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Numerical analysis of tips in viscous flow
1School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK.
Drops in viscous flow form sharp tips, transitioning to a jetting state above a critical flow strength. This study numerically investigates these stationary shapes and the jetting transition, finding universal tip shapes near the interface.
Area of Science:
- Fluid dynamics
- Rheology
- Interface phenomena
Background:
- Viscous drops and bubbles in flow develop sharp tips.
- A critical flow strength can induce a transition to a jetting state.
- Understanding these transitions is crucial for fluid mechanics.
Purpose of the Study:
- Numerically investigate stationary drop shapes in viscous flow.
- Analyze the jetting transition and tip behavior at high resolution.
- Determine the universality of tip shapes near interfaces.
Main Methods:
- Boundary integral method for axisymmetric flow equations (Stokes limit).
- Newton's method for solving stationary states.
- High-resolution numerical analysis of drop shapes.
Main Results:
- Identified critical parameters for the jetting transition, agreeing with theory.
- Found universal, geometry-independent drop shapes near the tip.
- Observed finite tip curvature due to surface tension, even at high deformation.
Conclusions:
- The jetting transition in viscous flows is characterized by universal tip shapes.
- Numerical simulations accurately capture experimental observations.
- Surface tension plays a key role in limiting tip curvature.
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