基于振荡座滴测定液滴表面张力的方法

doi:10.11949/0438-1157.20250018

摘要/Abstract

摘要：

表面张力是液体重要的物性参数，是影响各种化学反应和生物反应的关键因素之一，也是化学工程计算中必不可少的基础物性参数。振荡座滴法是一种高精度、高灵敏度地测量液体表面张力的方法。为了探讨基于振荡座滴法测量液体表面张力的有效性和影响因素，本研究在20℃下以蒸馏水、乙醇和乙二醇为实验对象，采用外径不同的不锈钢针头滴落液滴至聚对苯二甲酸乙二醇酯（PET）基板上，通过高速摄像记录液滴的振荡行为，并进行频谱分析。实验结果显示，虽然基于Rayleigh公式计算出的表面张力值普遍高于传统的悬滴法测量值，但振荡频率与液滴体积间存在线性关系。此外，实验还验证了不同图像采集帧率对频谱分析结果的影响。研究表明，振荡座滴法是一种有潜力的测量方法，尤其适用于高温条件下冶金熔体的表面张力测量。然而，目前该方法计算得到的表面张力值仍高于标准值，需要进一步优化模型以提高测量精度。

关键词: 振荡, 悬滴法, 润湿性, 表面张力

Abstract:

Surface tension is an important physical property parameter of liquid, one of the key factors affecting various chemical reactions and biological reactions, and an essential basic physical property parameter in chemical engineering calculations. The oscillating sessile drop method is a highly precise and sensitive technique for measuring the surface tension of liquids. To discuss the effectiveness and influencing factors in measuring liquid surface tension using the oscillating sessile drops method, distilled water, ethanol and glycol used as experimental objects at 20℃, and stainless-steel needles with different outer diameters used to drop droplets on the polyethylene terephthalate (PET) substrate, the oscillation behaviour of droplets was recorded by high-speed camera, and the frequency spectrum was analyzed. The experimental results show that although the surface tension calculated based on Rayleigh equation is generally higher than that measured by traditional pendant-drop method, there is a linear relationship between oscillation frequency and droplet volume. In addition, the experiment also verified the influence of different image acquisition frame rates on the spectrum analysis results. The research shows that the oscillating sessile drop method is a potential measurement method, especially suitable for measuring the surface tension of metallurgical melt at high temperatures. However, the surface tension calculated by this method is still higher than the standard value, which suggests that the model needs to be further optimized to improve the measurement accuracy.

Key words: oscillation, pendant-drop method, wettability, surface tension

中图分类号:

O 647.5

周玉祥, 林巧力. 基于振荡座滴测定液滴表面张力的方法[J]. 化工学报, 2025, 76(8): 4185-4193.

Yuxiang ZHOU, Qiaoli LIN. Determination of surface tension via oscillating sessile drop method[J]. CIESC Journal, 2025, 76(8): 4185-4193.

图/表 11

图1 振荡座滴法实验装置示意图

Fig.1 The schematic diagram of the oscillating sessile drop method experimental device

图2 标准悬滴法测定蒸馏水表面张力

Fig.2 Surface tension of distilled water measured by standard pendant-drop method

图3 液滴振荡过程中不同时刻的形态变化

Fig.3 Morphological evolution of oscillating droplets at selected time points

图4 软件测量得到的液滴高度的时域数据、接触角及对其进行傅里叶变换后得到的频域数据

Fig.4 The time domain data of droplet height, contact angle and frequency domain data obtained by Fourier transform measured by the software

表1 0.45 mm外径针头提取的座滴振荡特征频率的表面张力值

Table 1 Surface tension values from oscillatory drop frequencies extracted using 0.45 mm outer diameter needle

特征频率/Hz	液滴体积/μl	表面张力/(mN/m)
87.682	9.73	88.083
96.841	9.26	102.256
91.511	9.12	89.929
92.316	10.18	102.155
96.032	10.06	109.242
94.032	9.60	99.950
88.147	9.66	88.379

表2 不同液滴大小、特征频率计算的表面张力值

Table 2 Surface tension values calculated from different drop sizes and characteristic frequencies

针头外径/mm	特征频率/Hz	液滴体积/μl	表面张力/(mN/m)
0.45	87.682	9.7302	88.083
0.80	71.753	15.274	92.596
1.26	60.133	22.461	95.635
1.26	63.611	19.620	93.481
4.03	43.262	40.495	89.243

表3 不同采集帧率的特征频率计算的表面张力值（针头外径1.26 mm）

Table 3 Surface tension values calculated from characteristic frequencies at different frame rates （needle outer diameter 1.26 mm）

采集帧率/（帧/s）	特征频率/Hz	液滴体积/μl	表面张力/(mN/m)
1500	62.271	22.521	102.830
1500	60.065	22.674	96.323
1000	59.851	23.355	98.511
260	56.304	23.058	86.072

表4 乙醇与乙二醇表面张力的振荡座滴法与悬滴法测定值对比

Table 4 Surface tension measurement of ethanol and ethylene glycol： oscillating sessile drop versus pendant-drop method

特征频率/Hz	密度/(g/cm³)	液滴体积/μl	表面张力/(mN/m)
特征频率/Hz	密度/(g/cm³)	液滴体积/μl	振荡座滴法	悬滴法
乙醇
104.063	0.789	3.52	35.441	22.3
89.462	0.789	3.67	27.289	22.3
乙二醇
89.761	1.113	5.10	53.852	44.7

图5 特征频率随液滴体积的变化规律

Fig.5 Variation of characteristic frequency with droplet volume

表5 应用式（5）~式（7）计算得到的表面张力和式（9）中的α

Table 5 Surface tension calculated by Eqs. （5）—（7） and α in Eq. （9）

特征频率/Hz	密度/(g/cm³)	液滴体积/μl	表面张力/(mN/m)			α
特征频率/Hz	密度/(g/cm³)	液滴体积/μl	式（5）	式（6）	式（7）	α
95.314	0.998	11.278	120.282	190.005	195.779	1.621
96.841	0.998	9.261	101.955	196.142	165.949	1.648
91.511	0.998	9.124	89.701	175.145	146.003	1.557
92.316	0.998	10.184	101.893	178.240	165.848	1.571
87.682	0.998	9.730	87.821	160.795	142.944	1.492
71.753	0.998	15.274	92.319	172.554	150.264	1.221
60.133	0.998	22.461	95.348	215.829	155.195	1.729
63.611	0.998	17.825	84.674	135.616	137.821	1.370
43.262	0.998	40.495	88.976	218.186	144.823	1.738
104.063	0.789^①	3.520	35.414	30.660	57.469	1.173
89.462	0.789^①	3.670	27.289	28.607	44.283	1.133
89.761	1.113^②	5.100	53.842	126.313	87.374	1.683

图6 悬滴法验证文献[30]中纯铝在750℃的表面张力

Fig.6 Surface tension of pure aluminum verified by pendant-drop method at 750℃ (the original pendant-drop image is from Ref.[30])

参考文献 31

[1]	Wijshoff H. Drop dynamics in the inkjet printing process[J]. Current Opinion in Colloid & Interface Science, 2018, 36: 20-27.
[2]	Basilio P A, Torres Rojas A M, Corvera Poiré E, et al. Stream of droplets as an actuator for oscillatory flows in microfluidics[J]. Microfluidics and Nanofluidics, 2019, 23(5): 64.
[3]	Haber E, Douvidzon M, Maayani S, et al. A liquid mirror resonator[J]. Micromachines (Basel), 2023, 14(3): 624.
[4]	Wu N, Dai J L, Micale F J. Dynamic surface tension measurement with a dynamic wilhelmy plate technique[J]. Journal of Colloid and Interface Science, 1999, 215(2): 258-269.
[5]	Kim D, Jeong M A, Kang K, et al. Gravitational effect on the advancing and receding angle of a 2D Cassie-Baxter droplet on a textured surface[J]. Langmuir, 2020, 36(21): 6061-6069.
[6]	Mills K C, Brooks R F. Measurements of thermophysical properties in high temperature melts[J]. Materials Science and Engineering: A, 1994, 178(1/2): 77-81.
[7]	Kitahata H, Tanaka R, Koyano Y, et al. Oscillation of a rotating levitated droplet: analysis with a mechanical model[J]. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, 2015, 92(6): 062904.
[8]	Xiao X, Hyers R W, Wunderlich R K, et al. Deformation induced frequency shifts of oscillating droplets during molten metal surface tension measurement[J]. Applied Physics Letters, 2018, 113(1): 011903.
[9]	Fahimi K, Mädler L, Ellendt N. Measurement of surface tension with free-falling oscillating molten metal droplets: a numerical and experimental investigation[J]. Experiments in Fluids, 2023, 64(7): 133.
[10]	Strutt J W. Ⅵ. On the capillary phenomena of jets[J]. Proceedings of the Royal Society of London, 1879, 29(196/197/198/199): 71-97.
[11]	Lamb H. Hydrodynamics[M]. 6th ed. Cambridge: Cambridge University Press, 1932.
[12]	Milne A J B, Defez B, Cabrerizo-Vílchez M, et al. Understanding (sessile/constrained) bubble and drop oscillations[J]. Advances in Colloid and Interface Science, 2014, 203: 22-36.
[13]	Liang G T, Yu H B, Chen L Z, et al. Spreading and oscillation induced by liquid drop impacting onto sessile drop[J]. European Journal of Mechanics-B/Fluids, 2020, 79: 247-254.
[14]	Deepu P, Chowdhuri S, Basu S. Oscillation dynamics of sessile droplets subjected to substrate vibration[J]. Chemical Engineering Science, 2014, 118: 9-19.
[15]	Ding D, Bostwick J B. Pressure modes of the oscillating sessile drop[J]. Journal of Fluid Mechanics, 2022, 944: R1.
[16]	Korenchenko A E, Malkova J P. Numerical investigation of phase relationships in an oscillating sessile drop[J]. 2015, 27(10): 102104.
[17]	Singha P, Nguyen N K, Zhang J, et al. Oscillating sessile liquid marble — a tool to assess effective surface tension[J]. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2021, 627: 127176.
[18]	Mettu S, Chaudhury M K. Motion of drops on a surface induced by thermal gradient and vibration[J]. Langmuir, 2008, 24(19): 10833-10837.
[19]	Bashforth F, Adams J C. An Attempt to Test the Theories of Capillary Action by Comparing the Theoretical and Measured Forms of Drops of Fluid[M]. Cambridge: Cambridge University Press, 1883.
[20]	张禹负, 刘华. 一种水平旋转滴法测定接触角的方法及装置: 100380111C[P]. 2008-04-09.
	Zhang Y F, Liu H. A method and device for measuring contact angle using horizontal rotating droplet method: 100380111C[P]. 2008-04-09.
[21]	周斌, 李思维, 陈志勇, 等. 完全轮廓法计算液体表面张力的改进[J]. 清华大学学报(自然科学版), 2016, 56(12): 1352-1356.
	Zhou B, Li S W, Chen Z Y, et al. Full-profile fit pendent drop method for surface tension measurements[J]. Journal of Tsinghua University (Science and Technology), 2016, 56(12): 1352-1356.
[22]	de Ruiter J, Lagraauw R, van den Ende D, et al. Wettability-independent bouncing on flat surfaces mediated by thin air films[J]. Nature Physics, 2015, 11: 48-53.
[23]	Birdi K S. Handbook of Surface and Colloid Chemistry[M]. 2nd ed. Boca Raton, Fla.: CRC Press, 2003.
[24]	Costalonga M, Brunet P. Directional motion of vibrated sessile drops: a quantitative study[J]. Physical Review Fluids, 2020, 5(2): 023601.
[25]	McHale G, Elliott S J, Newton M I, et al. Levitation-free vibrated droplets: resonant oscillations of liquid marbles[J]. Langmuir, 2009, 25(1): 529-533.
[26]	Lim T, Han S, Chung J, et al. Experimental study on spreading and evaporation of inkjet printed pico-liter droplet on a heated substrate[J]. International Journal of Heat and Mass Transfer, 2009, 52(1/2): 431-441.
[27]	Sangiorgi R, Caracciolo G, Passerone A. Factors limiting the accuracy of measurements of surface tension by the sessile drop method[J]. Journal of Materials Science, 1982, 17(10): 2895-2901.
[28]	Sharp J S. Resonant properties of sessile droplets; contact angle dependence of the resonant frequency and width in glycerol/water mixtures[J]. Soft Matter, 2012, 8(2): 399-407.
[29]	Korenchenko A E, Beskachko V P. Oscillations of a sessile droplet in open air[J]. Physics of Fluids, 2013, 25(11): 112106.
[30]	Sun Y Q, Yousefi E, Kunwar A, et al. Study of the interfacial reactions controlling the spreading of Al on Ni[J]. Applied Surface Science, 2022, 571: 151272.
[31]	Gale W F, Totemeier T C.Smithells Metals Reference Book[M]. 8th ed. Amsterdam: Elsevier, 2004.