下沉流使粘性液体和空气之间的界面变形为尖端奇点
Sink flow deforms the interface between a viscous liquid and air into a tip singularity
摘要：
在我们的实验中，粘性液体和空气之间的界面被恒定流量的下沉流变形以形成尖锐的尖端。使用显微镜，记录界面形状，直至尖端尺寸为1 $\rm{μm}$。尖端处的曲率由尖端和槽之间的距离$h$控制。当接近临界距离$h^{\star}$时，曲率像$1/(h-h^{\star})^3$一样发散，尖端变成锥形。随着到水槽的距离进一步减小，锥体的开度角像$h^2$一样消失。除了头端在孔内外，未发现空气夹带的证据。
英文摘要：
In our experiment, an interface between a viscous liquid and air is deformed by a sink flow of constant flow rate to form a sharp tip. Using a microscope, the interface shape is recorded down to a tip size of 1 $\rm{μm}$. The curvature at the tip is controlled by the distance $h$ between the tip and the sink. As a critical distance $h^{\star}$ is approached, the curvature diverges like $1/(h-h^{\star})^3$ and the tip becomes cone-shaped. As the distance to the sink is decreased further, the opening angle of the cone vanishes like $h^2$. No evidence for air entrainment was found, except when the tip was inside the orifice.
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