Granular buoyant force in a two-dimensional intruder-particles bed system
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The document summarizes a study on granular buoyant force in a two-dimensional intruder-particle bed system using molecular dynamics simulation. The study models the forces between particles and the fluid using equations of motion. The simulation shows three stages: fluid condensation, an object intruding, and the system reaching equilibrium. Results for different object and fluid densities are presented and analyzed. The simulation found that the final state resembles a macroscopic system when the object density is larger than the fluid density. The study contributes to investigating density from a particle-level perspective.
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Granular buoyant force in a two-dimensional intruder-particles bed system
- 1. 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 1 Granular buoyant force in a two-dimensional intruder- particles bed system Dewi Muliyati1 , Nurhayati2 , Johri Sabaryati3 , Sparisoma Viridi4 1 FMIPA, Universitas Negeri Jakarta, Jakarta 13220, Indonesia 2 FST, Universitas Islam Negeri Ar-Raniry, Banda Aceh 23111, Indonesia 3 FKIP, Universitas Muhammadiyah Mataram, Mataram 83127, Indonesi 4 FMIPA, Institut Teknologi Bandung, Bandung 40132, Indonesia 1 dmuliyati@gmail.com, 2 firstnur1708@gmail.com, 3 joyafarashy@gmail.com, 4 dudung@gmail.com,
- 2. 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 2 Outline • Introduction • Theory • Simulation • Results and discussion • Conclusion
- 3. 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 3 Introduction
- 4. Buoyancy • It is an interesting phenomenon, especially if not only involving fluid and object densities as reported in 1873 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 4 G. Sigerson, "On a Cause of the Buoyancy of Bodies of a Greater Density than Water", Proceedings of the Royal Irish Academy. Science, vol. 2 (1875 - 1877), pp. 22-25, June 1873, url https://www.jstor.org/stable/20489980
- 5. Automatic observation • Today buoyancy can be ob- served using microcontroller that au- toma- tically mea- sures the data 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 5 P. R. Espindola, C. R. Cena, D. C. B. Alves, D. F. Bozano, A. M. B. Goncalves, "Use of an Arduino to studybuoyancy force", Physics Education, vol. 53, no. 3, p. 035010, May 2018, url https://doi.org/10.1088/1361-6552/aaa93a
- 6. Virtual laboratory • The phenomenon is still interesting to investi- gate through a virtual laboratory 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 6 J. M. Vitale, M. C. Linn, "Designing Virtual Laboratories to Foster Knowledge Integration: Buoyancy and Density", in M. E. Auer et al. (eds.), Cyber-Physical Laboratories in Engineeringand Science Education, chap. 7, pp. 163-189, 2018, url https://doi.org/10.1007/978-3-319-76935-6_7
- 7. Graphical concept 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 7 J. M. Vitale, L. Applebaum, M. C. Linn, "Coordinatingbetween Graphs and Science Concepts: Density and Buoyancy", Cognition and Instruction, vol. 37, no. 1, pp. 38-72, Jan 2019, url https://doi.org/10.1080/07370008.2018.1539736
- 8. 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 8
- 9. 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 9 Theory
- 10. Buoyant force • Object i with immersed volume Vi' in fluid with density ρf in environment with gravity , will have buoyant force of 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 10 . gVB ifi ′−= ρ g
- 11. Gravitational force • Object i with volume Vi with density ρg in environment with gravity , will have gravitational force of 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 11 . g gVG igi ρ=
- 12. Newton’s 1st law of motion • In equilibrium for object i 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 12 . ( ) ifig ifig ifig ifig ii i VV VV gVV gVgV BG F ′= =′−⇒ =′− =′− =+ =∑ ρρ ρρ ρρ ρρ 0 0 0 0 0 ′i h ih A AhV = gρfρ iB iG
- 13. 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 13 Simulation
- 14. Normal forces • Spherical grains i will have normal force from spherical grains j in the form of with 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 14 . ijijNijijNij vrkN ˆˆ ξγξ −= ( )ijjiij rRR −+= ,0maxξ
- 15. The other forces • Grains i will under influence of following forces – Buoyant force (slide 10) – Gravitational force (slide 11) 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 15
- 16. Molecular dynamics method • Newton 2nd law of motion • Forward finite difference 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 16 ++=⇒= ∑∑ j ijii i iii NGB m aamF 1 ( ) ( ) tatvdttv ∆+=+ ( ) ( ) ( ) ttvtrdttr ∆+=+
- 17. 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 17 Results and discussion
- 18. Stage 1: "Fluid" condensation 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 18 .
- 19. Stage 2: Object intruding 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 19
- 20. Stage 3: System equilibrium 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 20
- 21. Some final states 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 21 ρi / ρf = 2/2 ρi / ρf = 3/2 ρi / ρf = 4/2 ρi / ρf = 5/2 ρi / ρf = 6/2 ρi / ρf = 7/2 ρi / ρf = 8/2 ρi / ρf = 9/2
- 22. 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 22 0 0.04 0.08 0.12 0.16 0.2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 z t ziavg zbmax zbavg ρi / ρf = 2/2
- 23. 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 23 0 0.04 0.08 0.12 0.16 0.2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 z t ziavg zbmax zbavg ρi / ρf = 3/2
- 24. 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 24 0 0.04 0.08 0.12 0.16 0.2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 z t ziavg zbmax zbavg ρi / ρf = 4/2
- 25. 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 25 0 0.04 0.08 0.12 0.16 0.2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 z t ziavg zbmax zbavg ρi / ρf = 5/2
- 26. 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 26 0 0.04 0.08 0.12 0.16 0.2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 z t ziavg zbmax zbavg ρi / ρf = 6/2
- 27. 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 27 0 0.04 0.08 0.12 0.16 0.2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 z t ziavg zbmax zbavg ρi / ρf = 7/2
- 28. 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 28 0 0.04 0.08 0.12 0.16 0.2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 z t ziavg zbmax zbavg ρi / ρf = 8/2
- 29. 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 29 0 0.04 0.08 0.12 0.16 0.2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 z t ziavg zbmax zbavg ρi / ρf = 9/2
- 30. Code • Part of butiran.js https://github.com/dudung/butiran.js • Application https://rawcdn.githack.com/dudung/butiran.j s/f85fd1334dfd4d95a28ea2b254134f7603c6b 7d8/app/igdensity/igdensity.html 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 30
- 31. 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 31 Conclusion
- 32. Conclusion • Molecular dynamics-based simulation for investigating density from particles point of view has been built (based on butiran.js) • Final state is similar to macroscopic system if (individual particle) object density larger than (individual particle) fluid density, ρi / ρf ≥ 4/2 • Compaction of all particles will prevent further equilibrium 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 32
- 33. Acknowledgments • Author would like to thank to SNF Committee and FMIPA UNJ for the honour as invited speaker in parallel session 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 33
- 34. 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 34 https://osf.io/4umtr/
- 35. 29 Juni 2019 Jakarta, Indonesia SNF-UNJ 2019 35 Thank you