理论的哈密顿量,以及对自由能的偏导数建立重正化迭代过程,计算包括醇、醋酸、水在内的各种单组分缔合流体的表面张力,以及与表面张力曲率修正密切相关的Tolman长度。结果表明PC-SAFT方程+全局重正化群的方法可以准确预测缔合流体的临界表面性质,所得结果可用于改善经典成核理论对成核速率的预测。

Size-dependent surface tension of a cylindrical nanobubble in liquid Ar

In view of the continued disputes on the fundamental question of whether the surface tension of a vapour bubble in liquid argon increases, or decreases, or remains unchanged with the increase of curvature radius, a cylindrical vapour bubble of argon is studied by molecular dynamics simulation in this paper instead of spherical vapour bubble so as to reduce the statistical error. So far, the surface tension of the cylindrical vapour bubble has not been studied by molecular dynamics simulation in the literature. Our results show that the surface tension decreases with radius increasing. By fitting the Tolman equation with our data, the Tolman length σ = -0.6225 sigma is given under cut-off radius 2.5σ, where σ = 0.3405 nm is the diameter of an argon atom. The Tolman length of Ar being negative is affirmed and the Tolman length of Ar being approximately zero given in the literature is negated, and it is pointed out that this error is attributed to the application of the inapplicable empirical equation of state and the neglect of the difference between surface tension and an equimolar surface.

表面张力的尺度效应与托尔曼长度

介绍了表面张力的尺度效应、托尔曼长度、分子动力学和密度泛函方法.由于文献中所得结论有一定的分歧,所以表面张力尺度效应的研究有理论和实践意义.

基于Tolman长度的Lucas-Washburn渗吸模型改进及数值模拟

经典的Lucas-Washburn(L-W)渗吸模型用Young-Laplace方程计算毛管压力,但该方程在管径细小情形得出的毛管压力值与真实值存在较大偏差。本文运用Tolman长度改进Young-Laplace方程,提出一种改进的L-W渗吸模型,并将等截面圆管扩展至任意变化截面圆管,得到变截面圆管中润湿流体注入长度随时间变化的数学模型。该模型为二阶非线性常微分方程,无法求出解析解,为此提出一种数值解法。选取截面变化的毛细管道,通过数值模拟计算出润湿液体注入长度与时间的对应关系,对Tolman长度的改进效果进行检验和分析。结果表明:在研究范围内Tolman长度对L-W渗吸模型的改进效果表现出毛细管道半径越小,效果越明显的规律。圆管局部缩小能改变渗吸水运动状态,依次呈现出三种运动模式;圆管局部扩大会缓慢改变渗吸水运动状态,只呈现单一运动模式。