| 摘要: | 本論文以數值模擬方法探討不同基板與液滴熱傳導係數的比值與基板尺寸對蒸發固著液滴流動反轉現象的影響，旨在揭示基板熱性質與幾何尺度在液滴蒸發過程中對內部流場動態的調控機制。研究中模擬了液滴在蒸發過程中溫度場、濃度場與流場的演化，並系統分析基板與液滴熱傳導係數的比值與基板尺寸對流動反轉時機、流場結構及反轉機制的影響。
本研究定義了寬度熱導比及寬度厚度熱導比兩個無因次參數，其中寬度熱導比為基板寬度與接觸半徑的比值乘上基板與液滴熱傳導係數的比值，寬度厚度熱導比為寬度熱導比除以基板厚度與接觸半徑的比值，分別用來探討寬度熱導筆及熱導比對內部流場的影響以及寬度熱導比、厚度熱導比及熱導比三種變數對內部流場的影響。
本研究建構二維軸對稱模型，結合任意拉格朗日-歐拉(ALE)方法，模擬不同基板與液滴熱傳導係數的比值、基板厚度與寬度下的液滴蒸發行為，考慮蒸發冷卻效應與熱馬蘭哥尼效應的耦合影響。模擬涵蓋基板與液滴熱傳導係數的比值介於0.006 ~ 2，基板厚度與寬度採多種倍數設計。結果顯示，液滴內部可發展出四種主要流場型態(沿著液氣介面從接觸線往頂端的單一向上渦流、沿著液氣介面從頂端往接觸線的單一向下渦流、雙渦流與三渦流)，其發展取決於熱量主導機制。當寬度厚度熱導比較高時，基板較寬、較薄且熱導比較大，基板熱傳效應較強，因此較容易出現在介面上由接觸線往頂端的馬蘭哥尼流；反之，寬度厚度熱導比較低時，基板較窄、較厚且熱導比較小，基板熱傳效應較弱，因此較容易出現在介面上由頂端往接觸線的馬蘭哥尼流。
本研究首次提出基板寬度對內部流向的影響，修正了過去理論模型對不同基板熱性質與幾何尺寸對流動反轉影響的系統性探討之不足，所建構之流場相圖亦可為微流控設計、精密塗佈、噴墨列印與設計沉積裝置或改善咖啡環效應等技術提供理論指引。
;This study employs numerical simulations to investigate the effects of the ratio between substrate and droplet thermal conductivity and geometric dimensions on the flow reversal phenomenon in evaporating sessile droplets. The aim is to clarify how substrate thermal properties and scales regulate internal flow dynamics during evaporation. The simulations capture the evolution of temperature, concentration, and flow fields, and systematically analyze how conductivity ratio and substrate dimensions influence the timing, structure, and mechanisms of flow reversal. Two dimensionless parameters are introduced: the width–conductivity ratio, defined as the product of the substrate-width-to-contact-radius ratio and the ratio between substrate and droplet thermal conductivity, and the width–thickness–conductivity ratio, defined as the width–conductivity ratio divided by the substrate-thickness-to-contact-radius ratio.
A two-dimensional axisymmetric model is developed with the Arbitrary Lagrangian–Eulerian (ALE) method, covering the ratio between substrate and droplet thermal conductivity from 0.006 to 2 and multiple scale ratios for substrate thickness and width. Results reveal four primary flow patterns—single upward vortex along the interface from the contact line toward the apex, single downward vortex along the interface from the apex toward the contact line, double-vortex, and triple-vortex—whose development is governed by the dominant heat transfer mechanism. Higher substrate-width-to-contact-radius ratio (wider, thinner, more conductive substrates) favors Marangoni flow along the interface from the contact line toward the apex, while lower substrate-width-to-contact-radius ratio favors flow from the apex toward the contact line.
This work identifies, for the first time, the effect of substrate width on flow direction, addressing gaps in previous models. The constructed flow regime maps provide guidance for microfluidics, precision coating, inkjet printing, and mitigation of the coffee-ring effect. |
