導電液滴之泳動行為探討：電泳與擴散泳

Phoretic Motions of a Conducting Droplet: Electrophoresis and Diffusiophoresis

范莉雅(Li-Ya Fan)

指導教授 ： 李克強

國立臺灣大學/工學院/化學工程學系/博士(2022年)

https://doi.org/10.6342/NTU202202442

摘要

本研究以導電液滴為主體，探討其在電解質溶液中的電動力學行為：電泳與擴散泳。這兩種電動力學行為分別以施加外加電場與外加濃度場作為驅動力，來達成各種需要操控膠體粒子的實際應用，例如電沉積、藥物輸送、無膜水過濾、織物清潔、測量界達電位等等。而導電液滴模擬的液態金屬液滴，近年來因其高導電性且具流體性質的特性，引起越來越多學者的注意。特別是鎵以及鎵合金，因其低毒性、低蒸汽壓、高穩定性等特性被廣泛運用於生物醫學、微/奈米流體操控的應用中。

本研究採用假性光譜法中的正交配位法來做數值處理。透過空間映射、擾動法、子問題法等手法，搭配系統相對應的電動力學方程組和邊界條件來求解介電液滴之泳動度。值得注意的是，因為液滴內核假設內部為不帶電的流體，因此液滴內部之主控方程式皆為齊次微分方程式。為加快數值計算的速度，本研究進行數值計算前，會預先將液滴內的變數求出解析解並以邊界條件呈現其內部流動造成的影響。

第一部分探討電泳現象，透過討論不同物理參數：電雙層厚度、液滴內外黏度比、液滴表面帶電量，對泳動度的影響。因導電液滴會維持等電位面，因此不須討論馬克士威牽引力的影響，也有實驗相關研究指出也不須討論馬倫戈尼效應的影響，使得導電液滴的情況較為單純。液滴內外黏度比越低，電泳動度越快，這是因為單純只考慮流體黏力施加在液滴表面的關係。而在電雙層厚度約等於粒子半徑時，阻礙粒子運動的電雙層極化效應會很明顯。這部分也探討了造成導電液滴與介電液滴行為差異的原因，是由於缺少了馬克士威剪切應力的影響，導致導電液滴並不會有外部渦流的產生，因此也不會有固化點的出現。
第二部分探討擴散泳現象，除了第一部份討論的物理參數外，還加入了電解質溶液陰陽離子擴散係數差對泳動度的影響。在只考慮化學泳效應的情況下，導電液滴永遠會往電解質濃度高的方向前進。這使得導電液滴對於在一些生物醫學的應用中是具有潛在應用性的，比如說在進行藥物輸送的應用中，我們會希望藥物能夠自行往離子濃度高的方向走，這時導電液滴就非常適合作為藥物的載體。而我們也探討了電泳效應對擴散泳現象的影響，因電泳效應與化學泳效應會相互耦合或相互競爭，因此在某些特定的情況下會有固化點的出現。

綜上所述，可以發現導電液滴於電解質溶液系統具有許多有潛力的應用，也有許多值得探討的現象，無論在實驗上或理論預測上均可以看到。本研究利用理論模擬的方式預測此系統，無論在定性以及定量上都可做為學界與工業界進一步探討與應用的基礎。

關鍵字

電泳 ； 擴散泳 ； 電動力學行為 ； 導電液滴 ； 液態金屬液滴 ； 藥物輸送 ； 電雙層極化效應

並列摘要

Phoretic motions in electrolyte solutions, both electrophoresis and diffusiophoresis, of an arbitrarily charged conducting droplet such as a liquid metal droplet (LMD) are investigated theoretically in this thesis. The results obtained here have potential applications in various practical applications such as drug delivery and micro-/nanofluidic operations involving conducting droplets. Among them, the conducting LMD in particular has attracted ever-increasing research interests and endeavors in recent years. Gallium and its alloys, for instance, have been widely used in drug delivery and biomedical field due to their outstanding therapeutic performance as nanomedicines. The study here provides crucial information and design guidelines both in the fabrication stage and in vivo operations of these nanomedicines in terms of maximize their ultimate therapeutic performance.

In this study, the orthogonal collocation method in pseudo-spectral method was used for numerical processing via treatments of spatial mapping, perturbation method, sub-problem method, etc. The electrodynamic equations and boundary conditions corresponding to the system are used to solve the mobility of conducting droplets. Note that because the fluid inside the droplet assumes uncharged, the governing equations inside the droplet are all homogeneous differential equations. To speed up the numerical calculation, before the numerical calculation in this study, the variables in the droplet will be analytically solved in advance, and the influence of the internal flow will be presented with boundary conditions.

The first part discusses the phenomenon of electrophoresis, by discussing the effects of different physical parameters: the thickness of the electric double layer, the ratio of the viscosity between the inside and outside of the droplet, and the charge on the surface of the droplet, on the mobility Since the conductive droplet maintains the equipotential surface, it is not necessary to discuss the influence of Maxwell traction, and some experimental studies have pointed out that it is also not necessary to discuss the influence of the Marangoni effect, which makes the situation of the conductive droplet relatively simple. Moreover, as the droplet surface is equipotential, there is no presence of the electrokinetic Maxwell traction and the Marangoni effect. The less viscous the conducting droplet is, the faster it moves in general, as the droplet motion is determined solely by the hydrodynamic viscous forces upon the droplet surface. Severe motion-deterring double layer polarization (DLP) effect is observed for highly charged conducting droplets when the double layer thickness is comparable to the droplet radius. A comparison with a corresponding dielectric droplet is made, with the effect of the extra Maxwell traction examined in detail.

The second part discusses the phenomenon of diffusiophoresis. In addition to the physical parameters discussed in the first part, the effect of the difference in the diffusion coefficients of anions and cations in the electrolyte solution on the electrophoresis component is also added. In the case of only considering the chemiphoresis, a conducting droplet always moves up the chemical gradient toward the region with a higher concentration of ions in chemiphoresis. This implies that a perfectly conducting droplet like a Gallium or its alloy droplet is superior to the commonly utilized dielectric droplet like a liposome in drug delivery in terms of self-guarding itself toward the desired destination of injured or infected area in the human body, as specific ionic chemicals are often released there. Optimum droplet size yielding the fastest migration rate is predicted. And we also discussed the influence of electrophoresis component on diffusiophoresis. Because electrophoresis effect and chemical electrophoresis effect will couple or compete with each other, there will be solidification points in some specific cases.

In summary, it can be found that conducting droplets have many potential applications in electrolyte solution systems, and there are many phenomena worthy of discussion, which can be seen both experimentally and theoretically. This study uses theoretical simulation to predict this system, which can be used as a basis for further discussion and application in academia and industry, both qualitatively and quantitatively.

並列關鍵字

Electrophoresis ； Diffusiophoresis ； Electrokinetic phenomenon ； Conducting droplet ； Liquid metal droplet ； Drug delivery ； Double layer polarization

參考文獻

參考文獻

1. Van de Ven, T.G., Colloidal hydrodynamics. 1989: Academic press.

2. Seksek, O. and J. Bolard, Nuclear pH gradient in mammalian cells revealed by laser microspectrofluorimetry. Journal of Cell Science, 1996. 109(1): p. 257-262.

3. Fukuyama, T., et al., Directing and boosting of cell migration by the entropic force gradient in polymer solution. Langmuir, 2015. 31(46): p. 12567-12572.

4. Kim, S.H. and T. Fujii, Efficient analysis of a small number of cancer cells at the single-cell level using an electroactive double-well array. Lab on a Chip, 2016. 16(13): p. 2440-2449.