| 摘要: | 液滴於固體基板上的擴展與蒸發過程在噴墨列印、噴霧冷卻技術與表面塗層等工業應用中十分常見。此現象牽涉流體動力學、熱傳遞、相變等複雜的交互作用。本研究的核心在於探討熱馬蘭哥尼效應對液滴擴展行為的影響，評估其在不同基板濕潤性與溫度條件下，如何改變液滴內部的流場結構與抑制擴展半徑的程度。透過建構二維軸對稱模型進行數值模擬，並採用 ALE 方法追蹤液滴幾何形狀變化，模擬中引入蒸發冷卻效應以觀察其對液滴擴展過程中溫度場與速度場的影響。結果顯示，蒸發使液滴表面出現多個溫度局部極小值，進而產生多個熱馬蘭哥尼渦流，使液滴流場從向外擴展模式轉變為多渦流的流場結構，雖對擴展半徑略有抑制，但影響有限。另一方面，基板濕潤性會影響液滴的幾何形狀與擴展時間，進而改變液滴內部的熱傳條件與溫度梯度，形成不同程度的熱馬蘭哥尼效應與持續時間。舉例來說，較疏水的基板使液滴維持較高的高度，增加基板至液滴頂部的熱傳途徑，當考慮基板加熱效應時，會導致頂部加熱效果受抑，在液滴表面引起更大的溫度梯度，產生更強的熱馬蘭哥尼效應。然而，由於液滴在疏水性基板擴展時的平衡接觸角較大，使得液滴快速達到穩態形狀，其擴展時間相對較短。因此，即使熱馬蘭哥尼回縮效應較強，其能發揮作用的時間也相對受限，最終對擴展半徑的抑制效果反而不如親水基板顯著。;The spreading and evaporation of droplets on solid substrates are commonly observed phenomena in industrial applications such as inkjet printing, spray cooling, and surface coating. This process involves complex interactions among fluid dynamics, heat transfer, and phase change. The core objective of this study is to investigate the influence of the thermal Marangoni effect on droplet spreading behavior, particularly in terms of how it alters the internal flow structure and the extent to which it suppresses the spreading radius under varying substrate wettability and temperature conditions. A two-dimensional axisymmetric numerical model is constructed, employing the ALE (Arbitrary Lagrangian–Eulerian) method to track the evolving droplet geometry. Evaporative cooling is incorporated into the simulation to examine its impact on the temperature and velocity fields during the spreading process.
The results indicate that evaporation induces multiple local temperature minima on the droplet surface, leading to the formation of several thermal Marangoni vortices. These vortices transform the internal flow from an outward spreading pattern to a multi-vortex structure, slightly suppressing the spreading radius, though the effect remains limited. On the other hand, substrate wettability influences both the droplet geometry and the spreading duration, thereby affecting internal heat transfer conditions and surface temperature gradients, which in turn generate thermal Marangoni flows of varying strength and persistence.For example, a more hydrophobic substrate causes the droplet to maintain a higher profile, increasing the thermal transport path from the substrate to the droplet apex. When substrate heating is considered, this results in reduced heating efficiency at the top of the droplet, producing a larger temperature gradient along the interface and thus a stronger thermal Marangoni effect. However, due to the larger static contact angle during droplet spreading on hydrophobic substrates, the droplet quickly reaches a steady-state shape, resulting in a relatively shorter spreading duration. Consequently, although the thermal Marangoni retraction effect is stronger, its effective duration is limited, ultimately leading to a less significant suppression of the spreading radius compared to that on hydrophilic substrates.
Keywords: Marangoni effect, droplet evaporation, droplet spreading, ALE, substrate wettability. |
