Ceyda Sanli , Detlef Lohse , and Devaraj van der Meer

1. From antinode clusters to node clusters: The concentration dependent transition of floaters on a standing Faraday wave CeydaSanli, DetlefLohse, and Devaraj van der Meer Physics of Fluids, University of Twente, The Netherlands.

2. Observation: 5 mm antinode clusters f=19 Hz a=0.1mm adding more floaters 5 mm node clusters f=20 Hz a=0.35 mm • Ref: C. Sanli, D. Lohse, and D. van der Meer, arXiv: 1202.0051

3. Set-up: • Control Parameters: • D = floater size • θ=wetting angle • a= amplitude • f= frequency • h= depth of water • ϕ = concentration a, f shaker shaker ϕ= Area / Area floater total

4. From antinode clusters to node clusters: • Why the antinode clusters at low ɸ ? • Why the node clusters at high ɸ ?

5. Why the antinode clusters at low ɸ ? • Drift force*: • The drift force is always towards the antinodes for our floaters. • The drift force is a single floater force. * G. Falkovichet. al., Nature (2005).

6. Why the antinode clusters at low ɸ ? • Analogy with a static case: • bubble case • On a static curved interface: • heavy particles goes to a local minimum • heavy particle • case

7. Why the antinode clusters at low ɸ ? • Wave elevator: • Drift force*: • The drift force is always towards the antinodes for our floaters. • The drift force is a single floater force. t < T/2 t > T/2 * G. Falkovichet. al., Nature (2005). • T is the standing wave period.

8. Experiment • Correlation number c: antinodes nodes

9. Experiment I II III

10. From antinode clusters to node clusters: • Why the antinode clusters at low ɸ ? • drift force • Why the node clusters at high ɸ ? • look at the experiment more carefully

11. From antinode clusters to node clusters: 10 mm 10 mm antinode clusters at low ɸ node clusters at high ɸ breathing non-breathing

12. Attractive capillary interaction: air water • r(t) increases & decreases at the breathing antinode clusters. • r(t) is almost constant at the non-breathing node clusters.

13. Energy approach: • We calculate the drift and capillary energies based on designed clusters: • antinode cluster: • node cluster:

14. Energy approach: Observed and designed clusters • The inset bars indicate a length scale of 5 mm.

15. Energy approach: • E is the sum of the drift and capillary energies. • σ : surface tension • l : capillary length c • ΔE = E - E . antinode node • N : number of floaters

16. Comparison: • Experiment • Energy approach

17. Energy approach in detail: • E:capillary energy • σ : surface tension c • E : drift energy • l : capillary length d c • N : number of floaters

18. Conclusion: • The dynamics of the floaters is highly influenced by the floater concentration ϕ: • low ϕantinode clusters • high ϕ node clusters • Potential energy estimation of the designed clusters presents good agreement with the experiment both qualitatively and quantitatively. • Energy approach shows that the drift with breathing is the reason behind the node clusters at high ϕ.

19. Recent work: Macroscopic spheres on capillary Faraday waves • Dynamic heterogeneity and dynamic criticality : a=0.1 mm f=250 Hz ɸ=0.633 2 mm • 4 timesslowerthanreal time. • Ref: C. Sanli, K. Saitoh, S. Luding, and D. van der Meer, arXiv: 1309.3804

20. Back-up slides

21. Distances in the designed clusters:

22. Distances in the designed clusters: