當一顆液滴放置在固體表面上而開始自發性擴張，我們可以把這種潤濕現象歸類為完全潤濕。典型的例子如矽油在各種不同表面上連續的擴張行為，矽油液滴擴張半徑的變化與時間的關係則可以用Tanner's law來描述( R(t)~t^n，n=0.1 )。本研究使用多體耗散粒子動力學法，模擬在飽和蒸汽系統以及非滑移邊界條件下，液滴在完全潤濕表面上的擴張行為，並分別探討擴張系數、表面粗糙性質的改變對液滴擴張行為之影響。
模擬過程中，在平滑表面上液滴將會快速的自發性擴張，其擴張半徑將會隨著時間逐漸增加，而液滴接觸角將會隨時間逐漸下降。結果發現在液滴擴張的過程中，會有前驅膜的產生導致在量測擴張半徑時與Tanner's law不合，且隨著擴張係數上升其指數關係會有增加的趨勢。所以當我們將前驅膜的影響給去除時，液滴自發擴張的行為就與Tanner's law吻合，不受擴張係數而改變。而在粗糙表面上，液滴的擴張的速度明顯慢於平滑表面，其擴張半徑與接觸角的變化一樣遵循Tanner's law，並發現具有粗糙度的表面將會有效減緩前驅膜的生成，且粗糙孔洞大小的增加將會對前驅膜的擴張產生更大的阻礙。而在長時間下更可以發現，擴張後期因為大量的液滴粒子卡進孔洞中，此時液滴變得非常薄且擴張的速度將會非常緩慢。
我們在粗糙與平滑表面上的液滴施一固定方向的力，液滴在垂直施力方向上的擴張行為一樣遵守Tanner's law的描述，並且有前驅膜的生成。在平滑表面上液滴因施力開始流動，而液滴後端會因為沒有遲滯而滑動，因為在施力方向上，液滴流動的速度大於前驅膜生成的速度，因此看不到前驅膜的生成。此外，粗糙表面上則因為粗糙度具有遲滯並產生毛細力阻止液滴後端滑動。液滴的流動長度與時間的指數關係將會受到橫向前驅膜生成而受到影響，且當表面具有粗糙性質時，將會更加緩慢。

Liquid drops spontaneously spreading on a solid surface is referred to as the total wetting phenomenon. A typical example is the continuous expansion of a silicon drop on various surfaces. The time evolution of the drop radius can be described by the power law r(t) ∼ tn with the exponent 1/10, known as Tanners law. In this work, the spreading dynamics of a nanodrop on a total wetting surface under saturated humidity and no-slip condition has been explored by many-body dissipative particle dynamics simulation. The influences of surface roughness and wettability in terms of spreading coefficient on the spontaneous spreading behavior are studied.
It is found that the exponent n is 0.2 on smooth surface, and the exponent grows with increasing the spreading coefficient. The reason for the difference with Tanner’s law is that the formation of precursor film with the drop spreading process. As we remove the effect of the precursor film, the drop radius and contact angle behavior agree with Tanner’s law and the spreading law is independent of the spreading coefficient. In addition, The drop spreading velocity on rough surface is lower than that on smooth surface and the spreading process also follow Tanner’s law. It shows the surface roughness will prevent the growing of the precursor film and the resistance rises with increasing the cavity size. Furthermore, the drop spreading velocity is significantly lower and the drop becomes very thin for a long time because the most of the liquid beads stuck in the cavity.
The forced spreading that is similar to the thin film flow on the surface under external force are investigated as well. As a result, the drop spreading motion which is vertical to external force also consistent with Tanner’s law and the precursor film is produced in the spreading process with this direction. On the forced direction, the rear part of the liquid drop will slide on smooth surface due to without surface roughness that can make pinning force to impede the movement of the contact line. In contrast, the rear part of the liquid drop will pinning on rough surface. Moreover, the precursor film can’t be observed on forced direction, since the forced flow velocity is faster than the velocity of expansion with precursor. In addition, the flow velocity with the forced direction will be affected by the precursor and the surface roughness will make the flow velocity significant
slower.

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