奈米磁流體微滴生成系統之數學模型建立與驗證

Development of Nano-Ferrofluid Droplet Generator System and its Mathematical Model

李東祐(TUNG-YU LEE)

指導教授 ： 杜哲怡

中原大學/工學院/機械工程學系/碩士(2022年)

https://doi.org/10.6840/cycu202201708

摘要

本文建立一微滴生成數學模型，微滴可用於少量檢體的情況下進行疾病、DNA等檢驗，數學模型中考慮磁力、浮力、阻力以及界面張力進行微滴直徑推導，並建立固流磁三相耦合有限元素模型與微滴生成模型進行交互比對驗證。微滴生成系統包括母微滴層、微孔結構層、微滴觀察層與磁鐵，母微滴層內有奈米磁流體作為母體微滴，滴落時使用磁鐵帶動母微滴層內之奈米磁流體，奈米磁流體將被磁力向下吸引經過微孔結構層表面的微孔結構，並生成數百個微滴於微滴觀察層。依照實際微孔結構直徑，共使用兩個不同直徑的微孔結構進行驗證，直徑分別為144 µm及185 µm。由實驗結果可得出，數學模型與微滴生成實驗於直徑為144 µm時誤差為11%，而直徑為185 µm時誤差為18%。有限元素模擬與微滴生成實驗於直徑為144 µm時誤差為8%，而直徑為185 µm時誤差為9%。本文已成功建置磁控的微滴生成模型，並完成數學模型建立，並可預測出微滴直徑，另外，透過有限元素模型可更精準的預測微滴直徑與微滴生成狀況。

關鍵字

數學模型 ； 奈米磁流體 ； 微流道 ； 微滴

並列摘要

A droplet generation mathematical model was established in this study. The magnetic force, buoyancy force, drag force, and interfacial tension force was considered to derive the radius of droplet. Moreover, the solid-fluid-magnetic coupling finite element model was built. Then the droplet generator system was set up for verification the mathematical and finite element model. The droplet generator system consists of the cover layer, the parent droplet layer, the microstructure layer, the droplet observation layer, and the base layer. The parent droplet layer has a built-in nano-ferrofluid as the parent droplet. In addition, fluorinated oil containing surfactant was incorporated into the parent droplet layer and the droplet observation layer. Via the microstructure of the microstructure layer, the nano-ferrofluid passed through and generate droplets. There are two micro-hole size, 144 µm and 185 µm, were used to verify the relationship between the micro-hole size of the microstructure layer and the radius of the droplet after the generation. When the nano-ferrofluid was dripping, the parent droplet dripping needed to be driven by magnetic force in order to pass through the micro-hole to generate droplets. As a result, the error of mathematical model and the droplet generation experiment had of 11 % with a micro-hole size of 144µm and 18 % with the micro-hole size of 185 µm respectively. The error of finite element simulation and droplet generation experiments had a percentage error of 8 % with micro-hole size of 144 µm and 9 % with micro-hole size of 185 µm.

並列關鍵字

Mathematical Model ； nano-ferrofluid ； microfluidic ； droplet

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