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Steady-profile fingering flows in Marangoni driven thin films.
Jeanman Sur1, Thomas P Witelski, Robert P Behringer
1Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, NC 27708, USA.
Physical Review Letters
|February 9, 2005
Summary
Finite-amplitude fingering solutions were observed in viscous thin film flow driven by thermal Marangoni stresses. Experiments and computations reveal these fingers arise from a subcritical bifurcation, stabilizing at a prescribed wavelength.
Area of Science:
- Fluid dynamics
- Nonlinear phenomena
- Heat and mass transfer
Background:
- Thin film flow is crucial in various industrial applications.
- Thermally induced Marangoni stresses can drive fluid motion.
- Fingering instabilities can significantly alter flow patterns.
Purpose of the Study:
- To investigate the existence and characteristics of finite-amplitude fingering solutions in viscous thin film flow.
- To explore the role of thermal Marangoni stresses in driving these fingering phenomena.
- To understand the underlying bifurcation mechanisms leading to stable finger formation.
Main Methods:
- Experimental setup involving controlled thermal perturbations using an infrared laser and scanning mirror.
- Numerical computations to simulate the thin film flow and analyze fingering behavior.
- Analysis of spatially periodic perturbations at the contact line of the fluid film.
Main Results:
- Observation of steady-profile, two-dimensional traveling wave fingers in experiments.
- Demonstration that imposed thermal perturbations with a specific wavelength lead to fingers of that same wavelength.
- Experimental and computational evidence for a subcritical bifurcation mechanism.
Conclusions:
- Finite-amplitude fingering solutions exist in thermally driven thin film flows.
- The wavelength of these fingers can be controlled by initial perturbations.
- Subcritical bifurcation governs the emergence of these stable fingering patterns.