Fluctuation Theorem Application on 2-D Granular Materials Configurations

Fluctuation Theorem Application on 2-D Granular Materials Configurations

S. Viridi, S. N. Khotimah, Novitrian, Widayani

Nuclear Physics and Biophysics Research Division, Institut Teknologi Bandung, Bandung 40132, Indonesia

Solo, Indonesia, 16 September 2014 12nd International Conference on Advanced

Materials Science and Technology (ICAMST)

Outline

• Fluctuation theorem• Brazil nut effect• 2-d artificial configuration• Observation• Summary

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2nd International Conference on Advanced Materials Science and Technology (ICAMST) 2

Fluctuation theorem

• One of the FTs states that (Seifert, 2005)

which holds for finite length of time δt for entropy change Δs

• Constraints: steady state of constant force and constant temperature

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2nd International Conference on Advanced Materials Science and Technology (ICAMST) 3

sesp

sp

Fluctuation theorem (cont.)

• Second law of thermodynamics predicts that the entropy of an isolated system should tend to increase until it reaches equilibrium

• This theorem tells us that reverse process, where entropy decrease, could have high probability to happen

• It violates the law (in small scale during finite length of time)

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Brazil nut effect (BNE)

• Mixture of two different size of granular materials under vibration will produce seggreation larger grains on top, smaller grains on the bottom

• It holds also for only single intruder• It is observed in two- and three-dimension

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Brazil nut effect (BNE) (cont.)

• It has also the reverse BNE (RBNE) as reported (Hong et al., 2001)

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Brazil nut effect (BNE) (cont.)

• There is a crossover condition

BNE: ●, RBNE: ▪

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2-d artificial configuration

• It is based on real observation• Configuration are set artificially (Viridi et al.,

2014)• Time series of intruder and granular bed can

be analyzed

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2-d artificial configuration (cont.)

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Observation

• Number of contacts between grains are observed

• It is named as contactopy (Herrmann, 1993)Solo, Indonesia, 16 September 2014

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Observation (cont.)

• Potential energy

• Contact energy

Solo, Indonesia, 16 September 2014

2nd International Conference on Advanced Materials Science and Technology (ICAMST) 11

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Observation (cont.)

• Overlap between grains (Schäfer et al., 1996)

• Temperature T = mgDα • Entropy

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Observation (cont.)

• Center of mass posi-tion for mA/mB = 1

• Intruder movementseems to violateMPEP

• Change of COM forthe whole systemagrees with MPEP

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2nd International Conference on Advanced Materials Science and Technology (ICAMST) 13

Observation (cont.)

• For mA/mB = 1, γ = 1, and α = 8

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2nd International Conference on Advanced Materials Science and Technology (ICAMST) 14

Summary

• BNE obey second law of thermodynamics• RBNE has small probability to occur• FT does not violate second law of

thermodynamics for chosen parameters (mA/mB = 1, γ = 1, and α = 8)

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THANK YOU

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