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滤膜在过滤和分离领域具有非常广泛的使用, 但滤膜对溶液中的组分具有吸引或排斥作用, 导致粒子产生定向运动, 进而在膜附近产生粒子富集或“粒子禁区”等截然不同的效应, 目前对此认识尚不清楚, 粒子浓度分布不能实时准确测量是其中最大的困难. 本文以表面带负电荷的胶体粒子为模型物质, 利用胶体粒子结晶后粒子浓度可以实时原位测量的优势, 研究了纤维素滤膜对粒子运动行为的影响规律. 研究结果发现带电微粒会自发地在滤膜表面产生富集, 滤膜中微量阴阳离子释放导致的扩散泳效应是微粒朝向滤膜产生定向运动的主要原因, 基于扩散泳和粒子扩散两种机制构建了粒子运动方程和模型, 数值计算结果和实验结果定性一致. 此外, 粒子除了朝向滤膜的纵向运动之外, 壁面电渗流和横向扩散还会使粒子朝向壁面产生迁移, 导致管壁粒子数的增多.Membrane has many applications in the fields of filtration and separation, but due to the attraction or repulsion exerted by the membrane, the particles will experience a directional motion. As a result, two totally opposite effects, i.e. particle enrichment and exclusion zone, take place in the vicinity of the membrane, and the underlying reason is still not clear. In this work, colloidal particles with negative surface charge are used as a model substance, with the advantages of monitoring the particle concentration in a real time and in situ way, to investigate the influence of cellulose membrane on the movement of particles. The experimental results show that the particles are enriched in the vicinity of the membrane. The diffusiophoresis effect originating from tiny number of ions released by the film is the main reason of the directional movement of the charged particles. Based on the two mechanisms of diffusiophoresis and diffusion, we construct a model and make relevant numerical calculation, and the numerical results are qualitatively consistent with the experimental results. Moreover, in addition to the longitudinal motion of the particles towards the filter membrane, diffusio-osmotic flow and particles lateral diffusion also result in the migration of particles towards the container wall, and further increasing the particle number near the wall.
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Keywords:
- charged particles /
- filter membrane /
- diffusiophoresis /
- directional movement
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图 2 (a) t = 0.2 h和(b) t = 31 h两个典型时刻的反射光谱图, 以及与之对应的反射峰波长分布(c)和粒子体积分数分布(d)
Fig. 2. Reflection spectra at two typical time points (a) t = 0.2 h and (b) t = 31 h, and the corresponding peak wavelength distribution (c) and volume fraction distribution (d).
图 3 样品管中粒子浓度分布的演变过程 (a)不同时刻的Φ-L曲线; (b)不同位置的Φ-t曲线
Fig. 3. Particle concentration evolution in the sample tube: (a) Φ-L curves at different time points; (b) Φ-t curves at different locations.
图 4 纯水-滤膜-粒子溶液(WP)体系和溶液-滤膜-粒子溶液(PP)体系在不同时刻的粒子浓度分布
Fig. 4. Particle concentration profiles in water-film-particle (WP) system and particle-film-particle (PP) system at different times.
图 5 模型示意图(a)和数值计算结果(b)
Fig. 5. Schematic diagram of the model (a) and the numerical simulation results (b).
图 6 壁面粒子数的计算 (a) 粒子迁移量计算示意图; (b)增加的粒子数、减少的粒子数和粒子数净变化
Fig. 6. Calculation of particle numbers near the container wall: (a) Model used to calculate the number of migrated particles; (b) the increased, decreased and the net change of particle numbers.
表 1 滤膜中所含离子的成分、浓度以及相关离子的迁移率
Table 1. Ion species and concentration contained in the film and the mobility of relevant ions.
