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Temperature Oscillations in a Compartmetalized Bidisperse Granular Gas

Temperature Oscillations in a Compartmetalized Bidisperse Granular Gas. C. K. Chan 陳志強 Institute of Physics, Academia Sinica, Dept of Physics,National Central University, Taiwan. Collaborators. May Hou, Institute of Physics, CAS 厚美英 P. Y. Lai, National Central University 黎璧賢. Content.

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Temperature Oscillations in a Compartmetalized Bidisperse Granular Gas

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  1. Temperature Oscillations in a Compartmetalized Bidisperse Granular Gas C. K. Chan 陳志強 Institute of Physics, Academia Sinica, Dept of Physics,National Central University, Taiwan

  2. Collaborators • May Hou, Institute of Physics, CAS • 厚美英 • P. Y. Lai, National Central University • 黎璧賢

  3. Content • What is a clock? • What is special about a granular clock? • Unstable Evaporation/Condensation • Two temperature in a bi-disperse system • Model for bidisperse oscillation • Summary

  4. What is a clock ? Periodic motion sun, moon, pendulum etc … Periodic Reaction BZ reaction, enzyme circadian rhythm Periodic Collective behavior suprachiasmatic nuclei, sinoatrial node, comparmentalizedgranular gases, etc…

  5. BZ reaction From S. Mueller

  6. Granular Oscillation

  7. Second Law no clock? • Belousov-Zhabotinsky reaction A  B  A  B; Why not: A   B • Two-compartment granular Clock

  8. Molecular gases

  9. Properties of Granular Gases • Particles in “random” motion and collisions • “similar” to molecular gases But … • Inelastic Collisions / Highly dissipative • Energy input from vibration table • Far from thermal equilibrium  Brazil Nut Effect, Clustering, Maxwell’s demon

  10. monodisperse granular gas in compartments: Maxwell’s Demon v Eggers, PRL, 83 5322 (1999)

  11. Clustering • Granular gas in Compartmentalized chamber under vertical vibration D. Lohse’s group

  12. Maxwell’s Demon is possible in granular system Steady state: input energy rate = kinetic energy loss rate due to inelastic collisions Bottom plate velocity (input) Dissipation (output) characteristic kinetic temp Evaporation-condensation Unstable ! u Evaporation condensation N v

  13. Heaping

  14. n h 1-n Eggers, PRL, 83 5322 (1999) Flux model is always a fixed point large V stable; as V decrease  bifurcation ! uniform  cluster to 1 side

  15. What happens for a binary mixture? What are the steady state? How many granular temperatures ?

  16. Oscillation of millet (小米, N=4000) and mung beans (绿豆, N=400) F = 20Hz. Amp = 2mm

  17. soda lime glass 138 small spheres diameter : 2 mm 27 large spheres diameter 4 mm box height:7.7 cmx0.73cmx5 cm

  18. Effects of compartments + bidispersity: Granular Clock a=6 mm, f =20 Hz. Times: a=0, b=3.1, c=58.3, d=66.2, e=103.2 s. Markus et al, Phys. Rev. E, 74, 04301 (2006) Big and small grains. Explained by Reverse Brazil Nuts effects

  19. Granular Oscillations in compartmentalized bidisperse granular gas 2.6cmx5.4cmx13.3cm barrier at1.5 cm Steel glass balls Radius = 0.5 mm N = 960 f = 60 Hz

  20. Phase Diagram

  21. Model of two temperatures (B heats upA&Aslows downB) • Very large V, A & B are uniform in L & R, • As V is lowered, at some point only • A is free to exchange:  • clustering instability of A • TBR gets higher, then B evaporates to L • Enough B jumped to L to heat up As, • TAL increases A evaporates from L to R • A oscillates !

  22. Model Objectives • Quantitative description • A model to understand the quantitative data

  23. Binary mixture in a single compartment Change of K.E. of A grain due to A-B inelastic collision: Dissipation rate of A grain due to A-B inelastic collision: A B inelastic collision is asymmetric: A can get K.E. from B (B heats upA&Aslows downB) TB is lowered by the presence of A grains

  24. Binary mixture in a single compartment A B inelastic collision is asymmetric: suppose A gets K.E. from B (B heats upA&Aslows downB) TB is lowered by the presence of A grains Balancing input energy rate from vibrating plate with total dissipation due to collision:

  25. Flux Model for binary mixture of A & B grains in 2 compartments L R PRL, 100, 068001 (2008) J. Phys. Soc. Jpn. 78, 041001 (2009)

  26. is always a fixed point, • stable for V>Vc • For V<Vc, Hopf bifurcation  oscillation L R

  27. Numerical solution V>Vc V<Vc V<Vf V<Vc

  28. Model Results • V>Vc, A & B evenly distributed in 2 chambers • Supercritical Hopf bifurcation near Vc • V<Vc, limit cycle. Granular clock for A & B. • Amplitude D ~ (v-vc)0.5 [Hopf] • Period t ~ (v- vf)-a(numerical solution of Flux model) • V < Vf , clustering into one chamber • Saddle-node bifurcation at Vf (??? to be proved rigorously???)

  29. Oscillation amplitude: exptal data Numerical soln. of Flux model Vc-V (cm/s)

  30. Oscillation period

  31. Phase diagram

  32. Other interesting cases: Tri-dispersed grains : A, B ,C 3-dim nonlinear dynamical system  complex dynamics, Chaos…

  33. Other interesting cases: Bi-dispersed grains in M-compartments: 1 2 3 2(M-1)-dim nonlinear dynamical system  complex dynamics,……

  34. Summary • Dissipation is density dependent  “Maxwell demon” • Different collision dissipations in binary system  existence of two “granular temperatures” • Non-homogeneous temperature with homogenous energy input both spatially and temporally • Granular steady state + compartment  oscillations

  35. Thermophoresis or Janus ?

  36. A worm in a temperature bath

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