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Sink flow deforms the interface between a viscous liquid and air into a tip singularity
1School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom.
Physical Review Letters
|February 21, 2006
Summary
Researchers deformed a liquid-air interface into a sharp tip using sink flow. The tip shape and curvature were analyzed, revealing a critical distance where it forms a cone, with no air entrainment observed outside the orifice.
Area of Science:
- Fluid dynamics
- Interface physics
Background:
- Understanding liquid-air interfaces is crucial in various scientific and industrial applications.
- Deformation of interfaces can lead to complex phenomena like tip formation and air entrainment.
Purpose of the Study:
- To investigate the dynamics of a viscous liquid-air interface under controlled sink flow.
- To characterize the tip formation and curvature evolution at microscale.
- To determine conditions leading to air entrainment.
Main Methods:
- Microscopic observation of the liquid-air interface.
- Controlled deformation using a constant flow rate sink.
- Quantitative analysis of interface shape and curvature as a function of distance to the sink.
Main Results:
- A sharp tip was formed on the interface, with observable features down to 1 micrometer.
- Tip curvature diverged as a critical distance (h*) was approached, following a 1/(h-h*)³ relationship.
- The tip adopted a cone shape near h*, with its opening angle vanishing as h².
- Air entrainment was not observed, except when the tip was within the orifice.
Conclusions:
- The study provides a detailed characterization of tip formation in a deforming liquid-air interface.
- The observed scaling laws for curvature and cone angle offer insights into the underlying physics.
- The findings suggest specific conditions under which air entrainment is avoided.