Low-frequency oscillations and convective phenomena in a - PowerPoint PPT Presentation

Nicolás Rivas (n.a.rivas@ctw.utwente.nl) Physics of glassy and granular materials Multi Scale Mechanics Kyoto, Japan, July 2013 Low-frequency oscillations and convective phenomena in a density-inverted vibrofluidised granular system S. Luding, A.R. Thornton, C.R.K. Windows-Yule, D.J. Parker, N. Rivas

MOTIVATION When/how do granular materials flow? Discrete to continuum transition Collective dynamics of many-particle systems

SYSTEM GEOMETRY Wide Column A sin( ω t ) L X = 50 d L X = 5 d N = 3000 N = 300 control parameter S ≡ A 2 ω 2 / gd ∈ (20,400)

SIMULATIONS Event-driven algorithm Perfect hard spheres Collisions modeled by ˦˧˧ N , ˦˧˧ T and µ S , µ D , Solid walls boundary conditions (no top) Bi-parabolic sine interpolation

PHASES Leidenfrost state (A = 1.0d, ω = 7.0(d/g) 1/2 ) *color corresponds to granular temperature dense gas L X = 50 d

PHASES Convection state (A = 1.0d, ω = 12.0(d/g) 1/2 ) L X = 50 d

PHASES A = 1.0 20 400 Ê Ê Ê Ê Dimensionless Velocity (S) Oscillation Frequency ( ω ) Convection 16 256 Ù One Roll Two Rolls Ú Ï Ù Ï Ï Ú 12 144 Ù Ù Ù Ú Ú Ú Ù Ú Ï Ï Ú Ù Ï Ú Ï Ù Ù Ï Ï 8 64 Leidenfrost 4 16 ‡ ‡ ‡ ‡ ‡ ‡ ‡ ‡ Bouncing Bed Ê Ê 0 5 10 15 20 25 30 35 40 45 50 Container Length (L X )

PHASES A = 1.0 20 400 Ê Ê Ê Ê ? Dimensionless Velocity (S) Oscillation Frequency ( ω ) Convection 16 256 Ù One Roll Two Rolls Ú Ï Ù Ï Ï Ú 12 144 Ú Ú Ú Ù Ù Ù Ù Ú Ï Ï Ú Ù Ï Ú Ï Ù Ù Ï Ï 8 64 Leidenfrost 4 16 ‡ ‡ ‡ ‡ ‡ ‡ ‡ ‡ Bouncing Bed Ê Ê 0 5 10 15 20 25 30 35 40 45 50 Container Length (L X )

LOW-FREQUENCY OSCILLATIONS A = 1.0d, ω = 14.0(d/g) 1/2 (40 Hz for 5mm particles) 20 400 Convection 15 225 10 100 Leidenfrost 5 25 Bouncing Bed 0 0 5 10 20 30 40 50 5 d

LOW-FREQUENCY OSCILLATIONS 25 Vertical Centre of Mass (z cm ) 20 15 10 5 S = 400 S = 16 0 0 5 10 15 20 25 Time

LOW-FREQUENCY OSCILLATIONS 100 10 P.S.D. 1 0.1 S = 400 S = 16 0.01 0.03 0.1 0.3 3 10 25 Frequency

LOW-FREQUENCY OSCILLATIONS 100 10 P.S.D. 1 0.1 S = 400 S = 64 S = 256 S = 16 S = 144 0.01 0.03 0.1 0.3 3 10 25 Frequency

LOW-FREQUENCY OSCILLATIONS ω 0 ω 0 100 10 P.S.D. 1 0.1 S = 400 S = 64 S = 256 S = 16 S = 144 0.01 0.03 0.1 0.3 3 10 25 Frequency

LOW-FREQUENCY OSCILLATIONS 1. 0.9 A = 0.4 LFOs Frequency ( ω 0 ) 0.8 A = 1.0 0.7 A = 4.0 0.6 w C 0.5 0.4 0.3 0.2 016 64 144 256 400 S Dimensionless Velocity (S)

LFO’s MODEL Cauchy’s equations Forced harmonic oscillator

LFO’s MODEL Cauchy’s equations Forced harmonic oscillator 25 ρ s 20 15 ρ g z cm ξ ρ s h s 10 k = 4g ρ g 5 A fm sin( ω fm t ) 30 0 0 15 30 0 15 Density ( ρ ) Density ( ρ )

LFO’s MODEL 1. 0.9 A = 0.4 LFOs Frequency 0.8 A = 1.0 0.7 A = 4.0 0.6 w C 0.5 0.4 0.3 Dashed lines come from the model 0.2 016 64 144 256 400 S Dimensionless Velocity (S)

EXPERIMENTS We use PEPT (Positron Emission Particle Tracking) to track ONE particle Submilimeter, milisecond resolutions

EXPERIMENTS

EXPERIMENTS • Red = Simulations • Blue = Experiments

EXPERIMENTS

EXPERIMENTS Observed convection phenomena Inverse convective state

EXPERIMENTS Observed convection phenomena “Crystalline convection”

LFO’s Conclusions Vertically driven granular matter in density inverted states present low-frequency oscillations (LFOs). A forced oscillator model, obtained from considering a two phases continuum medium, agrees with simulation and experimental measurements.

LFO’s Prospective work Expand the model: Consider energy equation Solve full non-linear equation Study relevance of LFOs in wider systems

Phase-Coexisting Patterns with Segregation in Vertically Vibrated BINARY MIXTURE Binary Granular Mixtures I.H. Ansari, N. Rivas and M. Alam Back to Wide Geometry L X = 50 d N = 3000

Phase-Coexisting Patterns with Segregation in Vertically Vibrated BINARY MIXTURE Binary Granular Mixtures I.H. Ansari, N. Rivas and M. Alam • Black particles are heavy • White particles are light Mass ratio = 3 Same size

Phase-Coexisting Patterns with Segregation in Vertically Vibrated BINARY MIXTURE Binary Granular Mixtures I.H. Ansari, N. Rivas and M. Alam

Phase-Coexisting Patterns with Segregation in Vertically Vibrated BINARY MIXTURE Binary Granular Mixtures I.H. Ansari, N. Rivas and M. Alam Undulations + Gas • Black particles are heavy • White particles are light Mass ratio = 3

Phase-Coexisting Patterns with Segregation in Vertically Vibrated BINARY MIXTURE Binary Granular Mixtures I.H. Ansari, N. Rivas and M. Alam Leidenfrost + Gas • Black particles are heavy • White particles are light Mass ratio = 3

Phase-Coexisting Patterns with Segregation in Vertically Vibrated BINARY MIXTURE Binary Granular Mixtures I.H. Ansari, N. Rivas and M. Alam Leidenfrost + Gas

Phase-Coexisting Patterns with Segregation in Vertically Vibrated BINARY MIXTURE Binary Granular Mixtures I.H. Ansari, N. Rivas and M. Alam Conclusions Known phases can coexist in the vertical vibrated narrow box geometry, when mass binary mixtures are considered. Segregation occurs in most cases, although mixed states are also observed.