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

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

 shak er  Control Parameters:  D = floater size  θ = wetting angle  a = amplitude  f = frequency  ϕ = concentration ϕ = Area / Area floatertotal a, f Set-up:  h = depth of water

 Why the node clusters at high ɸ ?  Why the antinode clusters at low ɸ ? From antinode clusters to node clusters:

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

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

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

 Correlation number c : antinodes nodes Experiment

I III II

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

antinode clusters at low ɸ node clusters at high ɸ 10 mm breathingnon-breathing From antinode clusters to node clusters:

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

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

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

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

 Energy approach  Experiment Comparison:

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

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

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

Back-up slides

   Distances in the designed clusters: