Gravitational effects on coffee-ring formation during the evaporation of sessile droplets
Gravitational effects on coffee-ring formation during the evaporation of sessile droplets
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DOI：
10.1017/jfm.2023.493
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发表时间：
2023-07
影响因子：
3.7
通讯作者：
M. Moore;A. Wray
中科院分区：
文献类型：
--
作者：
M. Moore;A. Wray
摘要本文研究了细液滴蒸发时重力在溶质输运中的作用。在物理上相关的假设下，即接触线是固定的，且解psamclet数${Pe}$很大，我们确定了两个依赖于Bond数${Bo}$大小的渐近状态。当${Bo} = O(1)$为${Pe}\rightarrow \infty$时，溶质输运的渐近结构直接遵循表面张力主导的制度，其中平流驱动溶质向接触线移动，仅被局部扩散效应抵消，导致形成著名的“咖啡环”。“在${Bo} = O({Pe}^{4/3})$为${Pe}\rightarrow \infty$的特殊极限中，平流和扩散之间的相互作用与表面张力和重力之间的相互作用同时发生。在每个状态下，我们对溶质输运进行了系统的渐近分析，并将我们的预测与数值模拟进行了比较。我们确定了重力对新生咖啡环的影响，提供了溶质质量剖面的大小、位置和形状的定量预测。特别是，对于固定的psamclet数，随着重力作用的增加，咖啡环的高度减小，并且位于距离接触线更远的地方。此外，对于${Bo}$、${Pe}$和蒸发时间的一定值，经典咖啡环内部可能存在二次峰。次级峰的出现与液滴中心溶质谱中临界点类型的变化有关。起始和峰值特性均与${Pe}$无关。
Abstract We consider the role of gravity in solute transport when a thin droplet evaporates. Under the physically relevant assumptions that the contact line is pinned and the solutal Péclet number, ${Pe}$, is large, we identify two asymptotic regimes that depend on the size of the Bond number, ${Bo}$. When ${Bo} = O(1)$ as ${Pe}\rightarrow \infty$, the asymptotic structure of solute transport follows directly from the surface-tension-dominated regime, whereby advection drives solute towards the contact line, only to be countered by local diffusive effects, leading to the formation of the famous ‘coffee ring.’ In the distinguished limit in which ${Bo} = O({Pe}^{4/3})$ as ${Pe}\rightarrow \infty$, this interplay between advection and diffusion takes place alongside that between surface tension and gravity. In each regime, we perform a systematic asymptotic analysis of the solute transport and compare our predictions to numerical simulations. We identify the effect of gravity on the nascent coffee ring, providing quantitative predictions of the size, location and shape of the solute mass profile. In particular, for a fixed Péclet number, as the effect of gravity increases, the coffee ring is diminished in height and situated further from the contact line. Furthermore, for certain values of ${Bo}$, ${Pe}$ and the evaporation time, a secondary peak may exist inside the classical coffee ring. The onset of this secondary peak is linked to the change in type of the critical point in the solute mass profile at the droplet centre. Both the onset and the peak characteristics are shown to be independent of ${Pe}$.