Interface Roughening Dynamics of Spreading Droplets

1. Interface Roughening Dynamics of Spreading Droplets • Haim Taitelbaum (Bar-Ilan University) With: • Avraham Be’er, Inbal Hecht, Ya’el Hoss • Aviad Frydman • Yossi Lereah (Tel-Aviv U)

2. Hg 100mm Hg Ag, Au Ag, Au 1000A-0.1mm Glass Top-view The Experimental System Side-view Optical microscope + DIC, Video, CCD Camera

3. Data analysis Optical microscope + DIC + CCD camera Image analysis Frame Graber 0.04 sec resolution

4. Why does the Mercury Spread ??? 1. Rough Substrate 2. Reaction Hg-Ag

5. 50mm Silver 4200At = 5, 10, 15 sec t = 5 sec Bulk Spreading Kinetic Roughening t = 10 sec t = 15 sec

6. Tanner’s Law (Non-Reactive) t1 t2 q(t) R(t) H(r=0,t) Side view Bulk Spreading - Reactive Wetting

7. Reactive Wetting ?? Dynamical 3-D Shape ReconstructionSide View from a Top View ! Be’er & Lereah, JOM 2002 50mm

8. Differential Interference Contrast (DIC) • 1. Steps of 1/20 of l • Slope = Color • Calibration ! Ocular Lens 4. Analyzer 3. l Plate Light Source 1. Polarizer 2. Rochon Prism Objective Lens

9. 180 110 80 30 00 50mm

10. Silver 4200 A t=5, 15, 25 sec

11. t q(deg) R(mm) R ~ t time (sec) Silver 4200 A Reaction band Bulk spreading

12. Kinetic Roughening of Reaction Band Screen height - about100mm Ag thickness = 0.1 mm (foil) Hg initial radius - about 150 mm. Bulk height from surface - about 1 mm. Initial time here is 15 sec Total time of experiment = 5 min

13. Chemical Reaction Ag3Hg4 Ag4Hg3 Ag Optical microscope SEM Studies

14. h x h Ag Hg x In isotropic systems Top View W b - growth a – roughness

15. Silver 2000 A 1.2 The roughness exponent a 1 Slope=0.66 0.8 0.6 log W 0.4 Log W 0.2 0 0 0.5 1 1.5 2 2.5 -0.2 -0.4 log L 0.3 The growth exponent b NEW! 0.2 Slope=0.46 0.1 0 Log W log W 0 0.2 0.4 0.6 0.8 1 1.2 -0.1 -0.2 -0.3 -0.4 --------------------------------------- log t 1.2 End of Propagation The roughness exponent a 1 0.8 Slope1=0.76 Slope2=0.47 0.6 Log W Crossover behavior 0.4 log W 0.2 0 EW KPZ 0 0.5 1 1.5 2 2.5 -0.2 -0.4 -0.6 log L

16. NOISE – Substrate Roughness Exponents Results Material Thickness a b Silver 2000A 0.66 0.46 0.1mm 0.77 0.60 Gold 1500A 0.88 0.76 3000A 0.96 1.00 Universality Class ?? a+a/b=2

17. א' Silver foil 0.1 mm Average pin height – 250 A Average “row” distance – 10000 A Gold – 1500 A Silver – 2000 A Average pin height – 100 A Average pin width – 500 A Average pin height – 200 A Average pin width – 1000 A

18. Single Interface Growth Fluctuations Silver foil 0.1 mm Width time

19. 6 11 16 21 7 12 17 22 18 8 13 23 9 14 19 small 24 15 10 large 20 Non Monotonic Width Growth

20. 3. Non- Linear Growth 4. Surface Tension Qualitative Description of Non-Linear Interface Growth 2. noise 1. Initially flat interface

21. Quantitative Analysis of Fluctuations

22. Fluctuations and the Correlation Length Correlation Length from Interface Fluctuations Correlation Length from Roughness Exponent (a)

23. Width Fluctuations Crossover Length from Interface Fluctuations Crossover Length from Roughness exponent Gold - 1500 A Lc = 8 microns

24. Width Fluctuations Crossover Length from Interface Fluctuations Crossover Length from Roughness exponent Water Imbibition in Paper Family et al (1992) Lc = 9 mm

25. Persistenceof Growth Fluctuations Temporal Survival Probability Exponential Decay ? … (Also Spatial Survival Prob.) h Work in Progress…. BLUE RED x t height fluctuation field x 0

26. Summary Bulk Spreading • Side view from Top View • Reactive Wetting – q(t), R(t) Interface Roughening Dynamics • Growth Exponents • Growth Fluctuations Correlation Length, Persistence

27. References A. Be’er, Y. Lereah, H. Taitelbaum, Physica A 285, 156 (2000) A. Be’er, Y. Lereah, I. Hecht, H. Taitelbaum, Physica A 302, 297 (2001) A. Be’er, Y. Lereah, A. Frydman, H. Taitelbaum, Physica A 314, 325 (2002) A. Be’er and Y. Lereah, J. of Microscopy, 208, 148 (2002). I. Hecht, H. Taitelbaum, Phys. Rev. E 70, 046307 (2004). A. Be’er, I. Hecht, H. Taitelbaum, Phys. Rev. E, 72, 031606 (2005). I. Hecht, A. Be’er, H. Taitelbaum, FNL, 5, L319 (2005).