Droplet spreading on an oblique surface
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摘要: 液滴碰撞固体表面后铺展的现象广泛存在于航空航天和工农业应用中。在工程中，被撞击表面多不与液滴速度方向垂直，而前人对于液滴碰撞铺展的研究多基于垂直碰撞，其研究成果无法直接解决工程斜碰撞问题。通过实验研究液滴碰撞倾斜固体表面铺展形成液膜的演化过程，获得了不同表面倾斜角度和不同韦伯数条件下液膜形状的瞬态数据；基于新建立的液滴碰撞倾斜表面铺展理论，分析了液膜形状的瞬态变化过程，发现该理论可以合理预测小倾角下液滴的铺展，而对于大倾角下液膜在倾斜方向最大铺展宽度的预测，由于推导过程中将液膜上沿长度近似为常数，导致误差较大；为解决该问题，通过加入液膜上边沿长度的细致理论分析，建立了一个预测液膜最大形状的解析模型，预测结果相对实验结果的误差可从前人理论的61.8%降至3.2%。本研究提升了大倾角情况下液滴铺展预测的准确性，为工程应用提供了一个简洁准确的理论工具。Abstract: Droplet spreading on a surface is ubiquitous in a variety of applications including aerospace, industry, and agriculture. Majority of these impacts are oblique, while previous studies focused on orthogonal impacts. Oblique impacts cannot be understood directly by previous theories and/or models. Evolution of film formation following a droplet impacting an oblique surface is investigated experimentally. Evolution of the film shape is obtained under various inclination angles and Weber numbers. Based on a new theory of droplet spreading on oblique surfaces, evolution of the film shape is analyzed. It is found that the film shape at small inclination angles can be predicted reasonably, but the error between the predicted maximum lamella width along the inclination direction and the experimental data is relatively big at large inclination angles since the length of the upstream lamella is assumed as a constant in the theory. Modifications of the theory including more detailed analysis of the length of the upstream lamella lead to an analytical model which permits the theoretical determination of the maximum lamella shape. It is shown that the error between the predicted results and the experimental results can be reduced from 61.8% by the previous theory to 3.2%. The model provides a better prediction on the lamella shape at large inclination angles, and a more concise and accurate theoretical tool for engineering applications.
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Key words:
- droplet impact /
- oblique surface /
- spreading /
- prediction model
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图 3 液滴斜碰撞铺展过程（We=37.6）
Figure 3. Spreading process of droplets impacting on inclined substrates （We=37.6）
图 4 水平方向最大铺展宽度与倾斜角度的关系
Figure 4. The variation of the maximum horizontal width as a function of the inclination angle
图 5 倾斜方向最大铺展宽度与倾斜角度的关系
Figure 5. The variation of the maximum oblique width as a function of the inclination angle
图 6 小倾角下液滴演化的实验与模型预测结果（We=37.6）
注：图（a）中t=1时的黄线区域为液滴拉伸形成的影像，不是液膜
Figure 6. Droplet evolution at small inclination angles from experiments and model prediction （We=37.6）
图 7 大倾角下液滴演化的实验与模型预测结果（We=37.6）
Figure 7. Droplet evolution at large inclination angles from experiments and model prediction （We=37.6）
图 9 椭圆中心与碰撞点距离随表面倾斜角度的变化（We=37.6）
Figure 9. Distance between the ellipse center and the impact point as a function of the inclination angle （We=37.6）
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