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Contact Line Instability in Driven Films

This study investigates the contact line instability in driven films spreading under the action of gravity and centrifugal force, focusing on the experiments, theory, and quantitative connection between the two. The effects of optical perturbations, temperature gradient, and feedback control on the contact line distortion are explored. Additionally, the transient growth and non-normality of the contact line behavior are examined. The study also compares the theoretical predictions with experimental measurements of transient amplification.

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Contact Line Instability in Driven Films

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  1. Contact Line Instability in Driven Films Spreading under the action of: • gravity • centrifugal force (spin coating) - surface tension gradients

  2. Contact Line Instability:Experiments and Theory Jennifer Rieser Roman Grigoriev Michael Schatz School of Physics and Center for Nonlinear Science Georgia Institute of Technology Supported by NSF and NASA

  3. Transients & Hydrodynamic Transition Controversy in Contact Line Problem Important in Turbulent Transition? Quantitative connection between experiment and theory

  4. Optically-Driven Microflow Fluid flow FLUID Contact line

  5. Initial State (experiment and theory) Fluid flow The boundary conditions at the tail are different: experiment - constant volume theory (slip model) - constant flux

  6. Contact line instability 1 mm Silicone oil (100cS) on horizontal glass substrate

  7. Disturbance Amplitude(Ambient Perturbations) log(A) time (s) Undisturbed system allows measurement of only the most unstable wavelength and the corresponding growth rate. Numerous Previous Experiments: (Cazabat, et al. (1990), Kataoka & Troian (1999))

  8. Optical Perturbations Temperature gradient Top view Resultant Contact Line Distortion (fingers) Wavelength of perturbation, l Perturbation Thickness, w

  9. Finger Formation

  10. Disturbance amplitude (experiment) Wavenumber (2.5 mm-1) log(A) Contact Line Distortion Time (s)

  11. Feedback control One Mechanism: Induce Transverse Counterflow to Suppress Instability Other (Streamwise) Counterflow Mechanisms Film mobility reduced by: *heating the front of the capillary ridge *cooling front and heating back of ridge Effect of Feedback Depends on Spatial Profile

  12. Feedback control (experiment) The feedback is applied on the right side of the film. On the left the film evolves under the action of a constant uniform temperature gradient.

  13. Slip model of thermally driven spreading f Non-dimensional evolution equation for thickness:

  14. Initial State (experiment and theory) Fluid flow The boundary conditions at the tail are different: experiment - constant volume theory (slip model) - constant flux

  15. Linear stability Dynamics of small disturbances, :

  16. MeasuringEigenvalues ln(A) Contact Line Distortion ASYMPTOTIC GROWTH Growth rate β0(q) time (s) Wavenumber (2.5 mm-1)

  17. Dispersion curve Growth rates measured for externally imposed monochromatic initial disturbances with different wavenumbers. Linear stability analysis correctly predicts most unstable wavenumber, but overpredicts growth rate by about 40%

  18. Transient Growth NONLINEAR EFFECTS Wavenumber (25 cm-1) ln(A) Contact Line Distortion TRANSIENT GROWTH ASYMPTOTIC GROWTH Growth rate β0(q) time (s)

  19. Transient Growth & Non-normality Linear operator L(q) not self-adjoint: L+(q) ≠L(q) The eigenvectors are not orthogonal Normal (eigenvalues<0) Norm Time Non-normal (eigenvalues<0) Norm Time

  20. Transient Growth & Non-normality Non-normal (one positive eigenvalue) L2 Norm Time ln(A) Time

  21. Transient Growth in Contact Lines: Gravitationally-Driven Spreading (Experiments) de Bruyn (1992) Rivulets observed for “stable” parameter values Gravitationally-Driven Spreading (Theory) Bertozzi & Brenner (1997) Kondic & Bertozzi (1999) Ye & Chang (1999) Transient amplification: ~1000 Nonlinear (Finite Amplitude) Rivulet formation possible Davis & Troian (2003) Transient amplification: < 10 Thermally-Driven Spreading (Theory) Davis & Troian (2003) Grigoriev (2003)

  22. Transient Growth in Turbulent Transition Ellingson & Palm (1975), Landhal (1980), Farrell (1988), Trefethan et al. (1993), Reshotko (2001), White (2002, 2003)Chapman (2002), Hof, Juel & Mullin (2003) + (Eigenvalue) Linear stabilityfails in shear flows + Shear Flows are highly nonnormal Predicted transient amplification: 103-104 + Mechanism for Bypass Transition Transient Growth of Disturbances Finite amplitude nonlinear instability + Importance still subject of controversy

  23. Optimal Transient AmplificationTheory

  24. Transient Amplification Measurements dhf f (A (tf )) γexp≡e-bt = e-bt dhi dhi dhi A

  25. Transient AmplificationTheory and Experiment EXPERIMENT Wave number

  26. Modeling ExperimentalDisturbances 1  h (m) 0 0.4 1.0 1.4 X(cm)

  27. Localized Disturbancein Model Y X

  28. Transient Amplification(Quantitative Comparison)

  29. Optimal Transient Amplification (p norm) In the limit Transient Amplification is Arbitrarily Large

  30. Optimal Disturbance Grigoriev (2005)

  31. Summary + Transient Growth in Contact lines Quantitative connections between theory and experiment appear possible. + Work in Progress Transient growth vs q Transient growth in gravitationally driven films

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