A droplet of spectroscopy

A drop of spectroscopy

D. Terwagne, T. Gilet, N.Vandewalle & S. Dorbolo University of Liège - Belgium

The Phenomenon

Silicon oil (1.5, 10, 100 cSt) Silicon oil (1000 cSt) A

ω = 2πf

-> Vibrate the liquid surface How to avoid coalescence ?

Γ = Aω2 g

Y. Couder et al., Phys. Rev. Lett. 94, 177801 (2005)

1. Bouncing droplet mechanism 2. Resonant and rolling droplet

Plan

100 cSt10 cSt 10-1 100 101 102 0 50 100 150 200 250 300 350 1.5 cSt 10 cSt 100 cSt !th f (Hz)

Bouncing Threshold

10-1 100 101 102 0 50 100 150 200 250 300 350 1.5 cSt 10 cSt 100 cSt !th f (Hz) 10-1 100 101 102 0 50 100 150 200 250 300 350 1.5 cSt 10 cSt 100 cSt !th f (Hz) 1000 cSt 1.5 cSt Bouncing droplet Coalescence RDroplet=0.76 mm

Bouncing Threshold

10-1 100 101 102 0 50 100 150 200 250 300 350 1.5 cSt !th f (Hz) 1.5 cSt 1000 cSt ωc ωres ω ΓC 1 th th d(K + E) dt = −Pd− PF Md 2_x c dt2 = Mg(Γ cos(2πft) − 1) + F Apparent gravity Interfacial

Kinetic viscosity lubrication

Newton Energy lubrication force Bouncing droplet � F _{↔ �}Papp Lubrication force Dynamic of the air film

Droplet deformation

Bouncing droplet

mechanism

� F � Papp

T. Gilet et al., Phys. Rev. Lett. 100, 167802 (2008)

Bouncing droplet

mechanism

Bouncing droplet =

Damped driven harmonic oscillator

- surface tension = restoring force - viscosity = damping process

- minimum : system resonance frequency - divergence : droplet natural resonance

ωres ωc Threshold curve 10-1 100 101 102 0 50 100 150 200 250 300 350 1.5 cSt !th f (Hz)

Bouncing Threshold

Y0 3 Y0 4 Y0 2 100 10 10-1 0 50 150150 (Hz) (Hz) 200 250 Rayleigh spherical harmonics Ym l see GFM 2008 300 300 300 250 300_Y0 3 Y04 100 100 100 50 50_Y0 2

Spherical Harmonics

& Experimen Model Y0 2 Y0 3 Y0 4 Y0 5

see GFM 2008 Usually, fResonance(!) = αfR(!) with α → excitation geometry

Resonant Modes

! ! ! 10-2 10-1 100 0 0.5 1 1.5 2 2.5 3 3.5 R=0.765 mm R=0.812 mm R=0.931 mm A f c 2/g f/f_c fR (2) fR (3) fR (4) f α = 1.15 � fR(�) fc �2 = _3π1 �(�− 1)(� + 2) with fc= � σ/M M = 4/3πρR3

Roller Mode

! ! ! 10-2 10-1 100 0 0.5 1 1.5 2 2.5 3 3.5 R=0.765 mm R=0.812 mm R=0.931 mm A f c 2/g f/f_c Divergence ?

Roller Mode

Y1 2 Roller

Bouncing droplet mechanism

• Bouncing droplet = damped driven harmonic oscillator

• Threshold curve extrema -> resonance

Self-propelled droplet

• Roller

Mayonnaise droplet

Conclusions & perspectives

see GFM 2008 S. Dorbolo et al., New J. Phys. 10, 113021 (2008) T. Gilet et al., Phys. Rev. Lett. 100, 167802 (2008)

Thank You