Cl– ${\rm NO}_3^- $ ${\rm SO}_4^{2-}$ Na+ ${\rm NH}_4^+$ K+ (I) 离子浓度/( mol·L–1) 纯水 8.00×10–8 3.74×10–8 5.07×10–9 1.46×10–7 8.09×10–8 8.01×10–8 纯水 + 滤膜 3.06×10–6 1.49×10–7 3.59×10–7 3.21×10–5 2.04×10–6 1.12×10–6 (II) 离子迁移率/(m2·s–1) 2.03×10–9 1.9×10–9 1.07×10–9 1.33×10–9 1.98×10–9 1.96×10–9 
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[1] Zhou Q, Bao Y, Zhang H, Luan Q, Tang H, Li X 2020 Cellulose 27 335
Google Scholar
[2] 凤权, 武丁胜, 桓珊, 杨子龙, 应志祥 2016 纺织学报 37 12
Google Scholar
Feng Q, Wu D S, Huan S, Yang Z L, Ying Z X 2016 J. Textile Res. 37 12
Google Scholar
[3] Bhatt B, Kumar V 2015 J. Pharm. Sci. 104 4266
Google Scholar
[4] Liu S, Zeng J, Tao D, Zhang L 2010 Cellulose 17 1159
Google Scholar
[5] Florea D, Musa S, Huyghe J M R, Wyss H M 2014 P Natl. Acad. Sci. USA 111 6554
Google Scholar
[6] Lee H, Kim J, Yang J, Seo S W, Kim S J 2018 Lab on a Chip 18 1713
Google Scholar
[7] Chen C S, Farr E, Anaya J M, Chen E Y T, Chin W C 2015 Entropy 17 1466
Google Scholar
[8] Esplandiu M J, Reguera D, Fraxedas J 2020 Soft Matter 16 3717
Google Scholar
[9] Oh S H, Im S J, Jeong S, Jang A 2018 Desalination 438 10
Google Scholar
[10] Oh S H, Jeong S, Kim I S, Shon H K, Jang A 2019 J. Environ. Manage. 247 385
Google Scholar
[11] Zhang X, Tian J, Gao S, Shi W, Zhang Z, Cui F, Zhang S, Guo S, Yang X, Xie H, Liu D 2017 J. Membrane Sci. 544 368
Google Scholar
[12] Singh G, Song L F 2007 Journal of Membrane Science 303 112
Google Scholar
[13] Fahim A, Annunziata O 2020 Langmuir 36 2635
Google Scholar
[14] Wilson J L, Shim S, Yu Y E, Gupta A, Stone H A 2020 Langmuir 36 7014
Google Scholar
[15] Prieve D C, Malone S M, Khair A S, Stout R F, Kanj M Y 2019 PNAS 116 18257
Google Scholar
[16] 王林伟, 徐升华, 周宏伟, 孙祉伟, 欧阳文泽, 徐丰 2017 物理学报 66 066102
Google Scholar
Wang L W, Xu S H, Zhou H W, Sun Z W, Ouyang W Z, Xu F, 2017 Acta Phys. Sin. 66 066102
Google Scholar
[17] Wette P, Schöpe H J, Liu J, Palberg T 2004 Prog. Colloid Polym. Sci. 123 264
Google Scholar
[18] Wang S, Zhou H, Sun Z, Xu S, Ouyang W, Wang L 2020 Sci. Rep. 10 9084
Google Scholar
[19] Anderson J L 1989 Annu. Rev. Fluid. Mech. 21 61
Google Scholar
[20] Keh H J 2016 Curr. Opin. Colloid Interface Sci. 24 13
Google Scholar
[21] Velegol D, Garg A, Guha R, Kar A, Kumar M 2016 Soft Matter 12 4686
Google Scholar
[22] Shin S 2020 Phys. Fluids 32 101302
Google Scholar
[23] Chiang T Y, Velegol D 2014 J. Colloid Interface Sci. 424 120
Google Scholar
[24] Gupta A, Rallabandi B, Stone H A 2019 Phys. Rev. Fluids 4 043702
Google Scholar
[25] Gonzalez A E 2001 Phys. Rev. Lett. 86 1243
Google Scholar
[26] Niu R, Oguz E C, Muller H, Reinmuller A, Botin D, Lowen H, Palberg T 2017 Phys. Chem. Chem. Phys. 19 3104
Google Scholar
[27] Reinmueller A, Schoepe H J, Palberg T 2013 Langmuir 29 1738
Google Scholar
[28] Segre G, Silberberg A 1961 Nature 189 209
Google Scholar
[29] 苏敬宏2021 博士学位论文 (北京: 中国科学院大学)
Su J H 2021 Ph. D. Dissertation (Beijing: University of Chinese Academy of Sciences) (in Chinese)
[30] Rubinow S I, Keller J B 1961 J. Fluid Mech. 11 447
Google Scholar
[31] Musa S, Florea D, Wyss H M, Huyghe J M 2016 Soft Matter 12 1127
Google Scholar
[32] Shinde A, Huang D L, Saldivar M, Xu H F, Zeng M X, Okeibunor U, Wang L, Mejia C, Tin P, George S, Zhang L C, Cheng Z D 2019 Acs Nano 13 12461
Google Scholar
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